Manual JKSimMet V5.1

steady state mineral processing simulator Version 5.1 November 2001 Revised February 2003

Isles Road Indooroopilly Qld AUSTRALIA 4068 Telephone 07 3365 5842 Facsimile 07 3365 5900 Email [email protected] Internet www.jktech.com.au

JKSimMet is a powerful tool for analysis and simulation of mineral processing plant data. As the program developers do not control data collection, analysis or interpretation, it is the sole responsibility of the JKSimMet user to verify that input data are accurate, and that both process unit operation conditions and stream outputs are reasonable. In no event will JKTech Pty Ltd be liable for direct, indirect, special, incidental or consequential damages arising out of the use or inability to use the software or documentation. Note: The detailed descriptions of the mathematical models in this manual are provided for the information of the software licensees. These models are not public domain and they may not be used in other software without written permission from or a licensing agreement with JKTech Pty Ltd.

Copyright © 1987 - 2003 JKTech Pty Ltd All rights reserved. Both the software and documentation of JKSimMet are copyright.

JKTech Pty Ltd Isles Road Indooroopilly Queensland Australia 4068

Telephone - (07) 3365 5842 International: +61 7 365 5842 Fax - (07) 3365 5900 International: +61 7 365 5900 Email - [email protected] JKSimMet Internet URL- www.jksimmet.com JKTech Internet URL - www.jktech.com.au

Preface

Contents CONTENTS Page No

ACKNOWLEDGMENTS

iv

ABOUT THIS MANUAL

vi

1.

OVERVIEW

1.1 1.2 1.3 1.4 1.5

About JKSimMet Equipment Requirements Cautionary Tales Program Structure JKSimMet Support

2.

INSTALLING JKSimMet

2.1 2.2 2.3 2.4 2.5 2.6

Contents of the Package Computer Hardware/Software JKSimMet V5 Installation Compatability Between V4 and V5 What Is New in Version 5.0 What Is New in Version 5.1

3.

LEARNING JKSimMet

3.1 3.2 3.3 3.4 3.5

How JKSimMet Works The Mouse The JKSimMet Display JKSimMet Startup Working with an Existing Project 3.5.1 Selection of a Flowsheet 3.5.2 Simulation 3.5.3 Displaying the Simulation Results 3.5.4 Printing the Simulation Results 3.5.5 Summarising the Results - Overview 3.5.6 Summarising the Results - Report 3.5.7 Exporting Data from JKSimMet 3.58 Finishing a JKSimMet Session Making Changes to an Existing Flowsheet 3.6.1 Selecting the Flowsheet to Use 3.6.2 Altering Operating Conditions 3.6.3 Saving the Session 3.6.4 Graphing Your Results Creating a New Project 3.7.1 Starting a New Project 3.7.2 Define Flowsheet Name 3.7.3 Drawing a New Flowsheet 3.7.4 Create Connecting Streams 3.7.5 Adding a Circuit Feed Stream

3.6

3.7

Version 5.1 February 2003

1-2 1-4 1-5 1-6 1-7

Contents

2-2 2-3 2-4 2-5 2-6 2-8

3-2 3-6 3-7 3-8 3-9 3-10 3-11 3-16 3-20 3-22 3-23 3-25 3.25 3-27 3-27 3-29 3-33 3-35 3-38 3-38 3-40 3-41 3-44 3-47 Page i

Contents

Preface 3.7.6 3.7.7

3.10 3.11 3.12

Adding Water to the Circuit Adding Information Blocks and Labels to the Flowsheet 3.7.8 Entering Data 3.7.9 Define Data for Rod Mill 3.7.10 Examining Data 3.7.11 Rod Mill Circuit Exercises Learning Simulation Learning Graphing 3.9.1 Drawing a Graph 3.9.2 Defining the Graph Format 3.9.3 Definition of the Data to be Graphed 3.9.4 Easy Manipulation of the Graphing Features 3.9.5 Saving the Session 3.9.6 Graphing Limitations 3.9.7 Graphing Related Problems Learning Overview Learning to use Report Summary

4

USING JKSimMet

4.1

JKSimMet Description 4-2 4.1.1 JKSimMet Simulation Technique 4-3 4.1.2 JKSimMet Capabilities 4-3 4.1.3 JKSimMet Constraints 4-4 4.1.4 JKSimMet Expandability 4-5 Definition of Terms used in JKSimMet 4-6 The JKSimMet Cursor 4-7 The JKSimMet Menus and Toolbars 4-8 4.4.1 The Main JKSimMet Menu 4-9 4.4.2 The Functions Toolbar 4-9 4.4.3 The JKSimMet Tools Toolbar 4-11 JKSimMet Windows 4-12 4.5.1 The Session Window 4-12 4.5.2 The Project View Window 4-14 4.5.3 Equipment Data Windows 4-15 4.5.4 Port Data Windows 4-16 Building and Manipulating a Flowsheet 4-17 4.6.1 Loading a Project 4-17 4.6.2 Defining the Project Name 4-18 4.6.3 Defining the Flowsheet Name 4-19 4.6.4 Building the Flowsheet–Equipment Units 4-20 4.6.5 Building the Flowsheet–Connecting Ports 4-23 4.6.6 Flowsheet Related Problems 4-25 Editing the Flowsheet Data 4-26 4.7.1 The Equipment Data Window 4-26 4.7.2 Editing the Equipment Data 4-29 4.7.3 The Port Data Window 4-32

3.8 3.9

4.2 4.3 4.4

4.5

4.6

4.7

Page ii

Contents

3-47 3-50 3-54 3-55 3-57 3-58 3-60 3-63 3-65 3-65 3-67 3-70 3-71 3-72 3-72 3-73 3-78 3-84


Preface

Contents

4.12 4.13

4.7.4 Editing the Port Data 4-34 4.7.5 The Feed Data Window 4-40 4.7.6 Editing the Feeder Data 4-41 4.7.7 The Water Feeder Data Window 4-41 4.7.8 Editing the Water Feeder Data 4-43 Annotating the Flowsheet 4-46 4.8.1 Adding Port Information Blocks 4-47 4.8.2 Adding Equipment Information Blocks 4-51 4.8.3 Adding Labels to the Flowsheet 4-53 User-Configured Graphing – The Graph Definition Window 4-55 4.9.1 Define the Graph Format 4-55 4.9.2 Defining Data for Graphing 4-57 4.9.3 Viewing the Graph 4-62 Using Quick Graph 4-63 4.10.1 Opening the Quick Graph Window 4-63 4.10.2 The Quick Graph Toolbar 4-64 4.10.3 Features of Quick Graph 4-65 Using Overview 4-66 4.11.1 The Overview Window 4-66 4.11.2 Configuring an Overview Table 4-67 4.11.3 Recovery Mode 4-70 Printing in JKSimMet 4-72 Using Report 4-75

5

MODEL FITTING

5.1 5.2 5.3 5.4 5.5 5.6

5.10

Introduction to Model Fitting Data Collection Background How the Model Fitting Program Works A Simple Example Learning Fitting 5.6.1 Preparation for Model Fitting 5.6.2 Start Model Fitting 5.6.3 Selecting Data 5.6.4 Setting up the Parameters 5.6.5 Master/Slave Fitting 5.6.6 Fit the Model Parameters Checking the Fit Presentation of Model Fitting Results Problems Related to Model Fitting and Possible Solutions References

6

MASS BALANCING

6.1 6.2 6.3 6.4 6.5

Introduction to Mass Balancing Data Collection Background How the Mass Balancing Program Works A Simple Example

4.8

4.9

4.10

4.11

5.7 5.8 5.9


Contents

5-2 5-3 5-7 5-8 5-10 5-13 5-13 5-14 5-15 5-19 5-21 5-22 5-24 5-25 5-27 5-30

6-2 6-3 6-4 6-7 6-9 Page iii

Contents

Preface 6.6

6.7 6.8

6.9

6.10 6.11

Learning Mass Balancing 6.6.1 Preparation for Mass Balancing 6.6.2 Model Types for Mass Balancing 6.6.3 Selecting Data 6.6.4 Component 6.6.5 Water 6.6.6 Solution Controls 6.6.7 Carrying out the Mass Balance Checking the Balance Presentation of Mass Balancing Results 6.8.1 Overview 6.8.2 Printing the Mass Balance Results 6.8.3 Plotting Graphs Problems Related to Mass Balancing and Possible Solutions 6.9.1 The Middlings Problem 6.9.2 The Infinite Division Problem Metallurgical Accounting References

6-14 6-14 6-15 6-15 6-17 6-20 6-21 6-22 6-24 6-26 6-26 6-28 6-29 6-32 6-33 6-34 6-35 6-36

APPENDICES A1 A2 A3 A4

A10 A11 A12 A13 A14

Introduction A-2 Hydrocyclone (Model 200, 201) A-7 Single Deck Screen (Model 230) A-21 Efficiency Curve Models (210, 610, 211, 611, 203) (General Classifier Models) A-31 Efficiency Curve Variable d50c (Model 251) A-37 Crusher (Model 400) A-41 Rod Mill (Model 410) A-59 Perfect Mixing Ball Mill (Model 420) A-69 Autogenous Mill Model (Model 430) and Semi –Autogenous Mill Model (Model 431) A-81 Size Converter Model (Model 490) A-101 Variable Rates SAG Model (Model 435) A-103 High Pressure Grinding Rolls (Model 402) A-123 Simple Degradation (Model 480) A-141 Splitters (Models 810, 811, 812, 870) A-145

B

ERROR MESSAGES

C

JK BREAKAGE TESTING

A5 A6 A7 A8 A9

All Trade Marks acknowledged

Page iv

Contents


Preface

Acknowledgements

ACKNOWLEDGEMENTS More than twenty-five years of development has gone into the simulation models used in JKSimMet. This represents a huge contribution by the students and staff of the Julius Kruttschnitt Mineral Research Centre (JKMRC). There is not sufficient space available to acknowledge all the contributors separately, and only a few outstanding contributions are mentioned. The founding Director of the JKMRC, Professor Alban Lynch, and his co-worker, Dr T C Rao, developed the first practical models of grinding and classification, and successfully applied them at Mount Isa Mines. Professor Lynch and his successors Dr Don McKee and Dr Tim Napier-Munn have presided over subsequent developments. Dr Bill Whiten is responsible for the generalized model structure, many of the models, and the general purpose data-fitting routines. The simulator structure has gone through several software generations and hardware implementations. The original engine was programmed by Dr Alex Kavetsky, who has also contributed a great number of the models. The major contributors to the DOS simulator are principally Mr David Wiseman, and also Dr Fred Hess and Dr Thomas Kleine. The original documentation was developed by the Centre for Information Technology Research at the University of Queensland. The testing and debugging of JKSimMet has mostly been done by JKTech, headed by Dr Rob Morrison and assisted by Mr Chris Bailey, Mr Dennis Noreen and Mr Philip Baguley. Major thanks are due to the many sponsors who have contributed to the AMIRA projects which have resulted in the development of JKSimMet. Special thanks are also due to the organizations listed below which purchased pre-release copies and have helped by testing the software in an industrial environment: • ZC Mines Limited • Renison Limited • Billiton Research B.V. • Bougainville Copper Limited • Western Australian School of Mines (Kalgoorlie) Version 4 Six years of JKSimMet marketing have lead to the licensing of more than 150 sites world wide. Meanwhile, application and model development continue at the JKMRC. The development of Version 4 and revision of the manual has been the result of contributions from the all the JKTech team, in particular Michal Andrusiewicz and Phil Baguley.

Version 5.1 November 2001

Acknowledgements

Page v

Acknowledgements

Preface

Version 5.0 Version 5 is a complete rebuilding “from the ground up” of the JKSimMet interface to bring it into Windows 95/98. The major conceptual changes to the interface are due to Stephen Treloar-Bradford. Detailed implementation has been by Phillip Baguley and Phil Beak. The DLL engines were programmed by Phillip Baguley and Michal Andrusiewicz. The Help files were developed by Andrew Schroder. Cathy Evans has developed the V5 documentation. Ricardo Pascual developed the V4 to V5 conversion program. Rob Morrison provided overall project leadership. Version 5 provides a platform for future mineral process modelling at the JKMRC. Overall, the development of JKSimMet V5 represents a major achievement for the development team and a major investment in the future for JKTech Special thanks are also due to the V5 beta testers in industry. Version 5.1 Version 5.1 is an upgrade of Version 5.0 which operates in the Windows 2000 environment. Several extra models have been added to the extensive model library and many operability improvements have been made. A series of bug fixes is also included. The evolution of V5.1 has been accomplished as a joint project between the JKTech software group and the JKTech consulting group. Most of the changes have come from suggestions by many of the current users, assembled and tested by the JKTech consultants and coded by the JKTech software group.

Page vi

Acknowledgements


Preface

About this Manual

ABOUT THIS MANUAL This manual is intended for users at all levels of experience with the system. It has been designed for novice users at both computing and the use of mineral processing plant simulation. It provides a reference section for more experienced users, and it offers advanced information for those users who wish to fine tune their simulations in order to maximize the benefit of their tests. Depending on your experience you will wish to refer to different sections of the manual. If you have just bought the package and it is not yet installed on your system: • read Chapter 2 first, and then install JKSimMet on your computer.

If you are new to computing or JKSimMet: • work through the tutorial section in Chapter 3.

If you are familiar with JKSimMet simulation techniques: • read Chapters 4, 5 and 6.

If you wish to fine tune JKSimMet to your own requirements: • read Chapter 5.

Version 5.0 December 1999

About this Manual

Page vii

About this Manual

Preface

(Blank Page)

Page viii


Overview

Overview

CHAPTER 1

OVERVIEW


Chapter 1

Page 1-1

About JKSimMet

Overview

1.

OVERVIEW

1.1

About JKSimMet

JKSimMet is a mineral processing plant simulator which runs on the Intel Pentium family of computers under Windows 95, 98, ME, NT4 or 2000. It gives engineers the ability to design and optimize any crushing or grinding circuit including stages of classification. It allows engineers to: design a circuit on the graphics monitor • enter model and plant data • simulate the circuit • graph and print the results. •

JKSimMet performs steady state simulation of a range of comminution and classification operations. Process models of the following units are available: • • • • • • • • • • • • •

secondary and tertiary cone crushers jaw crushers gyratory crushers rolls crushers autogenous and semi-autogenous mills rod mill, ball mill HPGR crusher simple degradation vibrating screen DSM screen hydrocyclone classifier several general classifier efficiency curves several splitters.

New process models can readily be incorporated into JKSimMet by JKTech. This is done by defining their characteristics as steady-state models and creating an icon for each to represent them on the screen. JKSimMet is intended for use by plant engineers not necessarily skilled in either modelling or computing. For that reason, it has been written to operate in a user-friendly manner. Users select options from menus or lists and build flowsheets on the screen. This removes the need for specialized computer skills while maintaining flexibility.

Page 1-2

Section 1.1

Version 5. 1 November 2001

Overview

About JKSimMet The main features of JKSimMet are: • • • • • •

graphical user interface flowsheet specified interactively on the graphics screen models selected from a built-in library model parameters specified by the user range of data output displays and printed reports simple data transfer.

JKSimMet has been designed primarily as a powerful aid to an engineer. The principal application of JKSimMet for many users will be to carry out process analysis and optimisation of existing circuits. JKSimMet is also extremely useful for conducting conceptual design studies, where the purpose is to assess the suitability of different flowsheets to achieve a desired performance objective. Limitations

Provided that the data used in the process models are relevant to the ore being studied, JKSimMet can be used to generate detailed design information. Until experience is gained in detailed design studies using JKSimMet, it is recommended that design tasks be carried out in consultation with JKTech. It is important at the outset to understand what JKSimMet will and will not do. JKSimMet will predict the performance of a circuit within the limitations of the data and the models selected. JKSimMet will not determine of its own accord the best circuit, the best operating conditions or the changes that are required to ensure that a circuit operates efficiently. JKSimMet does not allow process constraints to be specified.

Constraints

The operator has an essential role in deciding the conditions to be simulated and in critically assessing the simulation predictions. This is a deliberate result of the design philosophy of JKSimMet, which places considerable emphasis on the process experience and knowledge of the operator. This point is amplified at the beginning of Chapter 4, and the reader is strongly advised to keep these points in mind when using the system for simulation analysis.


Section 1.1

Page 1-3

Equipment Requirements 1.2

Overview

Equipment Requirements

For successful operation of JKSimMet you must have: Computer System

Intel Pentium PC (or other fully compatible computer) with all of the following: • • • • • • •

Processor speed 400MHz minimum 128Mb memory minimum – 256Mb recommended CD-ROM Drive 1.4 Mbyte (3.5 inch) diskette drive 2 Gbyte or larger fixed disk drive (with 100Mbytes free space) A SVGA or fully compatible equivalent graphics controller (minimum) – Recommended an XGA graphics controllerr a suitable monitor – 15 inch minimum 17 inch recommended.

Printer

An MS Windows 95,98, ME, NT or 2000 compatible printer:

Operating System

MS Windows 95,98, ME, NT(4 sp5 or later) or 2000

Pointing Device

Microsoft Mouse or functional equivalent.

Equipment Tested

A wide range of equipment combinations has been successfully tested but if you are in doubt JKTech will be pleased to comment on a particular combination.

Page 1-4

Section 1.2


Overview

Cautionary Tales 1.3

Backup JKSimMet Diskette

Cautionary Tales

JKSimMet V5 is supplied on CD-ROM with an additional installation program on a 3.5 floppy disk. A hardware key (Hard Lock) is required for operation. It is recommended that you make a backup copy of the files on the Diskette. If you do damage your one and only copy of a JKSimMet diskette, you can acquire a new diskette from JKTech by notifying them and quoting the version number of your copy of JKSimMet.

Read.Me Print.Me

Any modifications to procedures since the production of this manual are in a file called READ.ME. Print this file and read it before going further.

Learn by Example

JKSimMet is a program which is rich in capabilities and easy to operate. The simplest way to become familiar with the techniques of using JKSimMet and the capabilities it has to offer, is to follow through a structured example. Such an example is provided with the package. This example assumes no experience with JKSimMet and leads you through a session exploring the use of the various modelling and simulation features of the program. We recommend that you spend some time working through the example in Chapter 3 until you are confident that you can apply JKSimMet to your own problems. The data analysis capabilities of JKSimMet are supported by examples in Chapters 5 and 6.

Backup Work

As you input each section of data (say a flowsheet or a data set) you should save your work to the hard disk. Usually you will want to overwrite your earlier version. If you do this regularly, then when, not if, there is a power failure or other mishap, your work up to the last save will be waiting for you on the hard disk; it will not have been lost forever. Once you are a proficient user of JKSimMet, you will be creating and using mathematical models of your plant. These models are stored on your fixed disk between sessions. It is possible, usually through carelessness but occasionally through computer malfunction, to lose information from the fixed disk. Therefore, we recommend that you make a backup copy of the information stored on your fixed disk frequently.

Backup Work Files

You should use the backup facilities within JKSimMet to backup simulator work sessions to a server or other archival storage such as a Zip Disk.

Windows Backup Alternatively, Project Data Files(*.JKSM5) only need be backed up. Version 5. 1 November 2001

Section 1.4

Page 1-5

Program Structure

1.4 Program Structure

Process Models

•

Main Program

•

Supporting DLL’s

•

Program Database

•

Project Databases

Models of the following units are supplied:

• • • • • • • • • • • • • • • •

Page 1-6

Program Structure

JKSimMet consists of the following software modules:

•

Custom Models

Overview

rod mill ball mill autogenous mill semi-autogenous mill cone crusher HPGR crusher two rolls crusher jaw crusher single deck screen DSM screen hydrocyclone rake classifier spiral classifier splitter combiner (sump, stockpile, bin) size converter degradation model

Contact JKTech if you are interested in adding other models to those listed above. A developer’s kit is also available for model development.

Section 1.4


Overview

JKSimMet Support 1.5

Documentation

JKSimMet Support

Three levels of documentation are supplied: user manual • model documentation • context sensitive Help files. •

Installation and Training

JKTech can provide assistance to install the system and can also provide on-site training to match particular user needs.

Courses

JKTech offers regular courses in simulation technology at various locations around the world and on-line.

Extended Backup

Continuing backup support is provided by JKTech either through a Maintenance Agreement, telephone or facsimile contact, or through visits by JKTech to site.

Email Help

JKSimMet project files can be sent electronically to JKTech via the Internet for assistance. Send files to [email protected]

Updates

Updates and bug fixes will be supplied for one year from date of installation/supply and are available under a maintenance contract thereafter.

Restrictions

A standard licence for the use of JKSimMet permits operation of the software on a single workstation only. Extension of the licence for additional workstations at a single site is available for a small fee. Distribution of copies of JKSimMet to other company sites is not permitted. Additional copies for other sites are available at reduced cost.

Hardware Key

JKSimMet will not operate without a hardware key. The standard key is suitable for a parallel port. Keys are also available to suit PCMCIA or USB ports.


Section 1.5

Page 1-7

JKSimMet Support

Overview

(Blank Page)

Page 1-8

Section 1.5


Installing JKSimMet

Installing JKSimMet

CHAPTER 2

INSTALLING JKSimMet


Chapter 2

Page 2-1

Contents of the Package

Package Contents

Installing JKSimMet

2.

INSTALLING JKSimMet

2.1

Contents of the Package

The JKSimMet system comes as a package containing this manual, a CD, a floppy disk and two “Hardlock” keys The manual contains information on the installation and maintenance of the JKSimMet software, a tutorial guide for firsttime users and a comprehensive reference chapter.

Page 2-2

Section 2.1


Installing JKSimMet 2.2

Computer Hardware/Software Computer Hardware/Software

For successful operation of JKSimMet you must have: Computer System

Intel Pentium PC or other fully compatible computer with all of the following: • • • • • • •

Processor speed 400MHz minimum 128Mb memory minimum (256Mb recommended) CD-ROM Drive 1.4 Mbyte (3.5 inch) diskette drive 2 Gbyte or larger fixed disk drive (with 100 Mbytes free space) A SVGA or fully compatible equivalent graphics controller (minimum) – Recommended XGA a suitable monitor – 15 inch minimum 17 inch recommended.

Printer

Any MS Windows 95, 98, ME, NT or 2000 compatible printer.

Operating System

MS Windows 95, 98, ME, NT(V4 sp5 or later) or 2000

Pointing Device

Microsoft Mouse or functional equivalent.

Equipment Tested

A wide range of equipment combinations has been successfully tested but if you are in doubt JKTech will be pleased to comment on a particular combination.


Section 2.4

Page 2-3

JKSimMet V5 Installation 2.3 JKSimMet V5 Installation

Installing JKSimMet

JKSimMet V5 Installation

JKSimMet V5 is a standard Windows Program. Step 1 Make a backup copy of any existing projects Step 2 If you have JKSimMet V5 installed already on your computer, go to: Control Panel Select Add/Remove, and Select JKSimMet V5 Uninstall Step 3 Insert CD-ROM in drive Step 4 From the Windows Start Menu, select RUN and then Browse to find Setup.exe on your CD Drive Eg. D:\Setup.exe Step 5 Press OK and follow the instructions on screen Step 6 The installation procedure will prompt you for the supplied floppy diskette and will copy your company specific copy of JKSimMet to enable the software. If you do not have an A: drive floppy disk, you can double click on the self exploding zip file to install JKSimMet.exe in your JKSimMet V5.1 directory. If an update is provided by email, you can copy it to a floppy disk or unzip as in the previous paragraph Note: The install program will also ask to update your HTML help file viewer. This will allow full use of JKSimMet V5 help.

Notes for Windows NT or 2000 installation

Page 2-4

Note 1: Your computer must be using NT4 with service pack 5 or later or 2000. Note 2: As JKSimMet V5 requires several device drivers, you must have full administrator privileges to install or uninstall JKSimMet.

Section 2.3


Installing JKSimMet

Making a Backup Copy

If you choose not If you choose not to use the default path (/Program Files/JKSimMet to use the default V5.1) for installation, you will need to modify the UnZip path for the JKSimMet V5.1.exe file. path for installation Modify this line to your install path

Non-English versions of Windows

If you are installing in a non-English version of windows, the spelling of the install path may be different. If this is the case you must modify the UnZip path to the correct spelling as discussed above.

2.4

Compatibility and Conversion Between V4 and V5

A conversion utility is included to transfer User directories from Version 4 into a series of flowsheets within one or more projects as specified by the user. These projects are then accessible to Version 5. Note that Versions 2 to 4 used Ryan McFarland (IBM) ProFort which is a 16-bit FORTRAN compiler. Version 5 uses MS Power Station FORTRAN which is a 32-bit compiler. (Now supported by COMPAQ/DEC). There may be minor differences in calculated parameters as a result of this change. The converted project will also be slightly ambiguous regarding data type in some cases because V2 to V4 used calculated data to store the results of simulation, mass balancing or model fitting. Version 5 has sufficient space to store several data types. Hence, it would be prudent to re-run a simulation, balance or fit to guarantee the integrity of the calculated data.


Section 2.4

Page 2-5

What Is New in Version 5 2.5

Installing JKSimMet

What Is New in Version 5.0

The short answer is just about everything. The interface has been redesigned to take advantage of the features of MS Windows 95. Interaction within each of the modules (i.e. simulation, fit and balance) has been standardised and has access to all of the data presentation and transfer tools.

Page 2-6

•

Flowsheets now provide for automatic drawing of equipment connections.

•

Flowsheets are expandable to 4 “pages”

•

Many flowsheets are accessible within a project

•

A generalised Select function is provided to allow subsections of any flow sheets to be simulated, fitted or balanced. This supersedes the multi-circuit feature of V4.

•

Data and flowsheets from other projects may be copied into the current project

•

Use of the Windows 95 operating system and a FORTRAN 90 compiler potentially removes the V4 limits on numbers of models etc.

•

The flowsheet can be annotated with Data Information blocks which provide stream information as well as access to equipment data. The previous annotation capability has been replaced by labels.

•

Project and flowsheet notes may be included as properties.

•

A Quick Graph Facility is now available for each piece of process equipment

•

The Overview Tool has been generalised to present many kinds of data

•

A configurable Report tool allows a selection of data to be printed, copied to clipboard and to a range of file types.

•

Comprehensive copy and paste capabilities are provided to assist transfer of data and results to other Windows applications.

•

Program configuration has been completely implemented within a relational database.

•

This will allow other JKSim** simulators to be incorporated as JKSimMet modules.

Section 2.6


Installing JKSimMet

What Is New in Version 5

•

There is also scope to include a series of “supplementary” examples within the defined model types. However, caveats about inappropriate use are still applicable.

•

The database structure and DLL engines will allow for seamless integration of models developed by others via a developers kit and a compatible compiler.

•

A number of Version 5 objects are also designed to be shared with new JKTech products such as JKMetAccount and the MLA Data Presentation program

•

Last and by no means least, the V5 structure provides for eventual expansion to a fully integrated dynamic simulator, at some time in the future.


Section 2.5

Page 2-7

What Is New in Version 5 2.6

Installing JKSimMet

What Is New in Version 5.1

The major change in V5.1 is compatibility with Windows 2000. Several new models including the HPGR, simple degradation and an improved range of splitters have been added and several more classifier icons included. In addition, the file structure has changed so that .JKSM5 files are considerably smaller and no longer grow with use. Compaction is no longer required. This change in file structure has resulted in much faster loading and saving. Many of the user settings which were “forgotten” on file save and load are now “remembered”. For example, the graph colours, the lock status and % passing size are now stored with the file, as are the default settings for data and error displays in port windows. Almost all of the reported bugs have been fixed and as many as possible of the feature improvements requested by users have been implemented.

Page 2-8

Section 2.6


Learning JKSimMet

Learning JKSimMet

CHAPTER 3

LEARNING JKSimMet


Chapter 3

Page 3-1

How JKSimMet Works

3. Learning JKSimMet

Learning JKSimMet

LEARNING JKSimMet

Learning JKSimMet is designed primarily as a tutorial exercise. It is anticipated that the first time user of JKSimMet might spend two to three hours working through this chapter step by step. In this way the user will gain sufficient confidence and knowledge to begin using the system in earnest. Given the nature and design of JKSimMet, the user will very quickly be able to learn the basic operating techniques. It is assumed that the user already understands the techniques of mineral processing simulation and also has some appreciation of the standard features of the MS Windows 95/98/ME/NT/2000 interface.

3.1 About JKSimMet

How JKSimMet Works

JKSimMet is a general-purpose computer software package for the analysis and simulation of mineral processing operations. The package is designed to service the diverse needs of plant and development metallurgists, who need to apply modern process analysis techniques to characterise plant behaviour and design engineers, who require accurate process simulation models to facilitate the evaluation of various plant designs. JKSimMet integrates all tasks associated with optimisation, design and simulation, including the storage and manipulation of models, data and results, within one package. It is fully interactive and operates with high-resolution colour graphics capabilities. These graphics facilitate the display of detailed plant flowsheets and accompanying information. The engineer using JKSimMet proceeds through a series of tasks: building a flowsheet diagram of the processing plant on the computer screen • assigning characteristics to the various process units and material flows of the simulation model • simulating the flow of materials through the simulated plant ( Or a subsection of the plant). • reviewing and presenting the results. •

Once a model has been built the engineer can alter the design and change the parameters as he sees fit until he arrives at a satisfactory design or an optimum operating condition for an existing plant.

Page 3-2

Section 3.1


Learning JKSimMet

How JKSimMet Works

The results may be graphed, printed in summary form and stored on hard disk or archived to diskette. The results can also be transferred to other suitable programs via the clipboard. Building a Simulation Model

Simulation is based on the ability to build a model that is representative of a real system. The behaviour or characteristics of the model must be similar to the characteristics of the real system. In order to build the model the engineer must analyse the overall plant and break it down into a number of sections (circuits), in such a way that the circuits are easily understandable and identifiable. The circuits are interconnected to form the total system. The data structure within JKSimMet V5 consists of the following: Project

A project is the container in which the user stores all of the data related to a particular body of work. The project contains one or more flowsheets and the associated equipment unit and stream data.

Flowsheet

A flowsheet is a graphical representation of a complete processing plant or a component section of that plant. The flowsheet can have internal recirculating streams. A flowsheet may be increased in size to represent a large, complex circuit. Either the complete flowsheet or selected sections of it may be simulated, mass balanced or model fitted. Note that this capability to select items for inclusion in simulation, modelling or massbalancing replaces the circuit-oriented flowsheets required by the DOS versions of JKSimMet.

Equipment and Ports


Version 5 introduces a new concept. Each flowsheet item is now a piece of equipment which can have any number of ports. These ports represent the connections to each piece of equipment. The reason for this change is to allow for future development of a dynamic simulator. This approach also will allow for pipes and conveyors to be modelled as pieces of equipment. Units and Streams still provide a convenient way of thinking about flowsheets and for practical purposes, the terms equipment and ports mean the same things as units and streams.

Section 3.1

Page 3-3

How JKSimMet Works

Learning JKSimMet

Units

A unit is any type of unit process such as a ball mill or a hydrocyclone classifier. JKSimMet allows you to select the appropriate unit from an exhaustive list of processing unit types and to display their pictorial representations (icons) on the screen. These units are identified within the system by a name which the user specifies. You can specify the orientation of the units (direction of flow through the unit left to right or vice-versa) and also the position of units on the flowsheet diagram.

Streams

A stream is a description of any flow of material. The description is usually in terms of solids flowrate, water flowrate and particle size distributions (plus assays for mass balancing if required). The stream connections between units are made by drawing lines connecting the appropriate feed and product ports on the units. JKSimMet automatically checks to ensure that the stream connections are valid. Each stream or port is named by JKSimMet as a combination of its equipment name and port name. The user can edit the equipment names as required but the port names for each piece of equipment are fixed.

The unit models currently available for simulation include: • • • • • • • • • •

Page 3-4

Feeder Stockpile Bin Pump sump Sump Splitter Gyratory crusher Two rolls crusher Jaw crusher HPGR crusher

Section 3.1

• • • • • • • • • •

Autogenous mill Semi-autogenous mill Rod mill Ball mill Single deck screen DSM Screen Hydrocyclone Spiral classifier Rake classifier Degradation model


Learning JKSimMet

How JKSimMet Works

Specifying Flowsheet Data

Once the flowsheet has been drawn the engineer must provide data for each process unit and also provide raw data in the form of flows and size distributions for the streams in the circuit. This is done by stepping through the process units and the streams one-by-one, adding circuit data and building up an annotated description of the modelled processing circuit on the screen. The unit data for the process equipment may come from previous experience, from a design database or they may be derived from plant data. The stream data can be entered in one of three size distribution formats, depending on the preferences of the user. The engineer can review or correct the data at any time after entering the data.

Flowsheet Simulation

Once the flowsheet has been specified and the required unit and stream data have been entered, the simulation can be run. The results of the simulation are stored and can be displayed on the screen or printed as required. The following options are available for examining the results: • • • • • • •

view the detailed data in the equipment and port data windows, view summary data for equipment and ports via data information blocks, view summary data in overview tables, view the size distribution data plotted as graphs on the screen or in printed form, generate configurable reports at summary or detailed level, copy-and-paste the data into other programs (eg. MS Excel) via the clipboard print the results to a Windows compatible printer or to a file.

Recorded data include: • • • •

flowrates of solids and water percentage solids pulp densities full particle size distributions.

After analysis of the results, you can alter the flowsheet, adjust the equipment parameters or port data and repeat the simulation process until you obtain a satisfactory result. Flowsheet Selection

A new capability in V5 is that a subset of the flowsheet may be selected for simulation, mass balancing or model fitting.


Section 3.1

Page 3-5

The Mouse

Learning JKSimMet 3.2

The Mouse

The Mouse

The standard two-button mouse is used as the pointing device in JKSimMet. In this manual we refer to "left-click" and "right-click" which simply means to press the left- or right-hand button on the mouse. The manual assumes that you are familiar with common mouse techniques such as double-clicking and click-and-drag.

The Cursor

In JKSimMet V5 the cursor (your position on the screen) is indicated by an arrowhead. When the cursor is over an equipment unit in the flowsheet window the cursor will change to indicate that the drop-down menu can be accessed by right-clicking on this zone. In data windows, the position of the active data cell (i.e. the cell where anything that you type will appear) is indicated by a thick grey border

Cursor Movement

The mouse can be used to move the cursor when working with JKSimMet. In the equipment and stream data windows the cursor control keys (also known as the arrow keys) may also be used to move the cursor from one data cell to the next.

Appearance

As with all MS Windows programs, the preferences which the user sets for the Windows desktop will provide colours and fonts for many of the tools and menus within JKSimMet.

Keyboard Access Most of the functionality of JKSimMet can also be accessed from the keyboard using standard MS Windows conventions.

Page 3-6

Section 3.2



The JKSimMet Display The JKSimMet Display

The JKSimMet V5 display uses windows to present the various types of data on the JKSimMet desktop. These windows include the following: • • • • •

flowsheet window, equipment and port data windows graph windows data overview window. the report window

Users may have as many windows open on the screen as they wish at any one time. An XGA video card and a large monitor are recommended for this strategy. Many of the windows are divided into several distinct areas which are accessed by selectable tabs. Each area is used to convey specific types of information. Note that most windows may be minimised for convenience. However, some non-critical changes (eg. an equipment name change) may require that a window be closed before other windows are updated.


Section 3.3

Page 3-7

JKSimMet Startup 3.4 JKSimMet Startup

Learning JKSimMet JKSimMet Startup

The instructions for starting JKSimMet V5 are as follows: Step 1 Right-click on the Windows Start button at the bottom left-hand corner of the screen to bring up the Start menu. Step 2 Move the cursor to select the Programs sub-menu. Step 3 Move the cursor to highlight the JKSimMet V5.1 program from the list displayed in this sub-menu and left-click to launch the program. The JKSimMet logo is displayed while the program is launching.

Having successfully launched the program you enter JKSimMet at the main JKSimMet desktop window as shown below. From here, the next step is typically to open a previously saved data set (note that each data set is known as a project in V5) or to enter the data for a new project. Section 3.5 describes the steps involved in working with an existing project. Alternatively, JKSimMet can be launched by selecting an existing project file (extension .JKSM5) and double clicking it. This launches JKSimMet with the chosen file as the active project.

The JKSimMet desktop window

Page 3-8

Section 3.4


Learning JKSimMet 3.5 About this Exercise

Working with an Existing Project Working with an Existing Project

As a first exercise in the use of JKSimMet follow the instructions in this section. They will show you how to: •

Load an existing demonstration project for a simple ball mill and hydrocyclone circuit. This project was created by JKTech and was installed with JKSimMet.

•

Use the simulation tools in JKSimMet to simulate the action of the circuit under predefined feed conditions.

•

View the results of the simulation on the computer screen and print selected results on the printer.

The files which define the flowsheet, process units and streams that make up the demonstration circuit are already on your computer. They were installed onto the hard drive during the JKSimMet installation procedures. They can be recalled by following a few simple steps outlined below.

Loading an existing project

Step 1

Left-click on the Open Project icon on the JKSimMet toolbar at the top left-hand corner of the JKSimMet window. This will open the Project View window as shown in the screen image below.

Open Project


Section 3.5

Page 3-9

Working with an Existing Project

Learning JKSimMet

Step 2

Left-click on the tab marked Saved in the Project View window. This displays a list of all the existing project files (along with a description of each project in the Object Description box)

Step 3

Move the cursor to the red book of the project which you want to load, in this case the Learner Flowsheets project, and left-click, hold and drag it across to the JKSimMet desktop to load the project. Note that when you click on a project name, its file name, complete with directory location appears in a strip at the bottom of the Project View window.

Step 4

Left-click on the main window to make it the active window.

3.5.1

Selection of a Flowsheet

Within each project the user can define one or more flowsheets to represent the circuit(s) which he wants to investigate. Each flowsheet can be expanded in size to make room for complex flowsheets. We will work with a flowsheet called Example Ball Mill – Cyclone simulation in the project Learner Flowsheets. Follow the steps outlined below to select this flowsheet as the active flowsheet. Loading an existing Flowsheet

Page 3-10

Step 1

Section 3.5

Left-click on the text box at the bottom right of the JKSimMet flowsheet window to view a drop-down list of the flowsheets which have been created in the Learner project.


Learning JKSimMet

Changing the size of the flowsheet window


Step 2

Move the cursor down the list to highlight the name of the flowsheet which you want to use (in this case Example Ball Mill – Cyclone simulation) and left-click on this to bring the chosen flowsheet into view on the main screen.

Step 3

If the flowsheet you want to work with is not completely visible in the window you can change the height and width of the window by placing the cursor on the bottom, right corner of the flowsheet window and left-clicking and dragging the window edge until it is the required size.

Drop-down list of flowsheets in this project

3.5.2

Simulation

The Example Ball Mill – Cyclone simulation flowsheet already contains all the stream data and parameters required to simulate this circuit. We will use the JKSimMet simulation capabilities to predict the product stream size distributions and capacity of the simulated circuit, but first we will find out how to look at the equipment unit data and port data.


Section 3.5

Page 3-11

Working with an Existing Project Key to the Demonstration Circuit

Learning JKSimMet

The demonstration circuit consists of a ball mill and a nest of four hydrocyclones. These equipment units are connected by streams. The streams enter and leave the equipment units through feed and product ports. Note that there are also two specialised units in this circuit, these being the Feed and the Water Feeder. The Feed unit allows new feed material to be introduced to a circuit as dry solids or a slurry. The Water Feeder allows the addition of water to the circuit.

Feed unit

Examining equipment and port data

Nest of four cyclones

Water Feeder

The data windows for each equipment unit and its associated streams can be accessed by placing the cursor over the unit and right-clicking the mouse button to view the pop-up menu. Left-clicking on the word Equipment on the pop-up menu brings the equipment data window into view. Left clicking on the name of a stream port in the pop-up menu (in the cyclone example these choices are combiner, underflow or overflow) brings the data window of that stream port into view.

Selectable tabs

Page 3-12

Note that the port and equipment data windows use selectable tabs to provide access to the several types of data which are available within each window. To view the available data left-click on each tab in turn.

Section 3.5


Learning JKSimMet Arranging windows on the desktop


If there are several windows open on the JKSimMet desktop the user has several options to organise the windows to suit their needs. The options available can be seen by left-clicking on the icon at the top, left-hand corner of the window which you want to move, close etc. Clicking on this icon brings into view a drop-down menu which allows the user to move, minimise or close the data window by selecting the appropriate command.

Minimise window button on open window.

Close window button

Left-click this icon to view drop-down menu to move, minimise or close this window.

Move a window Select the word Move on the drop-down menu and then move the mouse or use the keyboard arrow keys to move the window as required. To stop moving the window left-click with the mouse or press the Enter key on the keyboard. Alternatively a window can be moved by simply left-clicking and dragging on the window title bar to move the window to where you want it. Minimise/Restore To minimise a window select the word Minimise on the dropa window down menu or left-click on the minimise button at the top, right-

hand side of the title bar. This shrinks the window to a small title bar at the bottom of the JKSimMet desktop area. To return the window to its previous size and position left-click on the Restore button at the top, right-hand side of the title bar. Close a window Select the word Close on the drop-down menu or left-click the Close button at the top, right-hand corner of the window or hold the Ctrl key down and press the F4 key. Version 5.1 November 2001

Section 3.5

Page 3-13


Left-click this icon to view drop-down menu to move, minimise or close this window.

Learning JKSimMet

Minimise window button on open window.

Close window button

Restore window button on minimised window

Resize a window The width and height of the flowsheet window can be adjusted by selecting the word Size on the drop-down menu. The size of the (Flowsheet window can then be adjusted by using the arrow keys or by leftwindow only) clicking and dragging a corner of the window

Another alternative for arranging windows on the desktop is to use the options available under the Window menu on the JKSimMet menu bar. These options allow the user to arrange all of the windows in one operation, the choices for arranging the open windows being cascade, tile horizontal, tile vertical.. There is also an option Arrange Icons, which organises the icons of any minimised windows into rows at the bottom of the screen.

Concept: Convergence

To simulate a closed circuit, JKSimMet uses an iterative procedure. In the first iteration, an estimate (perhaps zero) of the circulating load is used. This allows the calculation of a better estimate of the circulating load to be used for the second iteration and so on. The procedure is repeated until the difference between succeeding estimates of the circulating load are less than a specified amount (the convergence limit). The circuit is then said to have converged. The convergence value is shown by JKSimMet during simulation. The tolerance limits can be changed by the user.

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Section 3.5


Learning JKSimMet

JKSimMet V5 uses a standardised approach for all of the analysis tools – simulation, mass balancing and model fitting. As shown in the Simulate window example below, the tabbed window for each tool offers a Control tab to define parameters and set the limits for the operation. It also has a Select tab which allows the user to choose a subset of the flowsheet components for simulation or balancing etc. Each selection list can be named and saved, allowing the user to analyse as many subsets as required. This capability was only available within the mass balancing module of earlier versions of JKSimMet. It should remove the need for multiple circuits in all but the largest multi-survey data sets. Once the Select list is defined, a simulation can be run.

General Approach

Running a Simulation


Step 1 To simulate the example left-click on the Simulation icon. This brings the Simulate window into view.

Step 2 A glance at the flowsheet shows which parts of the flowsheet have been selected to be included in this simulation as all of these items are outlined in blue on the flowsheet. In this example every item on the flowsheet is selected to be used in the simulation. Step 3 Run the simulation by left-clicking on the Start button at the bottom left of the Run Simulation tab area of the Simulate window. The simulation will now run iteratively through the circuit. As each iteration in the simulation is completed the values in the simulation window will be updated. Once the execution of the simulation has finished it is possible to assess the simulation results by looking at the values in the simulation window. More detailed information can be viewed via the port and equipment unit data windows. We shall first look at techniques for examining the data on the computer screen and then at printing the data.


Section 3.5

Page 3-15

Working with an Existing Project 3.5.3

Learning JKSimMet

Displaying the Simulation Results

The simulation has calculated the flows of through each of the various equipment units of the circuit and their ports. The Run Simulation tab has a section where the results of the simulation are summarised. The detailed data for each piece of equipment and port on the flowsheet can be examined individually by displaying the appropriate data window on your screen, as described in section 3.5.2. Data Display

The data windows contain all of the information that JKSimMet uses to perform the simulation and also show the results of the simulation. The port data windows list the raw and calculated values for mass flows of water and solid and the size distribution values while the equipment data windows show the model parameters used for simulation together with any data that result from the simulation (e.g. cyclone operating pressure). Step 1

Page 3-16

Section 3.5

To examine all of the data for any equipment unit or port in the circuit, move the cursor over the unit whose data you wish to examine. Right-click on the equipment unit to bring the pop-up menu into view (as shown below) and then move the cursor to highlight the required information (equipment or port name) on this list and click the left mouse button. This will bring the selected data window into view. In this example the Cyclone equipment data window is shown. Note that when a data window is the active window, the equipment unit to which the data relate is highlighted in red on the flowsheet.


Learning JKSimMet


Data window hydrocyclone

Step 2

for

There are several alternative methods to look at the port data associated with each equipment unit. One method mentioned previously is to return to the flowsheet, right-click on the equipment icon of the unit which the stream feeds into or flows out of and then left-click on the name of the port whose data you want to examine. The alternative method, which is useful if the equipment data window is already open, is to left-click on the Port Detail drop-down list at the top, centre of the equipment data window and then to select the name of the port whose data you want to view. Both of these actions bring up the port data window. The cyclone underflow data window is shown below as an example. Another way to access the equipment data window only works if the flowsheet is “locked”. If you have finished editing the flowsheet, you may click on the Lock the Flowsheet icon on the tool bar. The lock button will stay depressed indicating that the flowsheet icons can no longer be moved. This prevents “accidental”editing. In this locked mode a double click on an equipment icon will open its data window immediately.

Step 3


The port data window has three areas for the user to examine. The major part of the window is the area where the data are listed. Two selectable tabs allow the user to view the mass flow data for water and solids Section 3.5

Page 3-17


Learning JKSimMet

and their associated data and the size distribution data, simply by left-clicking on the appropriate tab. Note that a third tab is present here when component (e.g. assay) data have been included in the flowsheet data. The other areas of this window are the drop-down menus for Format (sizing format), Data type and Error which allow the user to choose how the data are presented. The Set SDs button which, as its name implies, allows the user to set the SD values for the data, will be discussed in a later section.

Left click on the drop-down lists to select the data format you wish to view.

Left click on a tab to view the associated data.

Concept: Data Formats

The JKSimMet user can view a variety of data in the stream data window by selecting the required format from the Format, Data Type and Error drop-down sub-menus. The size distribution data can be displayed in one of three formats - % retained at size, cumulative % retained at size or cumulative % passing size. The Data menu gives the user the option of displaying GSIM data types (experimental and calculated data only) or SDs data types (experimental data, calculated data, SDs and errors) or all data, which as the name implies, displays all of the data types including balanced and fitted data as separate columns.

˝

Page 3-18

Section 3.5


Learning JKSimMet Concept: Data Types

Exp (Experimental Stream Data)

Working with an Existing Project Data which the user has entered which are the results from sampling, sizing and assay.

Bal Calculated data which are the output of the (Mass-balanced data) mass-balancing procedure.

Changing column width

Fit (Model-fitted data)

Calculated data which are the output of the model-fitting procedure.

Sim (Simulated Data)

Calculated data which are the output of a simulation model.

SD

An estimate (standard deviation) of the accuracy of an experimental measurement (see chapters 5 and 6 for details).

Errors

The error is the difference between the measured or experimental data and the calculated data. Chapters 5 and 6 discuss errors in detail.

The user can change the width of the columns in which the data are presented in both the port data and equipment data windows. To change the width of a column move the cursor to the righthand edge of the cell at the top of the column whose width you wish to change. When it is positioned over the border line, the cursor will change from the usual arrowhead to a vertical line with arrows on each side of it; left-click and drag with this cursor to change the column width as required and release the mouse button when the column width is to your satisfaction.


Section 3.5

Page 3-19

Working with an Existing Project 3.5.4

Learning JKSimMet

Printing the Simulation Results

When you are satisfied with your simulation, you can print the results out on the printer. The printing facilities contain functions that: • • • • • •

print the raw and calculated data for a selected port, including SDs and errors if selected on the window display print all details for a selected equipment unit print the flowsheet print an overview table print a graph of selected data print a user-configured report.

The user can print quick or generic graphs, an overview table of data and a report once these have been created by the user. The overview, report and graph plotting functions are comprehensive and they are discussed separately from printing later in the manual. The printing functions are invoked via the main JKSimMet menu at the top of the JKSimMet desktop or from the Print button on the active window. A Print Preview functionis available in most cases.

Reports

The simulator can print reports in several formats, these are: • • • • •

equipment (a selection or individual) ports (a selection or individual) equipment feed streams (a selection or individual) overviews configured reports

Quick Text Printing

To print the contents of a port or equipment data window simply open the required data window and click on the Print Preview icon on the JKSimMet toolbar. A Print Preview window will display the data as they will be printed; clicking on the Print icon in this preview window prints the page(s) immediately. Alternatively, the data window contents can be printed immediately by clicking on the Print icon in the data window.

Flowsheet Print

The current flowsheet can be printed by selecting File on the JKSimMet main menu, selecting the Print Flowsheet option and then selecting the required option for colour or monochrome printing from the sub-menu. Selecting Print to Clipboard sends a copy of the screen image to the Windows clipboard from which it can be pasted into other suitable applications such as MS Word or MS Paint.

Page 3-20

Section 3.5


Learning JKSimMet


Graph Print

Quick or generic graphs can be printed via the Print icon on their window or copied to the clipboard.

Printing Simulation Data

Step 1

To print the simulation data, select each piece of equipment and port in turn, open its data window and click on the Print Preview icon. This will preview the pages to be printed. Click the Print icon on the Print Preview window toolbar to send the pages to the default Windows printer. If you do not want to print a page, close the Print Preview window by clicking its close button.

Data Type Selection

Step 1

Select the data to be displayed from either GSIM (grinding simulation which shows measured and calculated data), or SDs which also displays standard deviations and errors or All Data which shows all of the available data types. You may also wish to keep a printed copy of the circuit flowsheet. It is possible to print the flowsheet window as follows:

Print Circuit Flowsheet

Step 1

With the desired flowsheet as the active window, select the Print Flowsheet option on the File menu of the JKSimMet main menu. Then select the required option to print to file or clipboard in colour or monochrome from the four shown on the sub-menu. There will be a short pause while JKSimMet translates the screen data into a format suitable for the printer.

Report Printing

Step 1

Click on the report icon on the tool bar.

Step 2

Click on the Print icon on the Report window to print the default report. For details on the Report feature refer to section 3.5.6.


Section 3.5

Page 3-21


3.5.5

Learning JKSimMet

Summarising the Results - Overview

The Overview feature gives you a powerful means of summarising your data and checking it for adjustment problems. The overview window displays a configurable list for presentation of data from all selected streams. The overview window can display either actual experimental or calculated data. Alternatively the overview window can show calculated recovery data in cases where component data (e.g. assays) have been entered. Step 1

Left-click on the Overview Config icon on the main JKSimMet toolbar to bring the overview window into view. An overview list named Simulation results overview has already been prepared for this example.

Step 2

Resize the overview window by clicking and dragging the bottom right-hand corner of the window. This allows you to see all of the data summarised in the overview window. Alternatively you can use the scroll bar at the bottom of the overview window to view all of the data. You may also need to make the columns wider to see the data clearly. A typical use of the overview window would be to check that the % solids of all the simulated streams are within acceptable operating range. Is this the case in our example?

Note:

Page 3-22

Section 3.5

The % passing and passing size are set as a Flowsheet Property. These provide a very useful summary via the overview table.


Learning JKSimMet 3.5.6

Working with an Existing Project Summarising the Results - Report

The Report feature gives you a powerful means of summarising and printing both the port and equipment data. The Report window displays a list of all of the equipment units and ports on the current flowsheet and the user can select from this list the items which are to be included in the report printout. The report feature allows the user to select experimental or calculated data with or without SD values and/or error values. A typical use of the report feature would be to print a standard set of data for inclusion in a technical memorandum. Step 1

Left-click on the Report icon on the main JKSimMet toolbar to bring the Report window into view. Ensure that the prepared example report named Report Config Example is selected in the Report drop-down list.

Step 2

Click on the Print Preview icon in the Report window to see what the selected data will be look like when printed. Experiment with the various options in the Report window and use the Print Preview window to see how each option changes the printed report format.


Section 3.5

Page 3-23


Learning JKSimMet

The Report Print Preview window

Page 3-24

Section 3.5


Learning JKSimMet

3.5.7


Exporting Data from JKSimMet

While JKSimMet provides a range of options for examining your data, there may be occasions when it would be useful to be able to use JKSimMet data in a report or a presentation. Version 5 provides a copying facility which allows the user to copy data from the equipment and port windows to the Clipboard. These data can then be pasted into any clipboard compatible application such as a spreadsheet (e.g. MS Excel) or a word processor (e.g. MS Word). Note that there are two types of Copy buttons on the equipment and port data windows. These are: Copy Selected Cells to Clipboard

Copies only the data cells which are currently selected to the Clipboard.

Copy Grid to Clipboard

Copies all visible cells on the current tab to the Clipboard, including row and column labels.

Hint: If you wish to copy all of the tabs at once, use the print preview button and then the Copy to clipboard button on the Print Preview window. (Also see information on exporting data via tab-delimited and comma-delimited text files in Exporting data using Report in section 3.10)

3.5.8

Finishing a JKSimMet Session

You have completed your simulation of the ball mill and cyclone circuit and examined and printed both the flowsheet and the simulation data. In the next exercise we will attempt to improve the operation of the circuit by varying the parameters of some of the components, and then running simulations to observe the predicted effect. Before doing this, end the JKSimMet session as explained below. Note that JKSimMet will ask you if you wish to save the flowsheet over the original copy of Example Ball Mill - Cyclone on the hard drive. Normally you would save changes, but in this case we suggest that you do not do so because it will change the nature of the example for the next person who uses these exercises to learn JKSimMet.


Section 3.5

Page 3-25

Working with an Existing Project Ending the JKSimMet Session

Learning JKSimMet

Step 1

To quit from JKSimMet move the cursor to the File menu on the menu bar at the top of the screen and leftclick to view the drop-down File menu.

Step 2

Move the cursor down the File menu to select Exit.

Step 3

A pop-up window will ask you whether you want to leave the session. Left-click on the Yes button.

Step 4

Another pop-up window will ask you whether you want to save the last changes to the file. In this case left-click on the No button so that the Learner project file on the hard drive remains unchanged for the next user. In future if you want to save changes you have made to your own project file before exiting from JKSimMet, left-click on the Yes button to save the file.

Page 3-26

Save As

If you do not want to overwrite the Learner project, select Save As from the File drop-down menu. A Save As window will appear as shown below. This allows the user to save the file under any chosen name and in any chosen directory. The JKSimMet files are identified by the five-letter filename extension jksm5.

Section 3.5


Learning JKSimMet 3.6 About this Section

Making Changes to an Existing Flowsheet Making Changes to an Existing Flowsheet

Now that you have successfully simulated the ball mill and cyclone demonstration circuit supplied with JKSimMet, this exercise will extend your knowledge by showing you how to: •

• •

change the standard data provided with a test, in an attempt to improve the performance of the circuit under changing conditions re-simulate the circuit view the results of the altered simulation and plot selected results as a graph on the screen or using overview or on the printer.

The objective is to optimise the performance of the circuit by changing key parameters of the units and streams. The selection of these parameters is the engineer's job and you may well have your own ideas and wish to experiment. However, we have decided for this exercise to vary: • •

cyclone conditions to achieve a finer product throughput to compensate for a change in ore hardness.

This should have the effect of changing the performance of the grinding circuit that you are going to simulate. Note that there are two ways of changing the test circuit performance; you can change the parameters for the existing circuit components, as we are doing in this exercise, or you can replace or add components. We will see how to do the latter in section 3.7.

3.6.1

Selecting the Flowsheet to Use

In this and the following sections you will perform many of the same steps as in section 3.5 using a demonstration test. We will assume that you are starting a fresh session with JKSimMet and need to start the program and load the Learner Flowsheets project and the flowsheet named Example Ball Mill – Cyclone.

We begin by starting JKSimMet, loading the Learner Flowsheets and flowsheet named Example Ball Mill – Cyclone. Step 1


Start the JKSimMet program and load the demonstration project Learner Flowsheets, following the same procedure as you did in section 3.5.

Section 3.6

Page 3-27

Making Changes to an Existing Flowsheet Learning JKSimMet Step 2

Select the flowsheet Example Ball Mill – Cyclone in the drop-down list in the JKSimMet main window, following the same procedure as you did in section 3.5.1.

Step 3

Open the equipment data window for the Feed using the procedure outlined in section 3.3.6. Alternatively, lock the flowsheet using the Lock icon on the toolbar and double click on each piece of equipment when you wish to view the data window for it or its ports. The Feed is a special equipment unit which represents the flow of new material into a circuit. The Feed equipment data window allows us to examine the feed stream data, both mass flow and size distribution data. It layout is the same as that found in the port data windows which contain stream data.

The Feed equipment data window

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Section 3.6


Learning JKSimMet

Making Changes to an Existing Flowsheet

Step 4

Click on the Overview Config icon on the main JKSimMet toolbar to view the overview window. Make sure that the pre-defined Simulation Result Overview is selected on the drop-down list.

Step 5

Use the Print icon on the toolbar to print the overview window. This provides a printed record of the base results for the flowrates, % solids and other data from the original simulation.

Step 6

Click on the flowsheet window to make this the active window.

3.6.2

Altering Operating Conditions

One of the powerful tools which JKSimMet provides for the user is the ability to adjust the data for the components of the test circuit. While it is difficult and costly to experiment with real equipment, the JKSimMet simulator allows the engineer to experiment with a wide range of changes and to view the predicted results of these changes. Understanding the power of this adjustment method is important and this section proceeds by: • • •

showing you how to make changes and re-simulate providing exercises for you to practise familiarising you with some short-cuts and additional useful techniques.

The general technique is to decide the changes you want to make, select the component whose parameters you want to change, make changes to the parameters, re-simulate and observe the results. You then have the choice of making further changes, undoing the changes and trying some other ideas or accepting the changes and saving the file on disk as a permanent record. The parameters are characteristics of the equipment models and their ports which can be altered. In a real plant we can alter most equipment parameters (with varying degrees of difficulty and with varying degrees of expense!). A few stream parameters, such as the mass flowrate and feed size distribution can also be varied. Simulation allows us to vary any of the parameters which affect the process performance such as ball mill size and ore hardness with great ease.


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Making Changes to an Existing Flowsheet Learning JKSimMet The exercises in this section will investigate what happens when you change the following parameters: • • • •

the number of parallel hydrocyclones, and their key variables such as vortex finder and spigot sizes ore work index feed size distribution cyclone feed density.

You are welcome to experiment with changing other parameters of other components but we suggest that you follow the exercise until you are confident that you understand JKSimMet.

Concept: Changing Data Fields

Note that in the data windows some of the data values are displayed in blue characters and some in black. Blue

Blue text on a white background indicates that the user can change the displayed data. To change the data, highlight the old value by double-clicking on it, type in the new value and press Enter to register the change.

Black

Black text on a grey background indicates that the data cannot be changed by the user. These are result fields which are controlled by the JKSimMet system.

Step 1

Open the hydrocyclone equipment data window (by placing the cursor over the cyclone icon on the flowsheet, right-clicking to view the drop-down menu and selecting the word Equipment).

The hydrocyclone equipment data window

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Section 3.6


Learning JKSimMet


Step 2

Using the mouse or cursor control keys, move the highlight to the data entry box whose data you wish to change (in this example the Parallel data entry box).

Step 3

Double-click the left mouse button to highlight the number you wish to change (in this case the number of cyclones) and then type in the new value of 3.

Step 4

Left-click on the Simulation icon at the top of the screen. This brings the Simulate window into view.

Step 5

Left-click on the Start button in the Simulate window to start the simulation.

Step 6

The simulation will begin and you will see the iteration counter increase until the simulation converges.

Step 7

Click on the overview window to bring it into view and examine the results of this simulation with three cyclones. Now compare the circuit performance against your previous printout. Is it better or worse? (with respect to, say, cyclone overflow P80 or water split to underflow)

Steps 2 and 3 can be repeated before simulating to change other parameters of the hydrocyclone. Steps 1 to 4 can be repeated to change parameters for several components.

Concept: Water Addition to Equipment Units

JKSimMet allows for water addition to the feed port of an equipment unit by connecting a Water Feeder unit. The water addition can be specified in tonnes per hour or as the amount required to achieve a given feed density or simply as that determined from the densities of the combined feed streams (i.e. no water added). The water addition control method is specified in the Water Feeder equipment window using the drop-down list labelled Model.

Cyclone Variation Exercises

Step 1

Bring the cyclone equipment window into view and change the number of parallel cyclones back to 4.

Step 2

Change the vortex finder diameter from 0.365m to 0.390m and run the simulation. Note the cyclone pressure drop (by looking in the Performance Data table of the cyclone equipment window).

Step 3

Reset the vortex finder diameter to 0.365m.


Section 3.6

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Making Changes to an Existing Flowsheet Learning JKSimMet

Ball Mill Variation Exercises

Cyclone Feed Density Exercise

Page 3-32

Step 4

Change the spigot (Apex) diameter from 0.203m to 0.190m. Run the simulation again and observe the cyclone pressure drop.

Step 5

Reset the spigot diameter to 0.203m.

Step 1

Bring the ball mill product port data window into view and note the product 80% passing size.

Step 2

Bring the ball mill equipment data window into view and then select the work index for the simulated mill and increase the value of the index by 2.0.

Step 3

Run the simulation again and observe the increase in ball mill product size (which is displayed in the ball mill product port data window).

Step 4

Left click on the Simulate window to make it the active window. Left-click on the Control tab and then leftclick on the Start Condition drop-down list and select Experimental Data.

Step 5

Now view the circuit feed stream data by right-clicking on the Feed unit and selecting the Equipment option. Change the value of TPH solids for the feed, run the circuit simulation and observe the mill product stream 80% passing size. Repeat these steps until the original product size is achieved.

One of the easiest operating parameters to change in an actual plant is the pulp density of the cyclone feed. This exercise examines the effect on the grinding product of changing the cyclone feed density. Step 1

Place the cursor on the Water Feeder icon which is connected to the cyclone feed port on the flowsheet and right-click to view the drop-down menu. Move the cursor to highlight the Equipment option and left-click. The data window for the Water Feeder unit will appear.

Step 2

Move the cursor to the Model drop-down list and leftclick. Move the cursor to highlight the Water Feeder – Required % solids option and left-click to select this option.

Section 3.6


Learning JKSimMet

Feed Characteristic Variation Exercises


Step 3

Left click on the Required % Solids data cell to make it the active cell, type in the value 60.0 and press Enter.

Step 4

Run a simulation and observe the effect of this change in cyclone feed density on the streams in the circuit.

Ore type variations or changes to a crushing plant often cause alterations in the mill feed size distribution. This exercise examines the effect of a feed size change on the grinding product. Step 1

Bring the circuit feed stream data window into view by right-clicking on the Feed icon and selecting the Equipment option on the drop-down list.

Step 2

Left-click on the Sizing format drop-down list, move the cursor to highlight % Retained and left-click on this to make this the active sizing format.

Step 3

Left-click on the tab labelled Size Distribution to view the sizing data. Use the cursor or mouse to input the following new size distribution. Start at Size 1 16mm and input in the Exp column the following values; 0.5, 3, 8.5, 19, 17, 11, 8, 7, 5, 3.5, 2, 1.8, 1.5, 1.4, 1.3, 1.2, 1.1 and 1.0. JKSimMet will supply the last value of 6.2 at size 19.

Step 4

Run a simulation of the circuit and examine the cyclone operating conditions and product size.

3.6.3

Saving the Session

Once you have made changes to the test circuit data, you should remember that the changes have only been made to the copy held in the computer's memory. To record the changes for posterity, you must also make sure that the files on the hard drive have been updated. This is done by saving the test to the hard drive. It is good practice to save your work at regular intervals while you are making changes. This will protect your work against power failure, computer malfunction or mistakes that you will inevitably make from time to time.


Section 3.6

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Making Changes to an Existing Flowsheet Learning JKSimMet Saving the Session

Page 3-34

To save the session as it is now, perform the following steps: Step 1

Left-click on the File menu on the main JKSimMet menu bar.

Step 2

Move the cursor to highlight the Save As option and left-click to open the Save As window.

Step 3

Type the new filename in the File name box and select the directory in which you want to save the file. If required, you can create a new folder for storing JKSimMet files by clicking on the Create New Folder button.

Step 4

Once the filename and its directory have been entered, click on the Save button to save the file.

Section 3.6



Making Changes to an Existing Flowsheet Graphing Your Results

JKSimMet has a graphing facility which you can use to create graphs of your results on the display screen and to print these graphs. The facility has been designed so that users can produce graphs very simply using a selection of standard layouts in the Quick graph feature, while the Generic Graph Configuration window provides the flexibility for the user to develop customised layouts. The Generic Graph Configuration window allows the user to draw graphs of: • •

size distributions of all raw and calculated data for the streams in a circuit, equipment parameters such as efficiency curves for the raw and calculated data for classifying units in a circuit or appearance functions for ball mills,

Up to 15 curves can be drawn on a single graph and the user can have open on the screen as many graph windows as required. The flexibility which the Generic Graph Configuration provides also brings a certain amount of complexity and we shall avoid this here by first describing Quick graphing with the standard layouts. A tutorial on the full graphing features is given in section 3.8 (Learning Graphing). As an introduction to graphing we will look initially at the basic graphs which the user can create with a few clicks of the mouse.

About this Exercise

From the Example Ball Mill – Cyclone flowsheet, you will create a graph of size distribution data by: • •

selecting the circuit data to be graphed using the Quick graph facility.

The graph will be displayed on the screen. The sizing format for this graph will be selected from the available default graph formats. A drop-down list allows the user to change the sizing format to % retained, cumulative % retained, or cumulative % passing. Another drop-down list in the window allows the user to select either the experimental data, calculated data or the absolute error to be plotted on the graph. By using the buttons on the graph window you can add or remove gridlines as required. Drawing a Graph

Step 1


Place the cursor over the cyclone unit on the flowsheet and right-click to view the drop-down menu..

Section 3.6

Page 3-35

Making Changes to an Existing Flowsheet Learning JKSimMet Step 2

Move the cursor to select the word Graph from the drop-down menu. JKSimMet will open a window which graphs the stream data for the feed and products streams of the selected unit, as shown below. Buttons to add gridlines to graph

Drop-down list to select format of size plot

Drop-down list to select Experimental data, Calculated data or absolute error.

Plot single data set button

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Step 3

The graph which is displayed in the window is the default format of cumulative % passing size for the calculated data.

Step 4

Add gridlines to the graph by left-clicking on both the x-axis and y-axis gridline buttons. Your graph should now look like this.

Step 5

The final feature of this basic graph is that the user can select any port attached to the unit for its data to be plotted individually. Left-click on the Show Single Port button at the top left corner of the graph window to view only one data set on the graph and then select the required port from the drop-down list of port names (Single Port Selection list). Note that this drop-down list of port names is inactive until the single data set option has been selected.

Section 3.6


Learning JKSimMet Concept: Printing a Graph

Printing a Graph


Once you have set up the graph to your satisfaction you can print the graph window. Whether the graph is printed in colour depends on whether or not the printer connected to your computer can print in colour. Step 1

Use the Printer Setup option in the File menu to set the orientation of the paper to landscape or portrait as required.

Step 2

To print the graph click on the Print icon on the Quick Graph window. This will print the graph immediately.

Step 3

Quit from JKSimMet by selecting Exit from the File menu on the main JKSimMet menu. When asked whether you want to save any changes to your file respond with no in order to keep the original example for future users.


Section 3.6

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Creating a New Project 3.7 About this Section

Learning JKSimMet Creating a New Project

In this section you will build a JKSimMet project from scratch, just as you would do with a real project. The techniques covered in this Chapter are the initial steps in setting up a project and flowsheet which are common to all of the JKSimMet mass-balance, modelfitting and simulation tools. The first step in every new project is to build the flowsheet. Then some of the data required for the equipment and streams of the new circuit will be entered by you, the user, and some will be copied from an existing project. The techniques available to you for examining the data such as graphing and printing, will also be described in this section. This section will show you how to: • • • • •

create a new project and define new project and flowsheet names, build a flowsheet, re-use component data (such as for the ball mill unit) from previously created projects, define data for equipment units and streams, run a simulation and view the results for the new test you have created.

3.7.1

Starting a New Project

This exercise begins with the creation of a new project following the steps outlined below. Concept: Projects

A project consists of one or more flowsheets. It is only possible to work on one project at a time (although each project may contain several flowsheets). If you already have a project open and you create a new project, the new project will overwrite in memory the currently open project.

All of the projects that you create will be saved on the hard drive and will be quite separate from the Learner Flowsheets project. Step 1 Start JKSimMet and left-click on the Open Project icon in the toolbar. This will bring the Project View window on to the screen with the Saved tab active. Step 2 Left-click on the New tab to make this the active tab.

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Section 3.7


Learning JKSimMet

Creating a New Project

Step 3 Click on the red Default Project icon and drag it across on to the JKSimMet flowsheet window. This will load the Default Project which is a blank project, for you to work on.


Section 3.7

Page 3-39

Creating a New Project 3.7.2

Learning JKSimMet Define Flowsheet Name

The flowsheet window in this version of JKSimMet can accommodate much larger circuits than was the case in previous versions. Users can now draw a flowsheet which is larger than the screen. Scroll bars are used to move around the flowsheet window. In mass balance, model fit and simulation modes the user can select a subset of any of the units and streams for analysis.

Each flowsheet must be given a name so that the user can select the required flowsheet for display. In this case we are only creating a simple flowsheet with a single circuit, but it is still advisable to name the flowsheet. Define Flowsheet Step 1 Left-click on the JKSimMet flowsheet window to make this the active window and then right-click on any blank Name area of this window. Step 2 On the pop-up menu which appears, move the cursor to highlight the word Flowsheet and then move the cursor to highlight Properties on the sub-menu which appears and left-click to select this option. This will bring into view the Flowsheet Definition window.

Step 3 In the box labelled Title in the Flowsheet Definition window type in your own title for the flowsheet. The user can also type other details such as any comments on the flowsheet in the appropriate spaces in the Flowsheet Definition window. .Step 4 While the Flowsheet Definition window is open you should also take the opportunity to set the % passing size values which are used in the port data displays. Step 5 Close the Flowsheet Definition window by left-clicking on the Close icon in the window title bar. Note that the name of the flowsheet now appears in the drop-down list box at the bottom, right-hand corner of the flowsheet window Page 3-40

Section 3.7



Creating a New Project Drawing a New Flowsheet

To draw a new circuit directly on to a blank flowsheet window you will need to follow these steps: •

•

• •

select the units that make up your circuit and place their icons (pictures that represent the units) on the flowsheet (make sure that they are positioned so that it will be easy to connect the streams between them), connect the appropriate feed and product ports of the units with streams that represent the flow of material between the units, add feeders to carry the input material into the circuit, connect water addition points to the circuit.

Each piece of equipment on the flowsheet has a default name which can be edited by the user. Naming the components of the flowsheet is recommended as this makes it easier to identify the data later, for example when you want to define the operating parameters of an equipment unit or identify it in a report.

Concept: Unit Naming Conventions

JKSimMet identifies all components of a circuit by the names that you give to them. The program does not enforce any conventions in naming and you may select any name you wish. You may call the ball mill Bert if you wish, but you will no doubt find that naming a ball mill, Ball Mill or some abbreviation thereof, while somewhat less interesting, is in practice easier to remember. JKSimMet will not forget what Bert is, but you probably will!

You now have a blank flowsheet window on the screen in front of you and you can begin to draw in a new circuit. You must position the process equipment before connecting the ports of the new circuit. Create New Step 1 Equipment Units on the Flowsheet

To create a new equipment unit on the flowsheet first left-click on the Project View window to make it the active window and then left-click on the tab labelled New to make it the active tab. Note that once a project has been loaded there is only one item in the New list in the Project view window – Default Equipment .

Step 2

Double-click with the left mouse button on the Default Equipment book icon to “open” the book and display the list of equipment categories which are available to you.

Step 3

To view a list of the units which are available in each equipment category simply left-click on the plus-sign which is next to the category name. In this case, left-


Section 3.7

Page 3-41


Learning JKSimMet click on the Mill category to show the list of mills available.

Default Equipment book has been “opened” to show the list of equipment categories.

Step 4

Left-click on the icon of the equipment unit which you want to add to the flowsheet and drag it on to the flowsheet. In this case, click and drag the Rod Mill icon to the flowsheet, placing it in the position you want it to appear and releasing the mouse button to leave the unit in the required position.

Positioning A Unit

Equipment units may be moved around the flowsheet window whenever you want to move them, providing that the flowsheet is not locked. Simply place the cursor over the icon of the unit you wish to move, left-click and drag the equipment icon to its new position and release the mouse button to leave the icon in place. If there are streams attached to the unit they will remain attached after moving it.

Changing Feed Direction

In order to make flowsheet layout uncluttered, the orientation of equipment units can be changed so that the feed end is facing left or right as required. To change the feed direction move the cursor to the unit you wish to change and right-click to view the dropdown menu. Move the cursor to highlight the word Flip and leftclick to make the unit change from left-hand feed to right-hand feed or vice-versa. While it is possible to Flip units which have streams attached, it is better to plan the orientation of the units before you connect them together with streams or you may end up with some very convoluted pipework.

Deleting a Unit

An equipment unit can be deleted by placing the cursor over the unit on the flowsheet and right-clicking to view the drop-down menu. Select the Delete option from the menu and the unit (and any attached streams) will be deleted from the flowsheet.

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Section 3.7


Learning JKSimMet Concept: Re-using data


Re-using equipment data that have been created for a previous project is a convenient short-cut. It allows the engineer to quickly construct similar flowsheets based on the same components.

Use Existing Step 1 Equipment Units on the Flowsheet

To use equipment units which have been used in a previous project first left-click on the Project View window to make it the active window and then leftclick on the tab labelled Saved to make it the active tab. This brings into view a list of the projects which have been saved in the current directory on the hard disk. If the project which you want to access is in another directory, click on the Browse Directories button and select the required directory in the Select Directory window.

Step 2

Double-click with the left mouse button on the book icon of the project whose data you wish to re-use. This will display the list of flowsheets which are the components of the project. In this case we will look at the project called Learner Flowsheets.

Step 3

Left-click on the plus sign to the left of the flowsheet where the data you wish to re-use are located. This will reveal a list of the equipment units which are part of the flowsheet. In this case left-click on the plus sign for the Example Ball Mill Cyclone simulation flowsheet.

Step 4

Move the cursor to the icon of the equipment unit whose data you wish to re-use and left-click and drag the unit icon onto your current flowsheet. For the example you are working on, click and drag the Primary Mill and then the Cyclones units to the flowsheet you are building.

The first stage of building the flowsheet is complete and your flowsheet should look similar to the one shown below.


Section 3.7

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Learning JKSimMet

The Learner Flowsheets Example Ball Mill Cyclone circuit is a large, single-stage ball mill treating a coarse feed and producing a relatively coarse product. Another common circuit configuration is to use a rod mill followed by a ball mill to produce a finer product. The first part of this exercise will investigate the use of this arrangement. Because the ball mill is very large, it is necessary to configure the circuit with three rod mills in parallel. In reality, this is not a practical configuration without the use of a feed sump. However, for simplicity we will not draw a feed sump on the flowsheet at this stage.

3.7.4

Create Connecting Streams

The next step is to create streams to join the equipment units you have placed on the flowsheet. The combiner and product ports of each unit are represented on the equipment icons by a short grey line which resembles a short length of pipe with a flange at the end. Up to three streams can connect to a combiner port. Only one stream can connect to each product port. If an equipment unit has more than one product (for example, a cyclone has two products) there will be a separate product port for each product stream on the unit icon. The hydrocyclone icon is shown below as an example.

Cyclone combiner port with one stream connected.

Cyclone product (overflow) port with no stream connected.

Cyclone product (underflow) port with no stream connected.

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Section 3.7


Learning JKSimMet Connecting Ports


Step 1

To begin to draw in a stream to connect a combiner and a product port, first position the cursor over the combiner port of a unit.

Step 2

When the cursor has changed into a hand grasping a spanner with the word JOIN in black text above it, leftclick the mouse button. The word above the cursor will change to PROD to tell the user that the first connection has been made and to make the second connection by joining the stream to a product port.

Step 3

Move the cursor to the product port of the unit you wish to join.

Step 4

When the cursor is in the correct position to join the streams the cursor will change to a mirror image of itself, with the word PROD now in white text. At this position left-click the mouse button to make the second connection. The simulator will draw in the connecting stream on the flowsheet.

In the example flowsheet that you are building the units should be connected as shown in the picture below. Repeat steps 1 to 4 above to connect all of the units as shown. Note that your streams may follow slightly different paths, depending on the order in which you make the connections and the relative positions of the units on the flowsheet.


Section 3.7

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Learning JKSimMet

Errors in Connecting Streams

JKSimMet will not allow you to draw connecting streams which could not exist in a real plant. For example, JKSimMet does not allow you to draw connecting streams from one combiner port to another combiner port or from one product port to another when you draw in the circuit diagram.

Deleting Connecting Streams

If the user makes a mistake when drawing connecting streams the stream can be deleted as follows: Step 1

To delete a stream place the cursor over the equipment unit from which the stream emanates as a product and right-click to view the pop-up menu.

Step 2

Move the cursor to highlight the Delete option and to view its sub-menu which lists all of the items which can be deleted

Step 3

Move the cursor along the list in the Delete sub-menu to select the port name whose stream you wish to delete. Note that if you choose the combiner port from the Delete sub-menu all streams connected to that port will be deleted.

Concept: Unit Feed Ports

Each equipment unit has a three-stream combiner at its feed port (hence the name combiner used to denote the feed port). If there is more than one stream entering the unit, the combiner port data window displays the data for the combined feed streams.

Concept: Unit Product Streams

Each equipment unit has one, two or three product streams, depending on what type of unit it is. On the flowsheet, each product stream which leaves a unit is denoted by a product port (shown as a short grey line which resembles a short length of pipe with a flange at the end). Only one product stream flows from each product port.

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Section 3.7



Creating a New Project Adding a Circuit Feed Stream

The next step in building the flowsheet is to define a feed stream to the circuit. In JKSimMet V5 the source of new material to feed into a flowsheet is a special unit called the Feed. The Feed allows the user to enter the stream data which define the feed material, such as mass flows and size distribution.

Adding a New Feed to a Flowsheet

Step 1

Left-click on the Saved tab in the Project View window to view the Saved Equipment list. Double left click on the Learner Flowsheets Template.

Step 2

Left-click on the plus sign of the Example Ball MillCyclone Simulation circuit.

Step 3

Left-click and drag the Feed icon on to the flowsheet and place it near to the feed end of the Rod Mill.

Step 4

Left-click on the flowsheet to make this the active window.

Step 5

Draw in a connecting stream between the Feed unit product port and the Rod Mill unit combiner port.

3.7.6

Adding Water to the Circuit

The flowsheet diagram is now almost complete. The final task in drawing our circuit flowsheet is to make provision for water to be added to the rod mill and the cyclone feed.

Concept: Water Addition

Adding Water to a Flowsheet

In JKSimMet V5 all water additions are made by means of a special type of unit called a Water Feeder. Water may only be added to the feed port of an equipment unit. The water addition can be specified as either tonnes per hour of new water or controlled by the required percent solids of the unit feed stream. The choice of options is controlled by selecting the appropriate model in the Water Feeder equipment data window.

Step 1

Left-click on the New tab in the Project View window to view the Default Equipment list. If only the Default Equipment icon is visible, double-click on the closed book icon to view the list.

Step 2

Left-click on the plus sign of the Feed category icon to view the list of feed of feed options available.


Section 3.7

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Learning JKSimMet

Step 3

Left-click and drag the Water Feeder icon on to the flowsheet and place it near to the feed end of the Rod Mill.

Step 4

Left-click on the flowsheet to make this the active window.

Step 5

Right click on the Water Feeder icon and select Equipment from the Drop Down list.

Step 6

Enter an appropriate % solids value in the Water Feeder equipment window

Step 7

Draw in a connecting stream between the Water Feeder product port and the Rod Mill unit feed port.

Step 8

Repeat Steps 3 to 7, placing the second Water Feeder icon near the cyclone and connecting it to the cyclone feed port.

Step 9

It would be wise to record your work at this stage. Right-click on a blank area of the flowsheet, move the cursor to select Project and then select Save from the sub-menu.- or select File and then Save from the menu.

The circuit flowsheet is now complete and should now look like the flowsheet shown below. At this stage it is advisable to Lock the flowsheet by clicking on the Lock button on the JKSimMet toolbar. If required, the user can add various information such as stream name labels or equipment unit information blocks to the flowsheet. The techniques for annotating the flowsheet in this way will be discussed in the next section.

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Section 3.7


Learning JKSimMet


Concept: Locking the Flowsheet

Locking a flowsheet prevents the equipment units on the flowsheet from being moved accidentally. It is advisable to lock a flowsheet once you have finished drawing it, particularly large complex flowsheets, because if a unit is moved accidentally whilst trying to access data the flowsheet is redrawn and this may take several seconds for complex diagrams. Locking a flowsheet also allows users to access the equipment data window by double-clicking on the equipment icon on the flowsheet.

Concept: Port Naming Conventions

JKSimMet V5 automatically creates names for all of the ports on the flowsheet. Each port name is created by identifying which unit it is attached to and describing whether it is a feed or product port for that unit. For example, if the user has a nest of cyclones named Deslime Cyclones, their feed port will automatically be named Deslime Cyclone Combiner. The product ports are given the descriptors which are appropriate for the particular item of equipment. For example, cyclone product ports are overflow and underflow and flotation product ports are concentrate and tails.


Section 3.7

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Creating a New Project 3.7.7 Displaying Data on the Flowsheet

Concept: Information Blocks

Learning JKSimMet Adding Information Blocks and Labels to the Flowsheet

You can easily put information about the ports and equipment units on your new flowsheet. This is done by adding Information Blocks to the flowsheet. This is a very useful feature as it allows the user to examine the circuit performance in terms of port data and equipment data in pictorial form on the flowsheet. Each of the units and ports on the flowsheet can be annotated with an Information Block which can display data for that that item on the flowsheet. For equipment units the information block displays two items of data while for ports up to four items of data can be displayed. The user can select which data items are displayed in the information block. The information block can be placed in any position the user chooses on the flowsheet screen.

Firstly you will place information blocks on the flowsheet for some key ports. Adding a Port Step 1 Information Block To the Flowsheet Step 2

Make the flowsheet window the active window. Left-click on the Information Block Configuration button on the main JKSimMet toolbar. This opens the Configure/Assign Information Blocks and Labels window as shown below.

The Ports tab for configuring Port Information Blocks

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Step 3

Left-click on the selectable tab labelled Ports to configure the information blocks for the port data.

Step 4

Check that the box marked Allow Dual Data Types is empty. This will allow you to place four different data items in the information block. If this box has a tick in it you can place two data items in the information block and view two types of data (e.g. experimental and simulated data) for them both.

Section 3.7


Learning JKSimMet

Creating a New Project and view two types of data (e.g. experimental and simulated data) for them both.

Step 5

Decide which four data items from the Configuration list you want displayed in the port information block and then left-click on each in turn to place them in the block. For this example select Solids (t/h), % Solids, Vol.Flowrate and % Passing X. If you make a mistake or want to change any of the selected data items simply click on the Clear button below the list and repeat the selection process. Note that % - X mm and Y Passing Size are set from the Flowsheet properties window accessed via the tool bar icon or a left click on the flowsheet.

Step 6

From the data type drop-down list select the type of data which you want to display in the information block. In this case select Sim to display simulated data.

Step 7

Once you have the required configuration for the information block left-click on the Apply button to apply your selection to the information block. Note that this action places an information block legend on the flowsheet.

Step 8

From the list of ports at the left of the window select the port for which you want to add an information block. For this example, select the Ball Mill Combiner.

Step 9

Left-click on the Add New Block button to place the information block on the flowsheet. The new block appears behind and slightly to the side of the Port Legend block. Note that the information block has the name of the port across the top of it. This will help to identify which port the data relate to if the information block is not placed directly next to the port on the flowsheet.

Step 10

Repeat steps 3 to 8 for any other ports for which you want to display an information block.

The user can also add an information block for each equipment unit on the flowsheet. This allows the user to observe the effect of any changes to the circuit on unit parameters such as cyclone operating pressure. For the example which you are working on here, an information block for the cyclones would be useful.


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Adding an Step 1 Equipment Unit Information Block

With the Configure/Assign Information Blocks and Labels window as the active window, left-click on the selectable tab labelled Equipment to configure the information blocks for the equipment unit data.

Step 2

From the list of units at the left of the window select the equipment unit for which you want to add an information block. For this example, select the Primary Cyclones unit. The list of unit parameters in the Configuration section of the window will change to reflect the type of unit which has been selected, as shown below.

The Equipment tab for adding Equipment Information Blocks

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Step 3

Decide which two data items from the Configuration list you want displayed in the unit information block and then left-click on each in turn to place them in the block. For this example scroll down the list and select Cal Operating Pressure and D50c Cal. If you make a mistake or want to change any of the selected data items simply click on the Clear button below the list and repeat the selection process.

Step 4

Once you have the required configuration for the information block left-click on the Apply button to apply your selection to the information block for the selected unit.

Step 5

Left-click on the Add New Block button to place the information block on the flowsheet. Click and drag on the information block to place it where you want it on the flowsheet. Note that the information block has the name of the unit across the top of it. This will help to identify which unit the data relate to if the information

Section 3.7


Learning JKSimMet

Creating a New Project block is not placed directly next to the unit on the flowsheet.

Step 6

Repeat steps 2 to 5 for any other units for which you want to display an information block.

The final option for annotating the flowsheet is to add one or more Labels. This allows the user to type in their own text in a text box which can be formatted in a range of colours and styles.

Adding a Label to the Flowsheet

Step 1

With the Configure/Assign Information Blocks and Labels window as the active window, left-click on the selectable tab titled Labels to set up a label on the flowsheet.

Step 2

In the box marked Text type the text you want to display on the flowsheet. Note that as you type the Preview box shows how the label will look on the flowsheet.

Step 3

Select the required text justification by clicking on the radio button in the Text Alignment box. View the results of your selection in the Preview box.

Step 4

Select whether word wrap and/or borders are required for the text box.

Step 5

If you want to use a different background colour for the label click on the Background Colour box to view the palette of colours from which you can select a new colour.

Step 6

If the height and width of the label set by the Autosize function are not suitable for your label click on the Autosize On box to switch the Autosize function off. Then enter the required size (in millimetres) of the label in the boxes marked Height and Width.


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Step 7

When you are happy with the format of your text box as shown in the Preview, click on the Add Label button to place the label on the flowsheet. Click and drag the label to the required position. Note that once a label has been placed on the flowsheet its text and format cannot be edited.

Step 8

If you want to delete a label simply double-click on it to remove it permanently from the flowsheet.

The Labels tab for adding Text Labels to the Flowsheet

3.7.8

Entering Data

Having completed your circuit diagram the next step is to supply data for each component of the circuit. This can be done in two ways: Entering new data

The user can enter new data using the keyboard or by copying and pasting data from a spreadsheet.

Re-using the data from existing projects

The user can re-use the data for a unit created in a previous project by dragging onto the current flowsheet the icon of the unit from the existing project that is stored on the computer's hard disk. Once imported the data can be modified as required.

We have already seen how to re-use equipment unit data by using the icons for an existing ball mill and cyclones when drawing the Page 3-54

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circuit flowsheet for My RM-BM-Cyc Circuit. In the next section you will learn how to enter new data into the default equipment unit used on the flowsheet.

3.7.9

Define Data for Rod Mill

The only equipment unit in the new circuit without data is the rod mill. You will use the keyboard to enter a new set of data for the rod mill. The data to be entered are listed below and are also shown in the Rod Mill unit data windows opposite.

UNIT DATA FOR FLOWSHEET My RM-BM.CYC ROD MILL

Data which can be entered

Calculated During Simulation

ROD MILL Model Number of Rod Mills Data for Simulated Mill Internal Mill Diameter (m) Internal Mill Length (m) Fraction Critical Speed Load Fraction Ore Work Index

Lynch/Kavetsky 3 3.40 4.90 .650 .350 15.0

Data from Original Mill Rod Mill Constant Internal Mill Diameter (m) Internal Mill Length (m) Fraction Critical Speed Load Fraction Ore Work Index Feed 90% passing size (mm)

2079 3.40 4.90 0.650 0.350 14.1 11.5

Selection Function Data Function is constant below XC (mm) Intercept of function at Size 0 IN Slope of function with Size SL

7.43 -3.6 0.500

Calculated Data Change in breakage stages Number of breakage stages


1.53 7.30

Section 3.7

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Creating a New Project Equipment Unit Data Entry

Learning JKSimMet

Step 1

Place the cursor over the Rod Mill icon on the flowsheet and right-click to view the drop-down menu.

Step 2

Move the cursor down the drop-down menu to select the Equipment option.

Step 3

The unit data window for the Rod Mill appears on the screen, ready for you to enter the data listed above. Note that there are already data in the window. These data are typical values for a rod mill which have been selected as default data for this unit. You will replace these data with the values listed previously. Note: Notice that there are more data elements than will fit in the unit data window. As discussed previously you can view the various groups of data by left-clicking on the appropriate selectable tab.

Select tab to view this data group

Step 4

First change the name of the Rod Mill to Rod Mills No. 21,22,23 by clicking and dragging across the existing name to highlight it, typing in the new name and then pressing Enter. Note that the new name appears in the title bar of the rod mill data window as soon as you press Enter.

Step 5

Now change the number of parallel units to three by double-clicking on the number in the cell labelled Parallel and typing the number 3.

Step 6

Enter the data for the simulated and original mill in the data cells with blue text which are visible under the tab named Scaling. Left-click on a data cell to make it the active cell and then use the arrow keys to move the active cell as required. Note: It is possible to overwrite any of the values that appear in blue.

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Step 7

Left-click on the tab named Selection function and Calculated Data and type in the appropriate data from the list.

Step 8

Click on the Simulation icon on the main JKSimMet toolbar to bring the simulation window into view.

Step 9

Click on the Start button on the Run Simulation tab to simulate the circuit.

Step 10

Check the results and save the file if you are happy with the results.

Step 11

Print out equipment and port data as a base case for the exercises in the next section.

3.7.10 Examining Data Before we move on to the rod mill circuit exercises it is worthwhile to summarise the techniques which are available to the user for examining the large amount of data which exist in the flowsheet. Equipment Unit And Port Data Windows

The equipment and port data windows are the source of the most detailed data about these items. The user can have as many of these windows open on the JKSimMet desktop as he wishes. To make the desktop less cluttered, use the Minimise button to close the windows while allowing easy access to them. The windows will return to their original size and position when the Maximise button is clicked. In port data windows, the user can choose which data types to display (experimental, simulated etc.) by selecting the appropriate item from the Data drop-down list. Similarly the user can choose to view the size distribution data in one of three formats and can choose the error format by selecting the required type from the Format or Error drop-down lists respectively.

Quick Graph

The Quick Graph feature provides a quick and easy method to check for errors or discontinuities in sizing data by plotting a graph of cumulative percent passing or cumulative percent retained vs. size.

Tool window

The JKSimMet tool window (Mass Balance, Model Fit or Simulate window as appropriate) provides a summary of stream data showing the results which have been calculated by running the balance, fit or simulate tool.


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The flowsheet (streams and units) can be printed via the print icon. Selecting Print Flowsheet from the file menu allows the flowsheet to be printed or sent to the clipboard from where it can be pasted into MSPaint for editing or to any clipboard aware application.

Flowsheet print

3.7.11

Rod Mill Circuit Exercises

It is apparent that a more realistic circuit can be made with some further changes to the circuit data. These are: reduce the number of rod mills to one • alter the % solids in two places to allow for an addition of water. •

Reduce the number of rod mills from three to one. Add the finer feed cyclone parameters and scale the new feed rate, ball mill size and cyclones to suit one rod mill.

Single Rod Mill Exercise

Change Number of Rod Mills

Set Rod Mill Feed Density

Set Cyclone Feed Density

Page 3-58

Step 1

Make the Rod Mill equipment data window the active window.

Step 2

Change the number of rod mills to 1 and press Enter to register your change

Step 3

Position the cursor over the Water Feeder icon which is connected to the rod mill feed port and right-click to activate the drop-down menu.

Step 4

Move the cursor to select the Equipment option to bring the Water Feeder unit data window into view.

Step 5

Left-click on the Model drop-down list and move the cursor to select the Water Feeder – Required % Solids option

Step 6

In the Operating Conditions area of the data window overtype the 'Required % solids' field with the new value of 75.

Step 7

Press Enter to register your changes.

Step 8

Left-click on the flowsheet window to make it the active window.

Step 9

Position the cursor over the Water Feeder icon which is connected to the cyclone feed port and right-click to activate the drop-down menu.

Step 10

Repeat Steps 4 to 7 for the cyclone feed water addition, setting the required % solids to a new value (try 60).

Step 11

Simulate and examine the results.

Section 3.7


Learning JKSimMet


Note that the cyclone feed and product are now MUCH finer than before. This causes a problem with the simulation of the existing circuit because the cyclone model is NOT valid for large variations in feed size. A second set of cyclone model parameters is given below for you to try out. As an exercise, enter the data into the correct windows and run the simulation again. Examine the circuit data to see how the different cyclone parameters affect the circuit performance.

Cyclone Feed Size Exercise

CYCLONE DATA FOR FLOWSHEET My RM-BM CYC

Data which can be entered

HYDROCYCLONE Model Operating Variables Number of Cyclones Cyclone Diameter Inlet Diameter Vortex Finder Diameter Spigot (Apex) Diameter Cylinder Length Cone Angle

Nageswararao (m) (m) (m) (m) (m) (degrees)

3 .660 .280 .300 .175 .487 15.0

Model Constants KD0 (D50) KQ0 (Capacity) KV1 (Volume Split) (m) KW1 (Water Split) alpha (Efficiency Curve) beta (Efficiency Curve)

.000104 595.5 7.25 9.57 2.01 0.00

Calculated During Simulation

Calculated Data Water split to O/F Corrected D50 Operating Press.

80.93 .2019 161.4

Additional Exercises

Follow the same general sequence to:

(%) (mm) (kPa)

scale the new feed rate to produce the same product size, • adjust the size of the ball mill instead, • check the effects of a new set of cyclone parameters, • add a sump to the flowsheet, •

and anything else that may be of interest to you. For a quick summary of each, copy the Simulate tab to the clipboard and paste each result summary in sequence into a suitable spreadsheet for comparison of results. Version 5.1 November 2001

Section 3.7

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Learning Simulation 3.8

Learning JKSimMet Learning Simulation

Simulation within JKSimMet V5.0 is controlled via its own window (or tabbed dialogue). Which is accessed by clicking on the Simulate icon on the JKSimMet tools toolbar The Simulate window has three selectable tabs which provide access to the three data areas in the window. These are: Control • Select, and • Run Simulation •

The Control tab in the Simulate window

Control tab

The Control tab allows the user to set the parameters for the simulation. For the most part, the default values for the parameters should be appropriate. However, for flowsheets with very large flows, the convergence limit can be reduced to increase the “accuracy” of what goes in equalling what comes out. A choice of spline or linear size interpolation is available. The spline interpolation is well suited to grinding data while for sharply classified size distributions (which sometimes occur in crushing circuits), linear interpolation may be useful.

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Learning Simulation

This tool is a more general version of the select list used in the Mbal module of Version 4. The standard operating condition will be to select all equipment and streams. However, it is often useful to work with a subset of the flowsheet. To do this, the user defines a new select list as follows:

Select tab

Step 1

Step 2

Click on the New button to create a new select list. If you wish, you may give the list a name by typing a name into the Name text box. This name helps to differentiate this list from the other lists. Select only the equipment and streams which are part of the circuit of interest by placing a tick in the box next to the name of each in the select list. Ensure that all other select boxes are empty.

The Select tab in the Simulate window

For example, if you are working with a rod mill - ball mill circuit and wish to simulate and fit the rod mill only, do the following: • • •

create a new list by clicking on the New button, select the feed, water addition and rod mill, select the connecting streams.

Now run the simulation or fit as required. Using Subsets of a Flowsheet

When working with a subset of a flowsheet which does not contain a Feed unit, you must select the stream (or streams) which is (or are) are the feed to your chosen sub-circuit.

Renaming Streams in the Select list

In the Select list the stream names appear as Stream 1, Stream 2 etc. rather than the descriptive names which are visible in the port data windows. If you wish to give a stream a more meaningful name in the Select list, right click on its name and select Rename from the pop-up menu which appears. Type the new stream name into the text box and click on OK to confirm the change. Note that these names are only used in the Select list.


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Learning Simulation

Learning JKSimMet

The Select tab in the Simulate window

Run Simulation

This is the working tab which allows the user to start and stop a simulation. It also provides a summary of port data for those equipment ports which have been selected for inclusion in the simulation. The Run Simulation tab also displays the Convergence value and the number of iterations which the simulation algorithm has gone through. These values are updated while the simulation is proceeding.

Configure the Run Simulation data summary

To configure the summary table on the Run Simulation tab, click on each data column header in turn and select the required data from the drop-down list of port data which appears. If you want to change the % Passing Size X or the X% Passing Size values, open the Flowsheet Properties window (using the View option on the JKSimMet main menu) and type in the desired value. You will need to close and then reopen the Simulate tab to apply the new % Passing Size values. If you want to view the updated summary data values after each iteration as the simulation is proceeding, ensure that the Simulation Updates box on the Control tab has a tick in it. This feature allows the user to check the data for unrealistic values (e.g. cyclone underflow percent solids of 90%) and to stop the simulation if necessary. If the Simulation Updates box is not ticked, the summary data are not displayed until the simulation is complete

Exporting the simulation data summary

Page 3-62

The Copy to Clipboard button which is between the Start and Stop buttons, copies the simulation data summary to the clipboard. This feature can be used to easily compare several alternative simulations by copying the data summary and then pasting it into a clipboard compatible spreadsheet such as MS Excel for comparison. Section 3.8


Learning JKSimMet 3.9 About this Section

Learning Graphing Learning Graphing

The JKSimMet graphing module can plot graphs of simulation data or other types of data, including some equipment related data, on the computer screen or on the printer. The data can either be plotted simply using the JKSimMet Quick Graph feature to choose the appearance of the graph as in section 3.6.4 or the full graphing facilities can be used to configure the plot to the user’s requirements. This gives you the ability to prepare sophisticated graphs suitable for publication and presentation. In this section you will follow a prepared example that will guide you through the creation of a graph. The example is set up for simulated sizing curves for all streams in the Example Ball Mill Cyclone flowsheet. The steps you will follow are: • • • • •

Graph Definition

definition of the overall format of the graph including labelling of axes, tick marks and so on, definition of the data sets to be plotted and of the method for drawing curves, assembly of a graph from the definitions of data and format, note that while annotation of the graph is not available, an automated legend facility has been added. production of the final graphs on the screen and printer.

The Graph Definition window allows the user to define the format of the graph and to select which data sets are plotted on the graph, using three selectable tabs to access the data fields. Format tab

Define the overall features of the whole graph, including the titles to be used for the graph and its axes, the ranges of the axes, scaling and modification and the format of the number labels on the graph axes.

Data tabs

Define the sets of data values to be graphed, their range, and the shape and colour of symbols to be drawn at the data points. JKSimMet can plot up to 15 data sets on a single graph.


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Learning Graphing

Learning JKSimMet

It is a time consuming procedure to produce a final graph that looks exactly right. You will discover that you may refine your original definitions several times before you are satisfied. Reproducing original definitions from scratch also takes time. The Format tab of the Graph Definition window allows the user to set up a suite of formats which can then be recalled and applied to any data set.

Types of Data that can be Graphed

Up to fifteen curves can be drawn on a single graph. The types of data that can be used to produce curves are: Graphs of sizings of all raw and calculated data for the streams on a flowsheet. • Efficiency curves for the raw and calculated data for all the classification devices on a flowsheet. • Selected functions used in the mathematical models for all of the equipment units in a project. •

The Port Data and Equipment Data sections of the Graph Definition window both contain fifteen columns, each of which describes one curve. Thus the user can configure a named Graph Data Set which plots up to fifteen items, either all port data, all equipment data or a mixture of the two where this is appropriate.

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Learning JKSimMet 3.9.1 About this Example

Learning Graphing Drawing a Graph

The aim of this tutorial example is to create a single graph of calculated sizing data for the Example Ball Mill - Cyclone flowsheet, and in the process, to learn a stepwise procedure for using JKSimMet's graphing facilities. The example proceeds through the following steps: • • • • •

identifying the data sets to be graphed, and defining the representation of the data on the screen (Port Data tab) defining the appearance of the overall graph (Format tab) viewing the graph and progressively refining the layout display of the final graph. optionally, add a legend to the graph.

Before starting the graphing example, we suggest that you save the Learner project under a new name, for example Graph Demo. This will avoid corrupting the Learner Flowsheets file for future JKSimMet learners.

Step 1

Open the project Learner flowsheets and load Example Ball Mill - Cyclone flowsheet.

Step 2

Save the Learner project under a new name using the Save As option under the File menu.

Step 3

Left-click the Generic Graph Config button on the JKSimMet toolbar to bring into view the Graph Definition window.

3.9.2

Defining the Graph Format

The Format tab on the Graph Definition window provides various options for the user to define the overall appearance of the graph. These include: labels for the graph and for the X and Y axes • ranges, scaling and modification for the axes • format of the numbers at the tick marks along the axes. •

By creating named Format definitions users can save time when creating graphs in the future by re-using these previously defined graph formats.


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Learning Graphing Defining the graph format

Labels

Learning JKSimMet

For the tutorial example you will set up the graph format by following the instructions below: Step 1

Left-click on the New Format button at the top, right corner of the Graph Definition window, type the name of your graph format into the Name box and press enter to place the name into the Graph Format drop-down list. We will use Cum % Passing as the name in our example.

Step 2

In the Labels section of the Format tab enter an appropriate label for the Y-axis and press Enter. Leaving this field blank means that no axis label is required.

Step 3

Double-click on the Font button to set the format for the text of the axis label. Repeat this step for the Font Size. Font and Font Size not available in version 5.1.

Step 4

Repeat Steps 2 and 3 of this section for the X-axis label and for the graph title.

Axes and Data Interpretation

Within the Axes and Data Interpretation area of the Format tab do the following:

Range

Step 5

In the columns marked Min and Max type in the minimum and maximum data values required for the graph axes (i.e. the range) for both the X-axis and Y-axis. The values are .01 and 100 for the X-axis and 0 and 100 for the Y-axis.

Scale Factor

Step 6

Set the scale factor as required; 1 is the usual value and this is used for our example.

Plotting Scale

Step 7

Grid On

Step 8

Double-click in the Plot Style cell to view the dropdown list and select the required axis format from the list. In this case select Logarithmic for the X-axis and Linear for the Y-axis. If gridlines are required for the X-axis or Y-axis place a tick in the appropriate box in the Grid On column.

Number Formats

Step 9

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Section 3.9

Move the highlight to the number format column and double-click to view the available options on the drop-down list. Select the required format from the list. In the tutorial example use Decimal for both the X-axis and Y-axis.


Learning JKSimMet

Learning Graphing

The Format tab should now look like the example below.

Having defined the graph format you are now ready to define which data are plotted on the graph.

3.9.3 About this Section

Definition of the Data to be Graphed

The next step in creating a graph is to identify the data which are to be plotted and to define how the line and points which represent the data are to appear. This is done through the Port Data and Equipment Data tab sections of the Graph Definition window.

This section requires you to specify: the data set to be graphed (this is done by choosing the item type and then selecting one item from a list of those available), • the range of data to be graphed, that is the minimum and maximum values that are to appear, •


Section 3.9

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Learning Graphing •

Learning JKSimMet

the curve characteristics in terms of - interpolation method between points - solid line or no line between points - character used to represent each point.

Each definition of a data set to be plotted on a graph is named by the user and can be recalled and re-used within JKSimMet.

Note that the items which can be plotted on a graph include equipment unit data such as classifier efficiency curves, ball mill appearance functions, as well as the size distribution of the streams. In our tutorial example, we will plot size distribution data for the ports.

Invoking Data Definition

Item Selection

Step 1

Select the Port Data tab at the top of the Graph Definition window.

Step 2

To define a new data set, left-click on the button marked New, then type the name of your data set into the Name box and press Enter.

Step 3

Position the cursor in column 1 of the row labelled Port and double-click (or left-click and then press Enter) to view the drop-down list of port names. Move the highlight to the port data which you want to plot and double-click to select it.

Step 4

Once a port name is selected for plotting JKSimMet will enter a range of default values for the plotting format. The user can edit these as required.

Step 5

Move the highlight to the Format row and double-click. This brings into view the drop-down list of available graph plotting formats. Select the Format option from the drop-down list. For the tutorial example select the Cum % Passing option.

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Learning JKSimMet Data Type

Step 6

Learning Graphing Move the highlight to the Data row and double-click to view the drop-down list of data options.

Select simulated data (Sim) for this plot. Graphical Representation

Note that you can have either a point or a line to represent a data set. It is not necessary to have both. When a single data type has been chosen for plotting (e.g. Exp or Fit) both the line and point marker represent this data. However, when the paired data types have been chosen for plotting (e.g. Exp & Sim, Exp & Fit or Exp & Bal) the point markers represent the experimental data and the line represents the second item of the data pair (Fit, Sim or Bal as appropriate). This feature is useful for comparing the calculated data with the experimental data.

Line Type

Step 7

Position the highlight over the appropriate cell in the Line row, and double-click to view the list of available line types.

Select the required option from the Line drop-down list displayed, and press ENTER. Symbol at Points

Step 8


Move to the Point row and double click to view the list of symbols which can be used to represent the data points. This defines the symbol that is displayed to mark the coordinate points on each curve within the graph.

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Learning Graphing

Learning JKSimMet Select the required symbol from the list. Move to the Colour row and double click to view the list of colours which can be used to represent the data points and lines. Select the required colour from the list.

Colour

Step 9

Spline Interpolation

Step 10

The user can choose to use spline interpolation for the curve which is drawn for each data set. To use spline interpolation left click on the spline box to place a tick in it.

Graph Over Range

Step 11

Move the highlight to Min and Max rows and set the minimum and maximum plotting range values (on the x-axis) for each curve as required.

Steps 3 to 11 can be repeated to select up to 14 additional data sets to be drawn on the same graph.

3.9.4

Easy Manipulation of the Graphing Features

Now that you have a general understanding of the function and operation of the data and format definitions, it is easier to understand that the production of a quality graph may require several iterations to refine the appearance of the graph by adjusting settings through the format and data definitions.

The typical procedure for fine-tuning graphs is: • •

• • •

set up a format definition, display the graph defined by the data and format definitions already completed in section 3.8.2 (Defining the Graph Format) and section 3.8.3 (Definition of the Data to be Graphed), change the format definition items which are not to your satisfaction, display the graph again, repeat this define and display sequence until you are satisfied with the appearance of the graph.

Step 1

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Click on the Generic Graph Config icon on the main JKSimMet toolbar to bring the Graph Definition window into view.


Learning JKSimMet

Learning Graphing

Step 2

Click on the View/Refresh Graph button. JKSimMet will display the graph defined by the data and format definitions built earlier. Note that you can change the size of the graph window to make it easier to see the graph. Your graph should look similar to the one shown below.

Step 3

Use the Display X Axis Grid and Display X Axis Grid buttons on the graph window to add or remove gridlines. Similarly the legend can be added or removed by clicking on the Display Legend button on the graph window. Note that the position of the legend cannot be changed.

Step 3

Return to the Graph Definition window by clicking on the Edit Graph Definition button on the graph window. Select the Format tab and change the label settings.

Step 4

Click on the View/Refresh Graph button to view the adjusted graph.

This procedure can be repeated until you are satisfied with the resulting graph.

3.9.5 Saving the data

Saving the Session

It is often a good idea to save the project during graphing, in case something untoward happens to all that information you have just entered.


Section 3.9

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Learning Graphing 3.9.6

Learning JKSimMet Graphing Limitations

One Data Source A graph can contain data from only one flowsheet (the current flowsheet). However, you can set up a dummy circuit on a Limitation flowsheet and import key results (such as a product size distributions) from several other flowsheets. The dummy circuit can just consist of the equipment units to whose ports the required streams are attached. Note also that a single flowsheet may contain many independent simulation circuits.

3.9.7

Graphing Related Problems

If there are any problems an error message will appear on the screen. There are three levels of problems - refer to section 4.18 (Errors) if you are not familiar with them.

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Learning Overview

3.10 Learning Overview About Overview

The JKSimMet overview module provides a flexible and powerful tool for users to summarise, review and report results of mass balancing, model fitting and simulation work. The overview screen is fully configurable by the user, and can detail data attributes (e.g. volumetric flowrate) for any or all of the streams on a flowsheet. There is no limit on the number of overviews which can be created by the user for a particular flowsheet. One useful aspect of the overview facility is the ability to create any number of overview displays and to have more than one overview window open on the JKSimMet desktop at any time. These overviews can be readily printed, and so provide the ideal means to produce results in a format suitable for reports or presentations. In this section, you are guided through the procedure to set up a new overview display. The example is for display of simulation data in the Example Ball Mill-Cyclone simulation. The steps you will follow are: • • • • • •

Create a New Overview

creation of a new overview display selection of streams selection of data to be displayed selection of type of data to be displayed display recovery and stream data values printing the new overview.

Step 1

Left-click on the Overview Config button on the main JKSimMet toolbar to bring an overview window into view. As you can see, the overview window opens with the default setting which displays four columns of data for all of the streams in the current flowsheet. New Overview Select List button


Delete Overview Select List button

Section 3.10

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Learning Overview

Learning JKSimMet

Step 2

Left-click on the New Overview Select List icon at the top of the overview window to create a new overview list.

Step 3

Highlight the default name in the Name text box, type in a new name for your overview (Summary No.2 is used in the example) and press Enter. Your chosen overview name will now appear in the drop-down list at the top, left corner of the overview window. Also note that the name of the current overview selection appears in the title bar of the overview window.

Deleting Streams from the Overview

Step 4

The user can remove streams from the overview list by simply placing the cursor anywhere in the appropriate row and then clicking on the Delete Row icon to delete the row. In this example, remove the last stream from the list (Cyc Feed Water Add).

Change column and window size

Step 5

If a column is too narrow for you to read the text in it, place the cursor over the right border line in the title cell at the top of the column and click and drag the column border to the required width. If the Overview window is too small to view all of the data, click and drag the bottom, right corner of the window to change the window size as required.

Adding Streams to the Overview

Step 6

If you want to add a stream to the list (for example if you delete a stream by mistake) click on the Insert Row icon to add a new row to the bottom of the overview list.

Step 7

In this new row, place the cursor on the cell in the Equipment column and press Enter to view a dropdown list of the equipment units in the flowsheet. Select the equipment unit to which the required stream is connected and press Enter to place your selection in the cell.

Step 8

Move the cursor to the Port column and press Enter to view a list of ports associated with the equipment unit. Select the name of the port by which the required stream enters or leaves the equipment unit.

Selecting Stream Data for Display

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You will now select the stream data to be displayed in the overview.

Section 3.10


Learning JKSimMet

Learning Overview

Step 9

Place the highlight in the title cell at the top of the column whose data you wish to change. Press Enter to view a drop-down list of the types of stream data which are available for display. Select the type of data you want to include in the overview and press Enter to place this choice in the table. In this example, select TPH Solids for the first column.

Note that if you are using Mass Balance and have entered component data you may select Components from the list of data to be displayed in the overview. If you choose Components as the type of data to be displayed, you must then select the component you want displayed from your list of components. This is done by selecting the required component from a drop-down list which becomes available in the cell below the title cell in the Components column. This second row of the data selection cells is blank if any other type of data is selected for display.

Select Data Type

Step 10

To select the data type place the highlight in the title cell in the third cell down from the top of the column whose data you wish to change. Press Enter to view a drop-down list of the types of data which can be displayed, including Experimental data, the various forms of calculated data and data SDs. Select the type of data you want to include in the overview and press Enter to place this choice in the table. In this example, select Sim (simulated data) for the first column.

The other options - Experimental, Standard Deviation, and Error, are very useful for model fitting and mass balancing.


Section 3.10

Page 3-75

Learning Overview

Learning JKSimMet

As an exercise, set up the overview as shown below. Note that this window and some of the columns have been resized (as described previously) to make it easier to see all of the data.

Clearing a Column

To clear display data from a column, place the highlight on the top cell in the column to be cleared, press ENTER to view the dropdown list and select None.

Displaying Recovery Information

A useful feature of the overview facility is the ability to switch between actual data and recovery information. To view the recovery data, place a tick in the box labelled Recovery by left-clicking on the box. The overview window will now display stream data as a percentage of the stream chosen for the recovery basis, in this case, MILL FEED. The stream used for the recovery basis can be selected by placing the cursor over the name of the stream in the overview list and right-clicking. A pop-up window will ask you whether you want to make the selected stream the reference for the recovery

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Section 3.10


Learning JKSimMet

Learning Overview

calculations. Click on Yes to make the stream the basis for the recovery calculations. Note that this stream is now listed in bold text in the overview table to denote that all recoveries are calculated with respect to this stream.

Printing Overview

Exporting overview data

To print the overview display follow these steps: Step 1

With the Overview window as the active window, click on the Print Preview button on the overview window. This brings into view the Print Preview window.

Step 2

If necessary, change the orientation of the page to fit the overview data table by selecting the appropriate choice from the Orientation drop-down list.

Step 3

When the preview is to your satisfaction, click on the Print button at the top, right-hand corner of the Print Preview window to print it.

You may transfer an overview to the clipboard using the Copy to Clipboard and Copy Grid to Clipboard icons on the overview window. The Copy to Clipboard icon copies only the data cells selected by the user to the clipboard while the Copy Grid to Clipboard copies the title cells and all of the data cells to the clipboard. Alternatively, the overview data can be exported to the clipboard in its printed format (as shown in the Print Preview window) via the Copy to Clipboard button in the Print Preview window. Other buttons in the Print Preview window allow the user to save the printed form of the overview table as a tab-delimited, commadelimited or text file.


Section 3.10

Page 3-77

Learning to use Report 3.11 About Report

Learning JKSimMet

Learning to use Report

The JKSimMet Report feature provides a flexible tool for users to print the results of mass-balancing, model fitting and simulation work. The printed report is fully configurable by the user, and can present selected data for any or all of the ports or equipment on a flowsheet. There is no limit on the number of reports which can be created by the user for each flowsheet. One useful aspect of the report tool is the ability to create any number of report configurations which can be used to generate printed outputs as required. Each report can be readily viewed in a print preview window and then printed and thus provides the ideal mechanism for producing results in a format suitable for reports or presentations. The data in the reports can also be exported from JKSimMet in a range of formats (e.g. tab-delimited or comma-delimited text files) using the options available in the report Print Preview window. In this section, you are guided through the procedure to set up a new report configuration. The example is for printing a selection of simulation data in the Example Ball Mill-Cyclone simulation. The steps you will follow are: selection of port and equipment data for the report • selection of data types to be printed • viewing the report via the print preview feature • printing the report. •

Create a New Report

Step 1

Left-click on the Report button on the main JKSimMet toolbar to bring the Report window into view. As you can see there is a default set of selections made for the report.

Name of current report

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Section 3.12

Create New Report button


Learning JKSimMet


Step 2

To create a new report configuration click on the Create New Report button in the Report window. This brings into view a grid which lists all of the ports and equipment items on the current flowsheet. Note that none of the items in the grid are currently selected. Select All Items button

Selecting Data for the Report

Unselect All Items button

Step 3

To name the new report format double-click in the Name box to highlight the default name of the report configuration and then type in a new name for the report (the name Cyclone Data will be used here). Press Enter to confirm the name change.

Step 4

Select whether the report will print port data only or equipment data only or both port and equipment data by selecting the appropriate choice on the Print What drop-down list. In this case choose the option Both.

Step 5

Select the equipment and port items whose data you want to be printed in this report by clicking on the box next to the name of each to place a tick in the box. If you place a tick in the wrong box simply click on it again to delete the tick. Note that each equipment item and each port can be selected individually. For our example, select the Cyclone and Cyclone Feed Water Add equipment data and the Primary Mill product and Cyclone combiner, overflow and underflow port data for inclusion in the report. Note that a Select All Items and an Unselect All Items buttons have been provided on the Report window toolbar to help users in selecting data for the report.


Section 3.11

Page 3-79

Learning to use Report Selecting Data Types for the Report

Learning JKSimMet

Step 6

Next select the type of data to be listed in the report by placing a tick in the box next to the name of the required data types in the Data types to print area of the Report window. In this case only tick the simulated data (Sim) box.

Selecting Error Step 7 data for inclusion in a report

When working on fitting or mass-balancing data, the user can choose to include the data error in a report by placing a tick in the Error box in the Error Type area of the Report window. The user can then select from the adjacent drop-down list the particular error that is to be included in the report. In this case the error is not relevant so leave the Error box clear.

Selecting Port data

If you have included port data in your selected items, as is the case here, you can choose to print the Totals data and/or the size distribution data for the ports by placing a tick in the appropriate boxes in the Port data to print area of the Report window. Note that if Component data have been entered, these can also be selected for inclusion in the report here.

Step 8

The Report window should now look like the picture shown below.

Previewing a report printout

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Step 9

Once you have configured the report to your satisfaction, click on the Print Preview button to view the report as it will be printed.

Step 10

The Print Preview window opens at Page 1 of the printout with the Zoom setting at 25% of normal size. Change the Zoom setting to 100% by selecting this value from the Zoom drop-down list and also resize the Print Preview window to view the entire page width.

Section 3.12


Learning JKSimMet

Printing the report


Step 11

Use the Next Page and Previous Page buttons on the Print Preview window toolbar to view all of the pages in the report and check that they show the required data.

Step 12

To print the report simply click on the Print button on the Print Preview window toolbar. Alternatively the report can be printed directly from the Report window by clicking on the Print button on that window’s toolbar.

Preparing a Summary report

The Report window has a box marked Summary. When this box is ticked, the Report feature uses a summary mode to present the port and equipment data in the printed report in a different format. The user can choose to use whichever mode suits their requirements. In the case of the port data, Summary mode prints all of the data of a given type (e.g. Experimental) for all ports in one table. Each data type selected is printed as a separate table, with all ports listed in each table. This compares with the normal report mode which prints the data for each stream on a separate page, with all data types for each stream being listed on this one page for each stream. This difference between the Summary and normal mode is illustrated in the Print Preview windows shown below.


Section 3.11

Page 3-81


Learning JKSimMet

Print Preview Window showing Summary report data format

Print Preview Window showing normal report data format

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Section 3.12


Learning JKSimMet Exporting data using Report


A useful feature of the Report Print Preview window is the ability to export data in report form from the simulator in a variety of formats. Four buttons on the Print Preview window toolbar provide the following data export features: Copy data to Clipboard for pasting into other applications. Save the data as a tab-delimited file (suitable for importing into a spreadsheet such as MS Excel). Saves the data as a comma-delimited file (suitable for importing into a spreadsheet such as MS Excel or a word processing application such as MS Word). Saves the data as a text file. These data export options allow the user to transfer data to other applications for preparation of presentations and reports.


Section 3.11

Page 3-83

Summary


Summary

By working through this section on Learning JKSimMet, you have learned to: • • • • •

run a supplied demonstration simulation display and/or print the results of simulations change some of the simulation data re-simulate build your own flowsheet, import some of its data from a previous circuit and input new data.

You have also learnt how to plot graphs from the simulation results. In this way, you have learnt all the basic techniques necessary to use JKSimMet. Additional advanced techniques for model-fitting and for the maintenance of your system are covered in subsequent sections.

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Section 3.12


JKSimMet Reference

Using JKSimMet

CHAPTER 4

JKSimMet---REFERENCE


Chapter 4

Page 4-1

Using JKSimMet

JKSimMet Reference

4. Contents of this Section

USING JKSimMet

This chapter covers all the basic operational features of JKSimMet. While Chapter 3 is a tutorial, Chapter 4 is structured as a reference section. Section 4.1 (JKSimMet Description) contains an overview of JKSimMet. Section 4.2 contains some important definitions of key terms. Section 4.4 (Menus and Toolbars) describes the operating structure and its conventions while Section 4.5 describes the various types of windows used to display information in JKSimMet. Sections 4.6 to 4.8 contain the information on building and annotating a circuit flowsheet. Sections 4.8 to 4.11 discuss the options available for presenting data by graphing and summary tables.

4.1 About the Package

JKSimMet Description

JKSimMet is a computer software package designed to facilitate the simulation of mineral processing plant operations. Its development follows 30 years experience in the modelling and simulation of minerals processing at the Julius Kruttschnitt Mineral Research Centre. JKSimMet is designed for use by mineral processing engineers who may not be skilled in either computing or modelling. It enhances an engineer's capability to design and simulate all aspects of crushing and grinding circuits, including classification stages. JKSimMet allows engineers to: • • • • •

design a circuit on the computer screen enter model and plant data fit model parameters to that data run a simulation of the circuit present the data and results as flowsheets, text or graphs to print or export to file or to the clipboard..

Version 5 of JKSimMet is a user-friendly system which uses the MS Windows interface, with features such as switching between applications, import and export of data and figures via copy and paste functions and drop-down menus for quick editing and data manipulation now available to the user. In this version there is a common structure for all of the analysis tools (simulate, model fit and mass balance) and the engineer uses the same flowsheet and follows the same data entry procedures for all of the analysis modes. Page 4-2

Section 4.1


JKSimMet Reference 4.1.1 Process Models

JKSimMet Simulation Technique

JKSimMet performs steady state simulation of a range of comminution and classification operations. Units for which process models are available in JKSimMet include: • • • • • • • • • • •

Model Descriptions

Using JKSimMet

Stockpile Bin Pump sump Sump Splitter Gyratory crusher Two rolls crusher Jaw crusher Autogenous mill SAG mill HPGR

• • • • • • • • • • •

Rod mill Ball mill Ball mill (air swept) Screen, one deck DSM screen Hydrocyclone Spiral classifier Rake classifier O-Sepa classifier General air classifier Simple Degradation

These units may be combined in both simple and complex flowsheet circuits to enable the engineer to simulate the operations of plants or subsections of plants. Simulations may be controlled through the specification of model parameters, the selection of necessary process mathematical models, and the specification of operating data such as sizings and equipment sizes. The algorithms for each model are outlined in Appendix A.

4.1.2 Simulation Capabilities

JKSimMet Capabilities

In addition to the simulation capabilities discussed above, JKSimMet encompasses all the functions necessary for the engineer to use and maintain a number of data sets. JKSimMet provides process engineers and metallurgists with a powerful tool for conceptual design, tuning and monitoring process plants and their elemental circuits and units. It enables an almost infinite number and variety of circuit designs to be simulated so that the optimal design for the task and expected range of variation of input and flow conditions may be arrived at, or at least approximated, before expensive experiments with real plant are undertaken. Once operating, a plant can be modelled with JKSimMet to allow monitoring and fine tuning functions to be undertaken on an ongoing basis without interruption of the production. With the model-fitting tool the JKSimMet models can also be tuned to more specific user operating conditions; such that the simulation can more nearly approximate real plant conditions. Having said all this, however, JKSimMet does not and cannot


Section 4.1

Page 4-3

Using JKSimMet

JKSimMet Reference

replace the process engineer. It facilitates the simulation of circuit and plant designs; it does not design. Like any tool, the standard of the work that it does is, in the final analysis, directly related to the skill of the craftsman that uses it.

4.1.3 System Constraints

JKSimMet Constraints

While JKSimMet is a powerful and flexible system there are, necessarily, some constraints. These are: Size distribution

There is a maximum of 30 size fractions in the size distribution for any one stream.

Number of Flowsheets

There is no defined limit to the number of flowsheets which may be included in a project. However, the database will become very large and may cause slower systems to slow down perceptibly.

Model Fitting Constraints

In Version 5 • only one flowsheet can be simulated or fitted at a time. • up to 10 primary parameters (masters) may be selected • a further 10 can be “slaved” to each primary parameter. • up to 10 ports and 10 pieces of equipment can be selected to provide an objective function for model fitting. Note: The database structure introduced in Version 5 will allow for a substantial increase in these capabilities in future releases.

Page 4-4

Number and Type of Models

For a list of the available models refer to section 4.1.1 (JKSimMet Simulation Technique). The user can add new models with the optional software developers kit (see section 4.1.4). However, JKTech welcomes suggested new models which will be considered for subsequent releases of JKSimMet. JKTech can also develop custom models for an individual client.

Mass Balancing

The JKMBal algorithm can process up to 50 ports with data and 30 pieces of equipment.

Section 4.1


JKSimMet Reference 4.1.4 Package Expandability

Using JKSimMet JKSimMet Expandability

JKSimMet is a self-contained package providing within itself all the features required to build, execute and maintain a library of data sets. JKSimMet is supplied with process models for those units listed in section 4.1.1 (JKSimMet Simulation Technique). While these models cover many of the typical processes encountered in comminution processing, JKSimMet has been designed to facilitate the incorporation of new models. While the user cannot add new models to the system, recommendations to JKTech will be considered for inclusion in later releases. The user can, however, through the use of model-fitting, modify the models currently in the system by, for example, setting new regression equation constants. For sophisticated users a software developers kit (SDK) is available as an option. Use of the SDK requires knowledge of a suitable computer language such as MS C, or PowerStation FORTRAN. The SDK includes an editor which allows user-designed model tabbed dialogs to be added to JKSimMet. Additional multi-component modules are planned. These will be add ons at additional cost.


Section 4.1

Page 4-5

Definition of Terms 4.2 JKSimMet Components

JKSimMet Reference Definition of Terms used in JKSimMet

A number of the terms and names used within the JKSimMet system have a specific meaning which it is important to understand. These terms are defined here to avoid ambiguity. Project

JKSimMet is organised and based upon the concept of a project. A project can be considered as a portfolio in which the user stores one or more flowsheets and their related data.

Flowsheet

A flowsheet consists of one or many process circuit diagrams and related data. The flowsheet may contain one item of process equipment or many. Complex multi-stage circuits or many circuits in parallel are acceptable. The generalised select tool allows these to be considered one at a time or together.

Equipment

The process equipment is a component of the circuit. Each equipment item consists of: • an icon on the flowsheet diagram • a data window which details the process model and its model parameters.

Ports

A port is a model of a flow of solids and/or water into or out of an item of equipment. Each equipment unit has one input port to which up to three input connectors can be attached and one, two or three output ports, depending on the particular type of equipment. Only one connector can be attached to each output port. For the models in JKSimMet, the stream characteristics of interest are density, size distribution and solids and water flow rates. A port consists of: an input or output port attached to an equipment unit on the flowsheet • a data window which contains the port data (solids and water flows, size distribution and assays (as appropriate).

•

Page 4-6

Section 4.2


JKSimMet Reference 4.3

JKSimMet Cursor The JKSimMet Cursor

The cursor which indicates your position on the screen takes several forms in JKSimMet, depending on what operation the user is performing. The arrowhead cursor

This shape is the usual form of the cursor for pointing in all JKSimMet data windows, graph windows etc.

The Arrowhead with crosshair cursor

The arrowhead cursor with crosshairs appears when the cursor is positioned over an equipment unit on the flowsheet. The change in shape of the cursor indicates that the user can either move the equipment unit by left-clicking and dragging it on the flowsheet or can access the drop-down menu for that unit by clicking the righthand mouse button. Note that equipment cannot be moved if the flowsheet is locked (see 4.4)

The spanner cursor

The arrowhead cursor changes to the spanner in hand cursor when it is positioned over a feed or product port to which a stream can be connected. The orientation of the spanner and the word next to it changes to guide the user during the stream connection process. Note that if a port already has its maximum number of streams connected, the cursor will not change to the spanner when it is positioned over the port connection point. If you decide not to continue with a stream connection, press escape to return to the arrow cursor.


Section 4.3

Page 4-7

The JKSimMet Interface 4.4

JKSimMet Reference

The JKSimMet Menus and Toolbars

JKSimMet V5 has been developed to run under the MS Windows 95/98/ME/NT/2000/XP operating systems and makes use of the windows interface to provide easy and flexible access to the large amount of data stored in the JKSimMet software. A typical JKSimMet screen is shown below with various components of the screen labelled. Balance-ModelFitSimulate toolbar

Main Menu

Status bar

Functions toolbar

Session window

The various components of the JKSimMet menus and toolbars are described in detail in the following section and also in the comprehensive JKSimMet online help system.

Page 4-8

Section 4.4


JKSimMet Reference 4.4.1

The JKSimMet Interface The Main JKSimMet Menu

The Main Menu of the JKSimMet interface follows the standard Windows menu layout, with a selection of drop-down submenus which allow the user to access a range of commands. Each submenu is accessed by clicking on the appropriate word on the Main menu bar. The File submenu New opens the Project View window so that the user can load a new project. Open opens the Project View window so that the user can load a project. Close shuts the current Project. Opening a second (or a new) project also closes the current project after offering an option to Save the current project. Save saves the flowsheet and all the data associated with the units and streams as a data file. These data files are managed automatically by JKSimMet. Save As allow the user to save a copy of the current project under a new name and/or in a new directory. The default file name extension is .jksm5. Print displays a Print Preview window of the active window, allowing the user to print the active window if required. Printer Setup allows the user to select a printer and specify the number of copies printed etc. in the standard way. Print Preview allows the selected window to be displayed on screen as it would appear in the printed version. An option to copy the printed format to the clipboard is also offered by most print preview screens. Print Flowsheet provides options for the user to print the flowsheet to file or the clipboard in colour or monochrome. Exit closes JKSimMet. The user is prompted to save the current project if the project has not been saved recently.

4.4.2

The Functions Toolbar

Many of the functions which are available in the drop-down menus of the main JKSimMet menu can be accessed via the icon buttons on the Functions Toolbar.

Note that, if required, this toolbar can be moved to a more convenient place on the screen by simply clicking and dragging it. Similarly, the shape of the toolbar can be adjusted to your personal preference by dragging its edge. The buttons on the menu perform the following tasks: Version 5.1 February 2003

Section 4.4

Page 4-9

The JKSimMet Interface

JKSimMet Reference

The first five buttons on the Functions toolbar provide shortcuts to the standard New, File Open, Project Open, Save and Print options which also appear in the File menu of the main JKSimMet menu. These buttons open the Project Definition window and Flowsheet Definition window respectively. These windows allow users to enter names and descriptions of the active project and active flowsheet. The Information Block Configuration button brings into view the Configure/Assign Information Blocks and Labels window. This provides several options for displaying data and information on the flowsheet and is discussed in more detail in section 4.8. The Generic Graph Config button is a shortcut to bring the Graph Definition window into view. This window, which allows the user to configure a graph to their own requirements, is discussed in detail in section 4.9. Clicking on the Overview Config button opens a new Overview window which the user can configure to display a range of port data from the current flowsheet. More than one overview window can be open at a time. The configuration procedure is described later. The Report button is a shortcut to bring into view the Report window. This window provides the facility to select any of the port and equipment data for printing (see section 4.12) As its name suggests, the Toggle Tool Bar button toggles the JKSimMet Tool toolbar on and off (i.e. makes it visible or not). The Run button allows the user to run Simulate or Model Fit or Mass Balance – whichever is currently active. If none is active, the button has no effect. The Lock the Flowsheet button does just that, locking the flowsheet and preventing items on the flowsheet from being accidentally moved while trying to access data on the flowsheet. This is particularly useful when large, detailed flowsheets are being used as it minimises the time spent waiting for the screen to be redrawn if the user accidentally moves one item of equipment. Users can still change data while the flowsheet is locked. While the flowsheet is locked, double clicking on a piece of equipment will open its window. The Flowsheet Size drop-down list allows the user to set the size of the flowsheet at 1x1 or 2x2 panels, depending on the users requirements.

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Section 4.4



The JKSimMet Interface The JKSimMet Tools Toolbar

The JKSimMet tools toolbar allows the user to select which of the three available JKSimMet tools is to be used for analysis of the data.

To select mass balance, model fit or simulate mode, simply click on the appropriate button. Note that these buttons toggle from on to off. Pressing another button (or the same one twice) will close the current tool. The Run Mass Balance button brings the Mass Balance window into view. This window allows the user to select equipment and ports to be included in the mass balancing procedure. (Mass balancing is discussed in detail in Chapter 6). The Run Model Fit button brings the Model Fit window into view. This window allows the user to select equipment and ports from the flowsheet to be included in the model fitting procedure. For detailed information about the model fitting tool see Chapter 5. The Run Simulation button brings the Simulate window into view. This window allows the user to select equipment and ports to be included in the simulation procedure. The simulation tool is discussed in more detail in section 3.8.


Section 4.4

Page 4-11

JKSimMet Windows 4.5

JKSimMet Reference JKSimMet Windows

Version 5 of JKSimMet makes full use of the windows interface to allow users to view whichever data they choose on the screen at any one time by simply opening the required windows. This section describes briefly each of the main window types which make up the JKSimMet interface.

4.5.1

The Session Window

The session window is the driving seat of JKSimMet. In this window the user creates the flowsheets for analysis with the mass balance, model fit or simulate tools. After starting the JKSimMet program a blank session window is visible on the JKSimMet desktop, as shown below. The Session Window at JKSimMet Startup

The user has two options at this point – to create a new project or to load an existing (i.e. previously saved) project. To do either, the user must first bring the Project View window into view by clicking on the Open Project icon on the toolbar. To create a new project the user drags the Default Project on the New tab of the Project View window onto the session window. This loads a blank project in which the user can create one or more flowsheets, using the equipment from the Default Equipment file on the New tab of the Project View window or existing equipment from project listed on the Saved tab. The procedure for creating a flowsheet will be discussed in more detail in the following sections.

Page 4-12

Section 4.5


JKSimMet Reference

JKSimMet Windows

Alternatively, the user can load a previously saved project from the list which is visible on the Saved tab of the Project View window. This will also be covered in more detail in the following sections. Once a blank project or an existing project has been loaded in the session window the JKSimMet Toolbar is available, giving access to the mass balancing, model fit and simulate tools. Note that the toolbars can be moved and resized as required by the user. The Session Window after a Project has been Loaded


Section 4.5

Page 4-13

JKSimMet Windows 4.5.2

JKSimMet Reference The Project View Window

The Project View window gives the user access to previously saved projects, to the Default Project (a blank project) and also to the list of all of the equipment units which are available for use when adding equipment to a flowsheet. The default equipment list is shown in the picture of the Project View window below. Individual equipment units are accessed by double clicking on the Default Equipment book on the New tab and then on the appropriate book which contains the unit you are seeking. Once the required equipment unit icon is visible, the user can drag the icon onto the flowsheet in the session window in order to add it to the circuit. (Note that the Default Equipment is not available until a project has been loaded into the session window.)

Previously saved projects can be accessed by clicking on the Saved tab to view a list of all of these projects. If the required project has been saved in another directory (other than the default directory C:\Program Files\JKSimMet V5.1\User) the Browse Directories button allows the user to make this directory the active one and to view its list of files in the Saved tab. Note that when the Saved tab is selected, the current directory name appears at the bottom of the Project View window. Also, only files whose name includes the .jksm5 extension will appear in lists in the Project View window. To make a saved project the active project, simply drag the required project from the Project View window to the session window. If a project is already loaded in the session window, JKSimMet will warn you that loading this project will overwrite the current project.

Page 4-14

Section 4.5



JKSimMet Windows Equipment Data Windows

The data for each equipment unit can be viewed in the Equipment data window. The equipment data window for each unit is accessed by placing the cursor over the equipment unit on the flowsheet and rightclicking to view the drop-down menu. Selecting the word Equipment on the drop-down menu brings the equipment data window into view. User-defined name for unit (also used in window title bar)

Names of ports attached to this equipment unit

Number of parallel units

Buttons to print data Model type selected from drop-down list Buttons to copy and paste data

Selectable tabs give access to the various data types for the unit

Data area of the window (the actual contents and format varies according to equipment type and model selected).

Alternatively, when the flowsheet is locked, double-clicking on the equipment icon brings the equipment data window into view. Once the window is open the user can view or edit the equipment data as required. Note that while the contents and format of the data area of the window varies between equipment types and also the model chosen, the general layout of the window (Name text box, Model list etc.) is common to all equipment units. The data layouts for all of the equipment and model types are detailed in Appendix A. Click on a port name to open its data window. Hint: If you wish to see the information on all tabs in the data window at once, click on the printer icon on the tool bar to activate Print Preview.


Section 4.5

Page 4-15

JKSimMet Windows

4.5.4

JKSimMet Reference

Port Data Windows

The data for each port can be accessed in the port data window. The port data windows can be opened by two methods; the first option, if the relevant equipment data window is open, is to click on the port name at the top, right-hand corner of this window. The second route is to select the port name from the drop-down menu which appears when the user right-clicks on the flowsheet icon of the unit to which the port is attached. Drop-down list for selecting size distribution data format.

Drop-down list to select type of data to be displayed.

Drop-down list to select type of error to be displayed.

Button to open Set SDs pop-up window for defining data standard deviations.

Selectable tabs to access the mass flow, sizing and assay data associated with the port.

Buttons to copy and paste data.

The layout of the port data window is the same for all ports. Note that the name of the port shown in the window title bar is defined by JKSimMet, based on the name of the unit to which the port is attached and the appropriate name for the port according to its location on the equipment unit (eg. feed, underflow or overflow for cyclones or feed and product for ball mills). In the example above, the data window belongs to the Underflow port of the Primary Cyclones, so its name is Primary Cyclones Underflow. The data contained in the port data window are discussed in detail in Section 4.7.4 on entering data.

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Section 4.5


JKSimMet Reference

4.6

Building and Manipulating a Flowsheet


In JKSimMet V5 each flowsheet is stored as a sub-unit of a project. Therefore, to work with an existing flowsheet the user must first load the appropriate project into the session window or alternatively, to set up a new flowsheet the user must first load the blank Default Project into the session window.

4.6.1

Loading a Project

The first step in working with a flowsheet is to load the project in which the flowsheet is stored. This is done by opening the Project View window and dragging the project onto the session window, as described in section 4.5.1. In the example used here, the Default Project is being loaded so that the user can create a new project and set up a new flowsheet. If a project is dragged from the Project View window on to a session window where a project is already open, the user will be reminded that the project being loaded will overwrite the current project (in RAM-not the copy on disk) and be given the opportunity to save the open project before continuing. An alternative method is to select File Open from the menu bar.


Section 4.6

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Building and Manipulating a Flowsheet 4.6.2

JKSimMet Reference

Defining the Project Name

Whenever a file is saved, the file name is also the Project Name which is used to distinguish it from all the other projects in the Saved tab list of the Project View window. If you wish to save a copy of the project under a different name, use the Save As option on the File menu of the main JKSimMet menu. Selecting Save As opens the Save As window which allows the user to type in the chosen name for the file and to save it in any chosen directory. The filename will be given the extension .jksm5 which identifies it as a JKSimMet V5 file. You may also rename these files from Windows but it is a good idea to keep the .jksm5 file extension.

The user can also enter more detailed information about the project in the Project Definition window which is accessed by clicking on the Project Properties button. The default port selection may also be set from this window.

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Section 4.6


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The Project Definition window lists the name of the project and has text boxes for details such as the who set up the project, when the project was last saved and the number of flowsheets in the project. The user can edit the Done By, Done For and Comments text for the project. The text entered in the comments box appears in the Object Description section of the Project View window and can be useful in identifying a project in the list. Once all the required changes have been made in the Project Definition window, it is closed by clicking on the close button in its title bar. Note that it is not possible to edit the title of the project in the Project Definition window. The Project Name or Title is locked to the File Name. There are two other methods to bring the Project Definition window into view. One is to select the Properties option in the View menu on the main JKSimMet menu. The final method is to right-click on a blank area of the flowsheet and to select Project and then Properties from the pop-up menus which appear.

4.6.3

Defining the Flowsheet Name

Since a project can contain more than one flowsheet it is useful to give each flowsheet a name to make finding it easier. Once a flowsheet has been named, its name appears in the drop-down list at the bottom, right-hand side of the session window. To define the flowsheet name, click on the Flowsheet Properties button on the toolbar to open the Flowsheet Definition window. Alternatively, right-click on a blank area of the flowsheet and select Flowsheet then Properties from the pop-up menus which appear.

To change the name of the flowsheet simply highlight the text in the Title box, type in the new name and press Enter to register the name. The flowsheet name will appear in the drop-down list at the bottom, right-hand corner of the session window. The user can also edit the Comments text for the flowsheet. These comments appear in the Object Description section of the Project Version 5.1 February 2003

Section 4.6

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JKSimMet Reference

View window and can be helpful in identifying flowsheets when there is a large number of projects in the Saved file list. The final items which the user can edit in the Flowsheet Definition window are the values for the percentage passing size data for the stream size distributions. Changing the values here changes the values in all port data windows. These values appear in the port Information Blocks when these are used to annotate the flowsheet.

When all the required changes have been made, the Flowsheet Definition window is closed by clicking on the close button in its title bar.

4.6.4

Building the Flowsheet Equipment Units

-

When the Default Project has been loaded, the user is presented with a blank flowsheet. The first step in entering the data for the project is to build the flowsheet. This procedure is the same for all of the analysis modes which JKSimMet provides (mass balance, model fit and simulate). JKSimMet uses an equipment unit to represent each unit process on a flowsheet. For the purposes of flowsheet construction, the equipment unit is made up of: • a name (defined by the user) • an equipment unit type, including an icon • a data window containing equipment dimensions and model parameters. The first step in building the flowsheet is to place the appropriate equipment icons on the flowsheet . The user has two options when adding an equipment unit to a flowsheet. These are to select a new item of equipment from the Default Equipment list in the New tab of the Project View window or to copy an existing equipment unit by selecting it from the list of Saved items in the Project View window. The list of equipment which is available in JKSimMet is shown below in the same form as it appears in the Project View window.

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List of Equipment available in JKSimMet

The default equipment has typical values for the equipment dimensions, model parameters etc. as its default data. Re-using an existing equipment unit can save time entering the data for an item of equipment if a previously saved unit has suitable data associated with it. Adding a piece of equipment to the flowsheet

To add an item of equipment to the flowsheet open the Project View window and select an equipment unit from the list in the New or Saved tab as required. (Equipment in the New tab contains default parameter values and that in the Saved tab contains the values entered by the user for that particular item.) Click on the icon of the equipment unit and drag it onto the flowsheet.


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Adding equipment You may double click on an existing project to reveal its or flowsheets from flowsheets and then double click on each flowsheet to reveal its equipment. The equipment can be dragged and dropped into a new another project flowsheet. You may also drag a complete flowsheet from a saved project into the current project. Once an equipment unit icon has been placed on the flowsheet the Editing an user can edit or manipulate it in several ways. equipment unit on the flowsheet Move

To move a unit to a different position on the flowsheet place the cursor over the unit and hold the left mouse button down while you drag the equipment unit to its new position. When the unit is in the required position release the mouse button to place the unit. Any streams which are attached to the ports on the equipment will remain attached after moving it.

Lock

To lock a unit in place on the flowsheet click on the Lock button on the main JKSimMet Functions toolbar. This prevents accidental movement of the equipment unit when the user is working on other items on the flowsheet. Locking the flowsheet is particularly useful when working with large, complex flowsheets since accidentally moving a unit requires the flowsheet to be redrawn, a process which can take several seconds.

Equipment Properties

Most of the options for editing an equipment unit which are available to the user are presented in a pop-up menu which appears when the cursor is placed over the equipment unit and the right mouse button is clicked. Note that the options listed in the menu act on the equipment unit to which the pop-up menu is attached (and on its associated ports). The format of the pop-up menu is the same for all equipment units, except that the names of the ports change according to the type of unit (e.g. a ball mill would have only Combiner and Product ports listed, while the cyclone in the example below has Combiner, Underflow and Overflow).

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Building and Manipulating a Flowsheet The pop-up menu gives the user access to the following actions:

Add

Opens the Project View window to allow the user to add another equipment unit to the flowsheet.

Delete

Select the Delete option from the pop-up menu. This will open up a pop up sub-menu which offers a choice of deleting the equipment or its ports. Deleting the equipment also deletes its connected streams.

Equipment Opens the equipment unit data window. The user can examine and edit the equipment unit data as necessary. Combiner Opens the Combiner port data window. This allows the user to view or edit the stream data for that port. Underflow Opens the Underflow port data window. Overflow Opens the Overflow port data window. Graph

Opens the Quick Graph window which allows the user to view a standard suite of size distribution data plots for the ports which are associated with the equipment unit.

Flip

Changes the orientation of the equipment unit. This option flips the equipment unit so that the feed end of the unit changes from right to left or vice-versa.

Help

Opens the JKSimMet Online Help files. The help system is context sensitive and will open at the appropriate section of the help files.

4.6.5

Building the Flowsheet Connecting Ports

-

The flow of material (solids and/or water) between the equipment units on the flowsheet is represented by streams which connect the feed and product ports on the equipment units. Material enters and leaves each equipment unit via these ports. A port is a model of a flow of particles and/or water into or out of an equipment unit. For the purposes of flowsheet construction a port is made up of: • an input or output point on an equipment unit. • a data window with size distribution, solids SG and solids and water flowrates data


Section 4.6

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Building and Manipulating a Flowsheet Feed and Product Ports

JKSimMet Reference

A unit can have only one feed port to which up to three input slurry streams and one water addition can be connected. This feed port is called a combiner to highlight the fact that its data represent the combined streams if two or three streams are connected to this port. The number of product ports on an equipment unit depends on what type of unit it is; for example a ball mill has one product port, a hydrocyclone has two product ports. Each product port represents one stream discharging from the equipment unit and therefore only one stream can connect to a product port. Note that there are some specialised equipment units which do not have a feed port. These are the Feed unit which is a source of new feed (dry solids or solids and water) to a circuit and the Water Feeder which is a source of water additions to a circuit.

One stream attached to the Overflow product port .

Three streams attached to the feed port

One stream attached to the Underflow product port .

The flow of material between the equipment units is created on the flowsheet by connecting the feed and product ports of the appropriate equipment units. Connecting Ports To connect a product port to a feed port the user places the cursor over the product port of the equipment unit first. When the cursor changes to a hand grasping a spanner with the word JOIN next to it, left click to start the connection process. The word next to the cursor will change to FEED (or PRODUCT if you are connecting feed to product) in black text to tell you to what type of port you need to connect. Position the cursor over the port to which you want to connect the stream and when the cursor changes so that the spanner changes orientation and the word FEED (or PRODUCT) is now in white text, left click to make the connection. A connecting stream will be drawn on the flowsheet as soon as both ends are connected to the correct ports. Note that JKSimMet will not allow the user to connect a feed port to another feed port. Similarly, it will not allow a product port to be connected to another product port. Page 4-24

Section 4.6


JKSimMet Reference

4.6.6


Flowsheet Related Problems

As we have already mentioned in passing, JKSimMet detects many of the possible errors during the building of flowsheets and provides an on-screen error message. If you require a fuller explanation of the error the error number provides the key to the error messages section of the documentation. Refer to Appendix B. Having gained an appreciation of what error has been made and how it has occurred it is usually a simple matter to return to the offending stage in the setting up of the circuit or project and redo it. Getting the circuit design right depends on the skill of the design engineer.

Note that the auto stream drawing is computationally intensive. Allowing reasonable space between pieces of equipment will let the streams draw more quickly. Lock Stream Redraw

Due to the large amount of computation required for automatic stream drawing, editing a complex flowsheet can become quite time consuming. To minimuse this problem, the Lock Stream Redraw option available on the View drop down menu should be set. When this option is active, stream redrawing is disabled so that as many equipment item moves as required can be made. When all the equipment items are in place, the Lock Streams Redraw must be switched off to allow the streams to be drawn.


Section 4.6

Page 4-25

Editing the Flowsheet Data

4.7

JKSimMet Reference


Overview

Once the flowsheet has been configured with equipment units and their ports have been connected to form a circuit, the next step is to edit the equipment unit and port data. The data for these items are accessed by opening the equipment unit or port data window as required and typing the data into the appropriate places in the window.

Data Entry Conventions

There is a convention that the fields in the data window which are available for data entry have a white background. This helps the user to see at a glance which fields can be edited. The text fields and those which have a drop-down list for selection of a field entry have black text on a white background. Those fields which require a number to be entered are displayed as blue text on a white background. These conventions apply to both the equipment and port data windows. Note that the exact appearance and colours of each window will also depend on how your MS Windows desktop is set up.

4.7.1

The Equipment Data Window

Each equipment unit on the flowsheet has a data window associated with it. This data window contains all of the information about the equipment which JKSimMet requires to perform model-fitting and simulation tasks. Opening an equipment data window

An equipment unit data window can be opened in two ways. The first method is to place the cursor over the icon of the equipment unit on the flowsheet and right-click to bring the drop-down menu into view. Then move the cursor to select the Equipment option from the menu and left-click. The second method can be used to open an equipment unit data window when the flowsheet is locked. In this case, double-clicking on the icon of the equipment unit opens its data window.

Equipment data window layout

The basic layout of the equipment unit data window is the same for all types of equipment; the common interface features and those which vary between equipment types are discussed below.

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The features which are common to all equipment unit data windows are shown in the picture of a typical data window below.

Title bar

Port buttons

Print buttons

Name box

Copy and paste buttons

Model dropdown list

Number of parallel units

Selectable tabs

Equipment data area

A Typical Equipment Data Window

The common features found in all equipment data windows are as follows: Title bar

The title bar displays the name of the equipment unit.

Name box

The user can enter a name for the equipment unit in this box. Note that this name will be used to identify the equipment in various other tables in JKSimMet and will also be used to create names for the ports which are attached to the unit. For example, if you call your ball mill Bert its ports will be called Bert Combiner and Bert Discharge. It is advisable to use names which you can recognise easily.

Port buttons

The names of the ports which are attached to the equipment unit are listed here. Clicking on the name of a port opens its data window.

Model box

Clicking on the model name in the box brings into view a drop-down list of the JKSimMet models which are available for the equipment type. The user can select the required model by highlighting its name on the drop-down menu and left-clicking. The models listed here vary from one equipment type to another.


Section 4.7

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Parallel Units The number of parallel units represented by the equipment unit icon is entered in this box. Data transfer The four buttons in this area of the equipment unit data window allow the user to transfer data to and from JKSimMet and other programs by copying and pasting data to and from the clipboard. The buttons perform slightly different functions as follows: Copy Selected Cells to Clipboard


Paste Clipboard to Selected Cells

Pastes data from the Clipboard to the currently selected cells



Paste Clipboard to Grid

Pastes data from the Clipboard to the data cells. Data on Clipboard must correspond exactly to the data cells.

Print buttons The Print Preview button displays the print preview window which shows the data as they will appear when printed. This print preview window is often a useful means of viewing the data from several tabs at one time. The print preview window also provides several options to export the data to text file in a range of formats. The Print button immediately prints the equipment data.

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Data area

The lower section of the equipment data window contains the area where data such as equipment dimensions and model parameters are entered. The contents of this section of the data window vary from one equipment unit type to the next. The cyclone data window will be examined to illustrate the features of this data area.

Selectable tabs

These tabs provide access to the groups of data which describe the equipment unit. The number of tabs varies from one to seven, depending on the equipment unit and model type. In the cyclone data window there are three tabs which give access to the Operating Conditions, Model Parameters and Performance Data.

Section 4.7



Editing the Flowsheet Data Editing the Equipment Data

When a piece of equipment has been added to the flowsheet from the Default Equipment list, its data will be set to the JKSimMet default values for that particular type of equipment. The user can edit these values as required, replacing them with values which represent the actual equipment they want to model or simulate. Once they are familiar with JKSimMet each user will develop their own data entry routine. This section describes a step by step procedure for data entry as a guide for users. The equipment window for a cyclone will be used to illustrate the data entry procedures. The cyclone data window shown below is the default equipment hydrocyclone.

Each piece of equipment can be given a name chosen by the user. Changing the Equipment name To rename an equipment unit left-click on the text in the Name box to highlight it. Then type in the required name for the equipment and press Enter to register the change. The equipment name serves several purposes; it appears in the title bar of the equipment data window and is used to identify the equipment in other tables such as the Overview window and the Model Fit and Simulate dialogue windows. The equipment name is also used to create the names of the ports which are associated with the unit. For example, if you name a cyclone Primary Cyclone the ports will be called Primary Cyclone Combiner, Primary Cyclone Overflow and Primary Cyclone Product.

Defining the Number of Parallel Units

The equipment icon on the flowsheet can represent one unit of equipment or several units operating in parallel. The user defines the number of units operating in parallel by left-clicking on the number in the Parallel Units box to highlight it, typing the required number in the box and pressing Enter.


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Each equipment type has one or more process models associated Selecting the Equipment Model with it which JKSimMet uses in the Model Fit and Simulation procedures. The user can select which model is used to represent the equipment in the process by left-clicking on the drop-down list labelled Model and highlighting the required model to select it. Note that the contents of the data area of the equipment data window will change according to which model is selected. Accessing the Equipment data

When a model type has been selected, the contents of the data area of the equipment data window will change to display the appropriate data for that type of model. There is often too much information to be displayed in the available space so JKSimMet uses selectable tabs in the data area to provide access to groups of data. To view each group of data the user clicks on the selectable tab to bring it into view. If you want to view all of the equipment data at the same time a useful technique is to use the Print Preview window to display the entire contents of the equipment unit data window. To view the Print Preview window simply click on the Print Preview button at the top, right corner of the equipment data window. The window can be resized and the Zoom set to 100% to make the text easier to read. When you have finished looking at the data close the Print Preview window.

Editing the Equipment data by typing data

There are two methods to enter numerical data for an equipment unit. One option is to type the data into the appropriate data fields in the data area of the window. To do this, use the cursor to select the cell (denoted by the grey border around the cell), type the new value and press Enter to accept this value. If you make a mistake in data entry you can revert to the previous value by pressing the Esc key but this will only work if the Enter key has not been pressed. Note that if you enter a value which is outside the normal range for any data item a warning message will be displayed to tell you that the value is outside the normal range and asking whether the user wants to use this value or have it clipped to the maximum value of the normal range.

If you want to know what maximum and minimum values define the normal range for a data item double click on the cell for that item and the Parameter Detail information window will be displayed. This details the maximum and minimum acceptable Page 4-30

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values for the item and lists other information about the item which is not relevant here.

A typical Parameter Detail window

Entering Equipment data using copy and paste

The second method available for entering data in an equipment data window is to copy and paste the data. The values can be copied from the data window of another unit of the same type or from an Excel spreadsheet. The data are pasted into the appropriate cells in the data window by selecting those cells and then clicking on the Paste Clipboard to Selected Cells button.

Out of range data Note that, as before, if you paste a value which is outside the normal range for any data item a warning message will be displayed. If in your view, the value is reasonable, answer Yes to the warning message and your value will be used. However, when you use an out of range parameter, you should check your simulation results for reasonableness even more carefully than usual.


Section 4.7

Page 4-31

Editing the Flowsheet Data 4.7.3

JKSimMet Reference

The Port Data Window

Each port on the flowsheet has a data window associated with it. This data window contains all of the information about the material flowing through the port which JKSimMet requires to perform mass balancing, model-fitting and simulation tasks. Opening a port data window

A port data window can be opened in two ways. The first method is to place the cursor over the icon of the equipment unit on the flowsheet and right-click to bring the drop-down menu into view. Then move the cursor to select the name of the port whose data you want to view from the menu and left-click. The second method can be used to open a port data window when the equipment data window is the active window. In this case, clicking on the name of the appropriate port from the list on the equipment data window opens the port data window.

Port data window layout

The layout of the port data window is the same for all ports. The only feature which varies is the number of columns in the data area of the window. Title bar

Format drop-down

Data type dropdown list

Error dropdown list Printing buttons

Set SDs button

Copy and paste buttons

Selectable tabs Port data area

A Typical Port Data Window

The common features found in all port data windows are as follows:

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Title bar

The title bar displays the name of the port. The name is created by JKSimMet using the name of the equipment unit to which the port is attached and a name that identifies which port on that unit is being examined. In the example above the data window is the underflow port of the Primary Cyclones so the name of the port is Primary Cyclones Underflow.

Section 4.7


JKSimMet Reference


Format list

Clicking on the format box brings into view a dropdown list of the sizing data formats which are available. These are % Retained, Cumulative % Retained and Cumulative % Passing. The user can select the required format by highlighting its name on the drop-down menu and left-clicking.

Data list

The Data drop-down list allows the user to select which data types are displayed in the data area of the port data window. The number of columns in the data area varies depending on the data types selected.

Data transfer The four buttons in this area of the equipment unit data window allow the user to transfer data to and from JKSimMet and other programs by copying and pasting data to and from the clipboard. The buttons perform slightly different functions as follows: Copy Selected Cells to Clipboard








Data area

The lower section of the port data window contains the area where data such as mass flows and size distribution data are displayed.

Selectable tabs

These three tabs provide access to the groups of data which describe the flow of material through the port. The tabs are labelled Totals, Size Distribution and Components.


Section 4.7

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Editing the Port Data

When a piece of equipment has been added to the flowsheet from the Default Equipment list, its port data will be set to zero. The user can edit these values, replacing them with values which represent the material flows they want to analyse. Once they are familiar with JKSimMet each user will develop their own data entry routine. This section describes a step by step procedure for data entry as a guide for users. The port data window for a cyclone underflow of a Default Equipment cyclone which has just been added to the flowsheet is shown below. The data cells are blank except for the solids SG value which is set to the default value of 2.70. Note that if a Default Equipment unit is added to an existing flowsheet the solids SG value for the port data is automatically set to the same value as the flowsheet feed.

Default Port Format

You may set the default size format, data format and error format from the Project Properties window.

Selecting the Format for sizing data

If the data which describe the material flowing through the port includes sizing data you can select the format for this data to be displayed on the Size Distribution tab using the Format drop-down list. Click on the Format box to view the list of options, move the cursor to highlight the required format and click on it to select it. The available options are % Retained, Cumulative % Retained and Cumulative % Passing size

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Selecting the Data types for display

The user can select the types of data which are displayed in the data area of the port data window. To do this click on the Data box, move the cursor to highlight the required data group and click on it to select it. The available choices are: GSIM Displays two columns of data – Exp (experimental) and one other which is either Sim (simulated) or Fit (model fitted) or Bal (mass balanced), depending on which JKSimMet analysis mode is currently active. SD’s Displays the two columns as for GSIM, together with a column for experimental data standard deviations (SDs) and another for calculated Error. All Data Displays all of the data types which are available in JKSimMet – Exp, SD, Sim, Fit, Bal, and Error.

Selecting the Error type

The Error column in the data area of the port data window can display the absolute (Abs), percentage (Pct) or weighted (Wtd) error for the simulated (Sim), fitted (Fit) or Balanced (Bal) data as required. The user selects the required error type from the Error drop-down list.

Accessing the Port data

With mass flow, sizing and component data there is too much information to be displayed in the available space in the data area so JKSimMet uses selectable tabs to provide access to groups of data. In the case of port data windows the data is grouped as Totals, Size Distribution and Components. To view each group of data the user clicks on the selectable tab to bring its data into view. If you want to view all of the port data at one time a useful technique is to use the Print Preview window to display the entire contents of the port data window. To view the Print Preview window simply click on the Print Preview at the top, right area of the port data window. The window can be resized and the Zoom set to 100% to make the text easier to read. When you have finished examining the data close the Print Preview window.

Editing the Port data by typing data

There are two methods to enter numerical data for a port. One option is to type the data into the appropriate data fields in the data area of the window. To do this, use the cursor to select the cell (denoted by the grey border around the cell), type the new value and press Enter to accept this value. If you make a mistake in data entry you can revert to the previous value by pressing the Esc key but this will only work if the Enter key has not been pressed.

Entering Port data using copy and paste

The second method available for entering data in a port data window is to copy and paste the data. The values can be copied from the data window of another port or from an Excel spreadsheet. The data are pasted into the appropriate cells in the data window by selecting those cells and then clicking on the Paste Clipboard to Selected Cells button.


Section 4.7

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Editing the Flowsheet Data The Totals data tab

JKSimMet Reference

The Totals tab contains the mass flow data for solids and water through the port. If experimental values are available for these data they are entered in the appropriate data cells. Note that if a solids mass flow and solids SG have been entered, only one of the other data items is required and the remainder will be calculated by JKSimMet. For example if you enter the TPH solids and the % Solids, JKSimMet will calculate the TPH Water, Pulp Density and Vol. Flow. The user must ensure that the Solids SG is correct.

A Port Data Window with the Totals tab displayed

The size for the % Passing x mm and the percentage for the x % passes size data items can be set in one of two ways. If you want the values to be applied only to this port, double-click on the label of the item you want to change. This brings into view an Enter New Value window in which the required value is entered.

If you want to change the size for the % Passing x mm and/or the percentage for the x % passes size data items values for all ports, right click on a blank area of the flowsheet to view the pop-up menu and select Flowsheet and then Properties to bring the Flowsheet Definition window into view. The size for the % Passing x mm and the percentage for the x % passes size data items can be entered in the appropriate boxes in this window. (See section 4.6.3 for more information on the Flowsheet Definition window).

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Section 4.7


JKSimMet Reference The Size Distribution data tab


The Size Distribution tab contains the sizing data for the solids flowing through the port. If experimental data are available for these data they are entered in the appropriate data cells. The first step is to enter the sizes to which the data relate. The size values are in millimetres. Note that if the required size distribution is defined for the first equipment unit placed on a flowsheet, any further unit placed on the flowsheet will automatically use these size data in the port data windows. There are several options for entering the size data. The first option is to use the √2 button on the port data window to place a √2 size series in the Size column. The first step is to zero the size data by typing a zero in the Top Size box and pressing Enter. As the warning message will tell you, doing this will delete all size and sizing data. Then type the new top size in the Top Size box and click on the √2 button. JKSimMet places a √2 size series of 30 values from the user-defined top size down to zero. To truncate the size list simply type a zero where required in the column. The user can also edit individual values in the list as required. Alternatively, any or all of the size values can be entered by typing the values or copying and pasting them from another port data window. A useful shortcut is to store the most commonly used sizing series in an Excel spreadsheet so that these data can be copied and pasted whenever required.

A Port Data Window with the Size Distribution tab displayed

The Top Size must be chosen so that no material is retained at this size. Note that the sizes must be entered in descending order of size. If you try to enter a size which is larger than the size in the data cell above it, JKSimMet will not accept the value. The experimental sizing data should be entered next. Note that the size distribution data are constrained such that their total is 100%. If you try to enter a value which causes the total to be greater than Version 5.0 December 1999

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100% one of two things will happen; either the incorrect value is not accepted and the value in that data cell is unchanged or the value is accepted but the amount of material in the finest size fraction with material in is reduced to maintain the total at 100%. If any problems occur with entering the sizing data check that the data already entered are correct. JKSimMet will calculate the amount of material in the pan or sub-mesh fraction to make the total 100%. If the value calculated by JKSimMet is not the same as the value in your data, check the data which has been entered for keying errors. The Components If the user has defined a list of components to be used in mass balancing in the Mass Balance window then the Components tab in tab each port data window will be configured to accept data. In this case the user can enter component data such as assay data for solids flowing through the port. If experimental values are available for these data they are entered in the appropriate data cells. Note that the component data are only used in mass balancing in JKSimMet.

A Port Data Window with the Components tab displayed

If no component list has been defined by the user the Components tab will not contain any data cells.

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Section 4.7


JKSimMet Reference The Set SD’s button


Estimates of the accuracy of the experimental data can be provided by entering data standard deviations (SDs) for the data. To do this, make the appropriate selectable tab active and selects SD’s in the Data drop-down list so that the SD values can be seen in the data area. . There are two methods for the user to enter SD values for the data. The first method is simply to type in the required SD values in each data cell in turn. The second method uses the Set SD’s button to apply a selected SD model to all of the data on that tab. In most cases users will use the two methods to enter SDs by applying an SD model to all of the data and then fine tuning some SDs by typing new values in. To apply an SD model click on the Set SD’s button to bring the Select SD Values window into view.

The Select SD Values window lists a wide range of options for setting SD models. Select an option by clicking on it and then click on OK to close this window and return to the port data window. The Whiten error model is useful for sizings in grinding circuits (other than SAG feed) and acceptable for assays (at percent levels) in mass balancing. The SD model is a generalised two term error model ie it uses a fixed and a proportional term to estimate assay errors. These issues are also discussed in Chapters 5 and 6.


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The Feed Data Window

The Feed unit is a specialised equipment item which is the source of feed additions to a flowsheet. The feed material can be dry solids or solids plus water. As can be seen below, the Feed data window is very similar to the standard port data windows.

Opening the Feeder data window

A Feed data window can be opened in two ways. The first method is to place the cursor over the Feed icon on the flowsheet and rightclick to bring the drop-down menu into view. Then move the cursor to select the word Equipment from the menu and left-click. The second method can be used to open the Feed data window when the flowsheet is locked. In this case, double-clicking on the feeder icon opens its data window. The Feed data window has one feature in common with a standard equipment data window – the Name box where the user can define a name for the feeder. The remaining parts of the Feed data window are the same as a standard port data window with Totals, Size Distribution and Components tabs to access various groups of data. Note that the Feed has only one port, a product port. As it is the source of new material to be added to the circuit it does not have a feed port.

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Section 4.7



Editing the Flowsheet Data Editing the Feeder Data

The data entry procedure for the Feed follows the same pattern as for the port data windows. The user should enter a name for the Feed in the name box and then enter the mass flow and sizing data which describe the feed material on the appropriate tabs. (See sections 4.7.3 and 4.7.4 for more detailed information on entering data in port data windows).

4.7.7

The Water Feeder Data Window

The Water Feeder is a specialised equipment item which is the source of water additions to a flowsheet. Note that the Water Feeder has only one port, a product port. As it is the source of new water to be added to the circuit it does not have a feed port. Water feeders can only be connected to the feed port of an equipment unit.

Opening Water Feeder window

A water feeder data window can be opened in two ways. The first method is to place the cursor over the water feeder icon on the flowsheet and right-click to bring the drop-down menu into view. Then move the cursor to select the word Equipment from the menu and left-click. The second method can be used to open the water feeder data window when the flowsheet is locked. In this case, double-clicking on the water feeder icon opens its data window.

Water Feeder window layout

The layout of the water feeder data window is shown in the picture of the window below. As can be seen, some of the elements found on the equipment unit data windows appear here, such as the Name box and Model drop-down list. However, the layouts of the Operating Conditions tabs are unique to the water feeder data window.

Data tab for Water Addition model


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The features found in the water feeder data window are as follows: Title bar

The title bar displays the name of the water feeder.

Name box

The user can enter a name for the water feeder in this box. Note that this name will be used to identify the equipment in various other tables in JKSimMet so it is advisable to use names which you can recognise easily.

Model box

Clicking on the model name in the box brings into view a drop-down list of the three JKSimMet models which are available for the water additions to a circuit. The user can select the required model by highlighting its name on the drop-down menu and left-clicking.

Parallel Units The number of parallel units represented by the water feeder icon is entered in this box. For most purposes this value can be left as 1. Data transfer The four buttons in this area of the water feeder data window allow the user to transfer data to and from JKSimMet and other programs by copying and pasting data to and from the clipboard. The buttons perform slightly different functions as follows:

Data area

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Section 4.7

Copy Selected Cells to Clipboard








The lower section of the water feeder data window contains the area where data about the water addition are entered. The contents of the section varies between the three water addition models which are available.



Editing the Flowsheet Data Editing the Water Feeder Data

Data entry for the water feeder is a simple procedure. As a first step the water feeder can be named by the user by typing the required name in the Name box and pressing Enter. The chosen name is used to identify the water feeder in various tables in JKSimMet and it makes sense to choose a name which describes the water addition point e.g. Cyclone feed water addition. The next step in the data entry procedure is to select the required water addition model.

Selecting the Water Feeder Model

The water feeder has three water addition models associated with it which JKSimMet uses in the Mass Balance, Model Fit and Simulation procedures. The user can select which model is used to represent the water addition to the circuit by left-clicking on the drop-down list labelled Model and highlighting the required model to select it. Note that the contents of the data area of the equipment data window will change according to which model is selected. The water addition models are described below.

Feed Streams model

When this model is selected the water feeder does not add any water to the equipment unit to which it is attached. The water content of the feed to the equipment to which the water feeder is connected, is controlled by the water contents of its feed streams only. There are no data to be entered by the user on the Operating Conditions tab for this model.

Water Feeder data window with Feed Streams model selected


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Required % Solids When this model is selected JKSimMet adjusts the water addition to obtain the required percent solids in the equipment feed. The model user must enter the value of the required percent solids on the Operating Conditions tab. This model is useful in simulations, where the user can select the required percent solids for a feed port, e.g. a cyclone feed, and JKSimMet adjusts the cyclone feed water to cope with any changes in cyclone feed mass flows which are caused by other changes to the flowsheet.

Water feeder data window with Required % solids model selected

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Water Addition model


In this model the water addition is fixed at the value set by the user. The user must enter the value of the required water addition in the New Water Addition box on the Operating Conditions tab. This model is useful in mass balancing and model fitting where the user often has measured water addition data to be incorporated in the flowsheet. If the flowsheet data are being mass balanced the user can also enter standard deviation (SD) values for the water addition. After a mass balance, the “calc” result needs to be copied manually to “Exp” for use in simulation and model fitting.


Section 4.7

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Annotating the Flowsheet

4.8 Overview

JKSimMet Reference


JKSimMet allows you to annotate the flowsheet with three types of information – equipment unit data or port data in Information Blocks and user-defined text in Labels. These features are illustrated in the flowsheet shown below.

Label with text entered by user

Port data information block

Equipment data information block

Access

All of the annotation features are accessed through the Configure/Assign Information Blocks and Labels window. This window is brought into view by clicking on the Configure/Assign Information Blocks and Labels button on the JKSimMet toolbar.

The Ports tab of the Configure/Assign Information Blocks and Labels window

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4.8.1


Adding Port Information Blocks

Each feed and product port can be annotated with its own information block. This block shows the name of the port to which the data apply and displays up to four items of data for that port. The user can select from a standard list the data items which appear in the information block. Note that the four items selected appear in all of the port information blocks on the flowsheet. In other words, the user cannot vary the types of port data displayed from one port information block to the next. A Typical Port Information Block

Access the Ports Left click on the Configure/Assign Information Blocks and Labels Information Block button on the JKSimMet toolbar to bring the Configure/Assign Configuration tab Information Blocks and Labels window into view. Click on the tab labelled Port to make this the active tab. List of ports for which information blocks can be displayed

List of port data items, up to four of which can be selected for display in the information blocks.

Drop-down list of data types to be displayed.

Selecting the port The first step in adding a port information block is to decide whether to display one type of data (e.g. Experimental data only or data for display Simulated data only) or to view two data types (e.g. Experimental and Simulated) together. Note that ore feeder and water feed data can be accessed via the equipment table – (Section 4.8.2)


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Annotating the Flowsheet One data type

JKSimMet Reference

The default setting is for one type of data to be displayed. This means that the user can view the chosen data (e.g. experimental) for up to four different data items (e.g. TPH solids, % solids, Vol. Flowrate and % Passing size). The user can select the data type to be displayed from the drop-down list that appears in the lower part of the Configuration area. The available choices are Exp, SD, Sim, Fit, Bal, Calc Bal SD and Error.

Select required data type from drop-down list

The next step in the configuration is to select up to four items for display from the list of port data items. To select an item in the list simply click on it. As an item is selected it will be placed in the information block and at the same time it is removed from the configuration list. If you make a mistake when selecting the data items simply click on the Clear button at the bottom right corner of the information block window. This will clear the entire contents of the information block so that you can reconfigure its contents. Add an information block legend

Once you have configured the contents of the information block to your satisfaction, click on the Apply button. This creates an information block legend which shows the data type selected in the information block title bar and lists the names of the data items in the appropriate boxes. A Typical Port Information Block Legend (One data type)

Names of data item to be displayed in each box.

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Name of data type to be displayed.


JKSimMet Reference


To place the information block for a port on the flowsheet select Placing an information block the name of the port from the list at the left side of the window and on the flowsheet then click on the Add New Block button. The information block will appear on the flowsheet behind the legend information block and may be dragged to the required position. Note that the name of the port to which the data apply is displayed in the title bar at the top of the information block. A Typical Port Information Block (One data type) Name of port

Data values (legend information block shows which data items are displayed

Primary BM Combiner information block has just been added to the flowsheet and needs to be dragged to its correct position

Adding Port information blocks to the flowsheet

Deleting an information block

To delete the information block from the flowsheet simply click on the Close button at the top, right corner of the information block. Note that when an information block is deleted it does not reappear immediately in the list in the Configure/Assign Information Block and Labels window. To make the deleted port appear in the list close and then reopen the Configure/Assign Information Block and Labels window.


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The alternative to viewing one data type for four data items in an information block is to view two data types for two data items. In other words the user can choose to display, for example, experimental and fitted data for two items such as TPH solids and % solids. Displaying Dual Data Types in information blocks

To view two data types for two data items in the information block the user must click on the box labelled Allow Dual Data Types to place a tick in the box. The Configuration area of the Configure/Assign Information Block and Labels window will change to display two drop-down lists from which to choose the data type, as shown below. With the Allow Dual Data Types box ticked, two dropdown lists appear for selecting data types

The data type and data item selection procedures are the same as discussed previously but in the dual data type case the user must choose two data types (one from each drop-down list) and can only select two data items to display. When dual data type information blocks are being used, the title bar of the legend information block shows the names of the two data types selected for display as shown below. Typical Port Information Block Legend and Information Block for Dual Data Types

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Section 4.8



Annotating the Flowsheet Adding Equipment Information Blocks

Each equipment unit can be annotated with its own information blocks. Each information block can display one or two items of data for that equipment unit. The user selects the data items which appear in the information block from a standard list. Since the data to be displayed varies from one equipment type to the next, the user must configure the information block for each unit individually. Note that more than one information block can be configured for each equipment unit. Access the Equipment Information Block Configuration tab

Left click on the Configure/Assign Information Blocks and Labels button on the JKSimMet toolbar to bring the Configure/Assign Information Blocks and Labels window into view. Click on the tab labelled Equipment to make this the active tab. Note that the interfaces of the Port and Equipment tabs are similar; both have a list of the things for which an information block can be displayed on the left of the window and an information block configuration area at the right side of the window.

The Equipment tab of the Configure/Assign Information Blocks and Labels window

List of equipment units on flowsheet

Equipment unit information block will display one or two data items

When an equipment unit is selected, the data items available for display are listed here

Selecting the equipment unit for display

The first step in adding an equipment unit information block is to select the required equipment unit from the list at the left of the Configure/Assign Information Blocks and Labels window. Leftclick on the name of the unit to select it.

Selecting the equipment data for display

Once a unit has been selected, a list of the data items for that equipment unit type is displayed in the Configuration area of the window. The user can select one to two items from this list for display in the information block. To select a data item simply click on its name and the data item will appear in the information block above the list. To change the selected data items the user must use the Clear button to remove all selected items from the information block and to select the required ones from the list again.


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Add an equipment Once you have configured the contents of the information block to unit information your satisfaction, click on the Apply button to confirm the selection. Click on the Add New Block button to place the block equipment unit information block on the flowsheet. This creates an information block which shows the names of the data items and their values and also shows the name of the equipment unit in the information block title bar. A Typical Equipment Information Block Name of equipment unit

Data values

Names of equipment data items displayed

The information block can be dragged to the required position on the flowsheet. If you want to display more data for an equipment unit on the flowsheet a second (or third or more) information block can be configured for the unit and added to the flowsheet by repeating the standard procedure described above.

Two information blocks configured for ball mill.

List of cyclone data items displayed, ready to configure a second information block.

Deleting an information block

To delete the information block from the flowsheet simply click on the Close button at the top, right corner of the information block.

Water Feeder equipment unit information blocks

The Water Feeder equipment unit is a specialised form of the equipment unit. The data items which can be displayed in its information block include information about the experimental and calculated water additions and the SD and weighted error of the water addition.

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Section 4.8



Annotating the Flowsheet Adding Labels to the Flowsheet

The flowsheet can be annotated with labels in which the user can type text. The user can add as many labels as required to the flowsheet and the format of each label can be configured from a range of formatting options (e.g. background colour, with/without border). Note that once a label has been placed on the flowsheet it cannot be edited.

Access the Label Left click on the Configure/Assign Information Blocks and Labels Configuration tab button on the JKSimMet toolbar to bring the Configure/Assign Information Blocks and Labels window into view. Click on the Labels tab to make this the active tab. The Labels tab of the Configure/Assign Information Blocks and Labels window

Type label text here

Change the label background colour by double clicking here

Select format from these options

Preview of label is displayed here

Enter the label text

To enter the text which you want to display in the flowsheet label double click the default text in the Label Text box to highlight it and then type in the required text. As you type, the text appears in the Preview area of the window. The position of the text in the box can be adjusted by using the Enter key to add blank lines and the space bar to add extra spaces as required.

Format the label

The user can select the alignment of the text from the choices in the Text Alignment area of the window. The Label Properties area allows the user to wrap text in the label by clicking in the Word Wrap On box to place a tick in the box. Similarly the user can place a border around the label by ticking the Label Border On box. The user can use the Autosize function to set the height and width of the label box automatically. Alternatively, if the Autosize box is not selected the user can type the required dimensions of the text box into the Height and Width boxes which are situated above the Preview area of the tab.


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The user can change the default background colour of the label by Select the label background colour double clicking on the Label Background Colour panel of the window. This brings up the colour palette from which the user can select an existing colour or create a custom colour for the label. Add the label to the flowsheet

Once you have configured the label to your satisfaction, click on the Add Label button to place the label on the flowsheet. The label can be dragged to the required position on the flowsheet. Note that once the label has been placed on the flowsheet its format and contents cannot be edited or changed in any way

The Preview area shows how the label will appear on the flowsheet.

Delete a label from the flowsheet

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Click on this button to add the label to the flowsheet once you have finished formatting it.

A label can be deleted from the flowsheet by double-clicking anywhere on the label.

Section 4.8


JKSimMet Reference 4.9 Overview

Graphing in JKSimMet User-Configured Graphing – the Graph Definition Window

JKSimMet allows you to graph a wide range of data. The user has a choice of graphing tools – the Generic Graph Config tool which allows each user to configure graphs to their requirements and the Quick Graph tool which uses a JKSimMet-defined format to quickly produce a size distribution graph. The features of the user configured graphing are discussed in detail below, while Quick Graph is detailed in section 4.10 The user-configured graphing system is accessed by left-clicking on the Generic Graph Config button on the main JKSimMet toolbar. This opens the Graph Definition window. Note that when the Graph Definition window is opened for the first time in a project, a Graph window displaying the default data is also opened. This default graph window can be closed while the user configures the required format and data definitions.

4.9.1 Creating a Graph Format

Define the Graph Format

By creating named Format definitions users can save time when creating graphs in the future by re-using these previously defined graph formats. To create a new format, left click on the New Format button at the top of the Graph Definition window. The format is then configured in the Labels and Axes and Data Interpretation section of the Format tab. The Graph Definition window with the Format tab selected


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Graphing in JKSimMet

JKSimMet Reference

Labels

Labels for the graph as a whole and for the X and Y axes are specified by typing in the text for the labels and using the Font and Font Size drop-down lists to format them as required. To type text into a label, double-click on the existing text to highlight it and then type the replacement text. The text can then be set to the required typeface and size by selecting the required items from the Font and Font Size drop-down lists.

Axes and Data Interpretation

The axes and data interpretation section of the Format tab defines the ranges and scales of the axes. The components of the data interpretation section are: Min and Max

Defines the value at the origin (Min) and the maximum value (Max) for each axis. To change the value, highlight the existing number and then type the new value in its place. Caution: Watch out for zero points which cannot exist with logarithmic scales.

Scale Factor

Can be used to scale the axes, for example from millimetres to metres or from metric to imperial. The usual value is 1.0. To change the value, highlight the existing number and then type the new value.

Plot Style

Allows the user to choose the axis format as either linear or logarithmic. The plot style is changed by double clicking on the Plot Style box to bring a drop-down list into view.

The required option is selected from the list by highlighting it and then left-clicking.

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Grid On

JKSimMet will add grid lines to the X or Y axes if a tick is placed in the appropriate box by clicking on it. Gridlines can be removed by clicking on the box again to remove the tick.

Number Format

The format of the numbers at the tick marks can be changed by selecting the required format from the drop-down list in this column. The choices are Decimal, Scientific (Nx10n) or Engineering.

Section 4.9


JKSimMet Reference Re-using an existing Graph Format


Re-using previously defined graph formats saves time re-entering labels etc. when configuring graphs. To use an existing format, left click on the Graph Format box at top of the Graph Definition window. This brings into view a dropdown list of all the graph formats which have been defined in the current project. Move the cursor to highlight the required format and left-click to make this the current format. The Graph Definition window with the drop-down list of user-defined Graph Formats visible.

Select other existing userdefined formats from this list.

4.9.2

Defining Data for Graphing

The user must define which data are to be plotted on the graph. This is done by defining named Graph Data Sets using the Port Data and Equipment Data tab sections of the Graph Definition window. A Data Set can contain port data only, equipment data only or a mixture of port and equipment data as appropriate. A maximum of 15 items can be plotted on each graph.


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The default graph data set is displayed here

The Graph Definition window with the Port Data tab selected.

Creating a Graph Data Set

Each definition of a data set to be plotted on a graph is named by the user and can be recalled and re-used within the JKSimMet project. By creating named Graph Data Sets users can save time when creating graphs by re-using these previously defined data sets. To create a new data set, left click on the New Data button at top of the Graph Definition window. The data set is then configured in the Data Selection sections of the Port Data and Equipment Data tabs. Note that the items which can be plotted on a graph include equipment unit data such as classifier efficiency curves, ball mill appearance functions, as well as the size distribution of the streams. For the sake of simplicity, the Port and Equipment Data tabs are discussed separately here.

Port Data The various data cells in the Data Selection area of the Port Data tab are discussed below. Each column in the Data Selection area is used to configure the data presentation for one port. Note that the user can select an individual port more than once in the Data Selection area. For example, if the user wanted to present the experimental data for a port with green dots and the simulated data with a blue line, it would be necessary to configure this format in two separate columns.

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Section 4.9


JKSimMet Reference Port Selection


The first row of the Data Selection area is labelled Port and it is in this row that the user defines the name of the port whose data are to be plotted on the graph. Double click on the Port cell to view a list of the port names on the current flowsheet. Move the highlight to select the required port and press Enter to make the selection. Note that once a port name has been selected, JKSimMet places a standard set of choices in the formatting cells in that column. The user can edit these if required. To remove a port from the selection to be graphed and clear all the other selections in its column, double-click on the Port cell and select None from the drop-down list of port names.

Format

The Format defines which type of plot is presented for the port. Double-clicking on the Format cell brings into view the drop-down list of available graph plotting formats.

Move the highlight to the required format and left-click to select that format. Data

Move the highlight to the Data row and double-click to view the drop-down list of data types which can be selected for graphing.

If the single data type options are selected (Exp, Sim, Fit or Bal), both the line and point markers for these data represent the chosen data type. However, when the paired data types are selected for plotting (e.g. Exp & Sim), the data point markers represent the experimental data and the line represents the second item of the data pair (Fit, Sim or Bal as appropriate). This feature is useful for comparing the calculated data with the experimental data.

Line

The Line option allows the user to choose the style of line which will be used to represent the data. The choices are accessed by double-clicking on the Line row cell and selecting the required line style from the drop-down list. Note that the user can choose to have no line plotted by selecting the option None on the list.


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Point

JKSimMet places a marker at every data point on the graph. The user can select the style of marker to be used for the port from a list of point marker styles. The choices are accessed by double-clicking on the Point row cell and selecting the required marker style from the drop-down list. Note that the user can choose to have no point marker plotted by selecting the option None on the list.

Colour

The user can choose what colour is used to display the line and point markers on the graph. To view the list of available colours, double-click on the Colour cell. Move the highlight the required colour and left-click to select it.

Spline

The user can choose to use spline interpolation for the curve which is drawn between the data markers for each port. To use spline interpolation left-click on the spline box to place a tick in it.

X Min and X Max The user must define the minimum and maximum plotting range values (along the X axis) for the data. These values are typed into the appropriate cells Equipment Data Many of the formatting cells on the Equipment Data tab perform the same function as in the Port Data tab. Only those cells which perform different functions are discussed below.

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Each column in the Data Selection area is used to configure the data presentation for one item of equipment. Note that the user can select an individual item of equipment more than once in the Data Selection area. For example, if the user wanted to present the corrected efficiency of a cyclone with red dots and the reduced efficiency with a blue line, it would be necessary to configure this format in two separate columns. The Graph Definition window with the Equipment Data tab selected.

Equipment

The first row of the Data Selection area on the Equipment Data tab is labelled Equipment and it is in this row that the user selects the item of equipment whose data are to be plotted on the graph. Double click on the Equipment cell to view a list of the equipment names on the current flowsheet. Move the highlight to select the required item and left-click to make the selection. Note that once an item of equipment has been selected, JKSimMet places a standard set of choices for that particular equipment type in the formatting cells in that column. The user can edit these if required. To remove an equipment item from the selection to be graphed and clear all the other selections in its column, double-click on the Equipment cell and select None from the drop-down list of equipment names.

Function

The Function cell defines which type of data function is presented for the equipment. Double-clicking on the Function cell brings into view the drop-down list of available functions. The list of functions will change according to the type of equipment which has been selected. Move the highlight to the required function and left-click to select that function. The remaining formatting cells perform the same function as those on the Port Data tab and have been discussed in the previous pages.


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Graphing in JKSimMet 4.9.3

JKSimMet Reference Viewing the Graph

Once the user has defined a graph format and a data set, the graph can be viewed by clicking on the View/Refresh Graph button at the top, right corner of the Graph Definition window. This opens the Graph window with the selected data plotted.

The name of the data set is shown in the Graph window title bar

The Graph window

The Graph window has several features which allow the user to make changes to the appearance of the graph without returning to the Graph Definition window and to print or copy the graph. These are accessed via the buttons on the Graph window toolbar.

The Display X Axis Grid and the Display Y Axis Grid buttons allow the user to add and remove gridlines from the graph. The Display Legend button adds or removes the legend. Note that if the legend overlaps the plot area of the graph this can be overcome by making the Graph window wider. The Edit button makes the Graph Definition window the active window, allowing the user to edit the format or data definitions. The Refresh button redraws the graph. This allows the user to update the graph after changing data or formats. The Copy to Clipboard button copies the graph to the clipboard from where it can be pasted into word processing documents, presentations etc. The Print Graph button immediately prints the graph to the currently selected printer. The printed graph will have the same appearance (overall size, relative dimensions etc.) as it does in the graph window. The size of the graph can be changed by adjusting the Graph window as required. Note that a message window may appear while JKSimMet spools the graph to the printer.

Page 4-62

Section 4.9



Using Quick Graph Using Quick Graph

JKSimMet allows you to quickly view size distribution data in a standard form via the Quick Graph window. The user can change a limited range of features of the Quick Graph such as adding or removing gridlines, plotting data as percent retained or cumulative percent passing etc. If more choices are required in defining the graph format the Graph Definition window should be used.

4.10.1

Opening the Quick Graph Window

To view a Quick Graph for a stream the user must first place the cursor over the equipment unit to which the stream’s port is attached and right-click to view the drop-down menu. Select the Graph option to view the Quick Graph window

Selecting the Graph option from the menu brings the Quick Graph window into view. The name of the equipment unit to which the data relate is shown in the title bar of the Quick Graph window. Note that, by default, the graph plots the size distribution data for all of the ports connected to the equipment unit as a cumulative weight percent passing size format. These settings can be changed using the buttons on the Quick Graph window toolbar.


Section 4.10

Page 4-63

Using Quick Graph 4.10.2

JKSimMet Reference The Quick Graph Toolbar

The Quick Graph feature is designed as a means for users to quickly view on the screen a standard graph of size distribution data. This helps users to compare size distributions and to check the sizing data for discontinuities. The type of data which are plotted and a limited range of the Quick Graph features can be changed via the buttons on the Quick Graph window toolbar.

The functions of these buttons are described below. The Show Single Port button displays the size distribution data for one port only on the graph. The user can select which port’s size distribution is displayed using the Single Port Selection list which is described below. The Show All Ports button displays on the graph the size distribution data for all of the ports connected to the equipment unit. The Display X Axis Grid and Display Y Axis Grid buttons allow the user to add and remove gridlines on the graph. If the gridlines are switched on, clicking on the button again removes the gridlines from the graph. The Sizing Format drop-down list allows the user to select the format for plotting the size distribution data. The options are % Passing (cumulative weight % passing), % Weight (weight % retained) and % Retained (cumulative weight % retained). The Single Port Selection drop-down list allows the user to select which of the ports attached to the equipment unit has its sizing data displayed on the graph when the Show Single Port button is selected. The list of port names changes to reflect the type of equipment unit selected. Note that this list is only accessible when the Single Port button is selected; when the Show All Ports option is selected this drop-down list is inactive (greyed out). The Data Type drop-down list allows the user to select the type of data to be plotted on the Quick Graph. The choices are Experimental, Calculated, Absolute Error and Exp and Cal (both experimental and calculated data plotted on the graph). Note that the type of data plotted as Calculated (mass balanced, fitted or simulated) depends on which JKSimMet tool is selected at the time.

Page 4-64

Section 4.10


JKSimMet Reference

Using Quick Graph

The Print Graph button immediately prints the graph on the currently selected printer. The graph bitmap image is enlarged to fit the page and as a result the printed graph can appear jagged. If a smoother printed graph is required, copy it to the clipboard and paste it into a suitable file for printing (e.g. a word-processing program). The Copy to Clipboard button places a copy of the graph on the Clipboard. This can then be pasted into other programs such as a word processing document or a presentation file.

4.10.3

Features of Quick Graph

The Quick Graph window has some features which help to user to analyse the data which are presented on the graph. These are described below.

Viewing the port data window

Quick Graph provides a data window for any of Quick Graph. To do this data window he wishes window into view.

Identifying lines on the graph

While Quick Graph does not provide a legend, the user can find out which port a line represents on the Show All Ports graph by pointing at the line with the cursor. When this is done a pop-up label displays the name of the port to which the data relate.

Identifying data points on the graph

On the Show Single Port graph the user can find out what the X and Y values are at any data point by pointing at the data marker with the cursor. When this is done, a pop-up label displays the X and Y values at that data marker.


shortcut for users to quickly access the the ports whose data are plotted on the the user simply clicks on the line whose to examine. This brings that port data

Section 4.10

Page 4-65

Using Overview

JKSimMet Reference

4.11

Using Overview

Overview

JKSimMet allows you to collate a wide range of data using the Overview feature. An Overview table provides a summary of the stream data for any or all of the ports on the flowsheet. Chapter 3 provides a tutorial on the use of Overview.

Access

The Overview feature is accessed by clicking on the Overview Config button on the main JKSimMet toolbar. This brings the Overview window into view. Note that the user can have as many overview windows open as required, with each displaying a different overview configuration. A typical overview window with default settings displayed

When first opened, the overview window displays a default set of data. The user can define one or more overviews to display the required port information.

4.11.1

The Overview Window

The overview window consists of two main areas, the Overview toolbar and the data display area. The overview toolbar contains a number of buttons which perform the functions described below. The Select List is a drop-down list of all of the overview configurations which have been set up for the current flowsheet. The Name box is a text box where the user can type a name for the current overview. The New Overview button adds a new overview to the select list.

Page 4-66

Section 4.11


JKSimMet Reference

Using Overview

The Delete Overview button deletes the currently selected overview. A dialogue window requires the user to confirm that the overview is to be deleted. As the name implies the Insert column and Delete Column buttons add and delete a data column in the overview table. As their names imply, the Insert Row and Delete Row buttons add and delete port data rows in the Overview table. The Recovery box allows the user to set the overview table in Recovery Mode where recovery data are presented in place of the actual mass flow data. The Copy to Clipboard and Copy Grid to Clipboard buttons copy the overview table to the clipboard. This allows the data to be pasted into other software packages. The Print Preview button opens the print preview window, allowing the user to see the overview table as it will be printed. The Print button prints the overview table on the currently selected printer.

4.11.2

Configuring an Overview Table

The first step in configuring an Overview table is to create a new overview and to name it. Create a new Overview

To create a new Overview click on the New Overview button on the overview window. This displays a default data set which shows four data columns for all of the ports on the flowsheet.

Name an Overview

JKSimMet allows the user to create as many overviews as required and therefore it is useful to name each one so that it may be recalled from the Select List for display. To name an overview click on the text in the Name box to highlight it and then type in the new name. Press Enter to register the change. Note that the name now appears in the Select list box and also in the title bar of the overview window.

The next step in configuring the overview is to decide which data are to be displayed in the table and in which order. Before doing this it may be necessary to make the Equipment and Port columns wider in order to read the names of these items. If the window is too small to view all of the data the user can adjust the window to the required size.


Section 4.11

Page 4-67

Using Overview

JKSimMet Reference

The width of each column in the overview table can be adjusted by placing the cursor over the right border of the title cell for the column and clicking and dragging the border until the column is the required width.

Make a data column wider

The Overview window can be resized by clicking and dragging any Resize the Overview window side or corner of the window. The user can arrange the order in which the port names appear in the table by selecting the required port name in each row. Firstly the user must select the equipment unit to which the port is attached and then the name of the port itself. To select an equipment unit for display in the list double click on the appropriate cell in the column labelled Equipment. This brings into view a drop-down list of all the equipment units on the flowsheet. Move the cursor to highlight the required equipment unit name and press Enter to register the change. If a row of blank cells is required to help make the table easier to read the user can select None from the list of equipment names. All other cells in this row will remain blank.

Select an equipment unit for display

Select a port name Once an equipment unit has been selected in the Equipment column the user can select the required port. To do this, doublefor display click on the appropriate cell in the column labelled Port to bring into view the drop-down list of ports associated with the equipment unit. Move the cursor to highlight the required port name and press Enter to register the change. The default overview table may contain more or less data rows than are required. Rows can be deleted or added as required using the Delete Row or Insert Row buttons. Delete a row from To remove a row of port data from the list in the overview simply the overview table click anywhere in the row and click on the Delete Row button. A JKSimMet dialogue window will ask you to confirm that you wish to delete this row. Click on Yes to remove the row from the overview table. More than one row can be deleted by highlighting two or more adjacent rows and using the Delete Row button as described above. Add a row to the overview table

Page 4-68

To add a row to overview table click anywhere in a row in the table and then click on the Insert Row button. Note that the new row is always added immediately above the cursor position and by default this row contains data from the first port of the first unit in the equipment unit list. You can select the information to be displayed in the new row by clicking on the relevant cells and selecting from the drop down lists.

Section 4.11


JKSimMet Reference

Using Overview

Once the list of port names has been defined the next stage in configuring the overview is to define which data are displayed in the data columns. All of the data which appear on the Totals tab of the port data window (e.g. TPH solids, % solids) are available for display in the overview table. If component data have been entered for a port these can also be selected for display. As well as defining what data items are displayed the user must also define what data type (e.g. experimental, fitted etc.) is displayed in each column. The user can configure as many data columns as required to display the port data. Select a data item Each column displays the values of a selected data item. To define the data item place the cursor in the title cell at the top of the data for display column and double click. This brings into view the drop-down list of all available data items.

Move the highlight to select the required item and press Enter to confirm the selection. Note that an item can be selected in more than one column. This allows the overview to display, for example, one column with experimental data, one with data SDs and one with fitted data. Selecting the option None from the drop-down list results in all other cells in the column being blank (a feature which can help to make large tables easier to read). Note that the available size markers are set from the Flowsheet Properties window. If the Component data item has been selected at the head of a Select a component name column the user must select the name of the component in the second row of the title section for the column. To select the for display component name double click on the second row cell in the column to view a list of components available for display. (The list of names will vary according to the component names which the user has defined). Move the highlight to select the required component and press Enter to make the selection. Note that the second row cell remains blank if Component has not been selected as the data item.


Section 4.11

Page 4-69

Using Overview

JKSimMet Reference

Select a data type Each data item has several data types associated with it and the user can choose which of these is displayed in each column. Double for display clicking on the third row cell in the column brings into view the drop-down list of data types.

Move the highlight to select the required component and press Enter to make the selection. Add a data column to the overview

Clicking on the Insert Column button adds a new data column to the overview table. Each new column is added to the left of the cursor position. The newly added column is configured with experimental data for TPH solids and so must be configured to the users requirements.

Remove a data column from the overview

A column can be deleted from the overview table by placing the cursor anywhere in the column and then clicking on the Delete Column button. A JKSimMet dialogue window will you to confirm that you want to delete this column. Click on Yes to delete the column. More than one column can be deleted by selecting two or more adjacent columns and using the Delete Column button as described above.

4.11.3

Recovery Mode

The overview window can also display recovery data for the appropriate data items. Clicking on the Recovery box to place a tick in it changes the overview window to recovery mode, (as denoted by the words Recovery Mode in the title bar). Conversely, removing the tick from the Recovery box returns the overview to its normal display mode. Note that recovery values are only presented for TPH solids, TPH water, volumetric flowrate data and for component data. Any other data columns in the overview table remain blank in recovery mode.

Page 4-70

Section 4.11


JKSimMet Reference

Using Overview A Typical Overview Window in Recovery Mode

The stream port with respect to which all of the recovery values are calculated is indicated by its name being shown in bold text in the table. This port is known as the recovery basis port. The default recovery basis port is the circuit feed.

Change the recovery reference stream

The user can change the recovery basis port by placing the cursor over the name of the new recovery basis port in the overview table and right clicking. A JKSimMet dialogue window will ask you to confirm that the chosen port is to be the basis for the recovery calculations. Click on Yes to confirm the change. The recovery value sin the overview table will change to reflect the change in recovery basis.


Section 4.11

Page 4-71

Printing in JKSimMet 4.12

JKSimMet Reference Printing in JKSimMet

Overview

JKSimMet provides the facility to print data, graphs and the flowsheet. The basic procedure is the same, regardless of which item you want to print.

Printing the Flowsheet

The flowsheet can be printed in colour or black and white to the printer or copied to the clipboard. Select File from the main menu followed by Print Flowsheet and select the desired option.

Printing Equipment and Port Data

To print individual equipment or port data, the window containing the required data must be the active window. Once the required window is active, click on the Print button on the JKSimMet toolbar. This will bring the print preview window into view to allow the user to check that the appearance of the printed document is satisfactory.

Print Preview for Cyclones equipment data window

Page 4-72

Section 4.12


JKSimMet Reference

Printing in JKSimMet

Note that the printed format allows the user to see all of the data that are contained on all selectable tabs in the data window. The data which are displayed on separate tabs in the window are printed in consecutive areas of the printed data. It is worth checking that the columns in the printed tables are wide enough for the data values to fit. If the columns are too narrow, close the print preview window, make the column in the data window wider and then open the print preview window again. Print Preview window

The Print Preview window which opens when the Print button is clicked shows how the printed form of the data will appear. By default, the print preview window shows the printed page at 25% of full size. The user can view the print preview at other magnifications by selecting the required view from the Zoom dropdown list. Similarly, the user can change the orientation of the paper by selecting the required orientation (portrait or landscape) from the Orientation drop-down list. The print preview window can be resized by dragging its lower right corner. The example below shows the Cyclones print preview window from the previous figure which has been zoomed to 100% and resized to show all of the data.

Print Preview window at 100% zoom factor with window resized to view all data

To print the data as shown click on this Print button


Section 4.12

Page 4-73

Printing in JKSimMet

JKSimMet Reference

If the printout comprises more than one page the user can move between pages by clicking on the Next Page or Previous Page buttons. Once the print preview is satisfactory, click on the Print icon in the Print Preview window to print the data. To remove the Print Preview window from the screen close its window.

Printing Overview The user can configure one or more Overview tables to summarise data selected by the user (see section 4.11 for details of the tables Overview features). Printing the overview table follows the standard procedure of making the overview window the active window and then clicking on the Print button on the JKSimMet toolbar. This brings the Print Preview window into view and allows the user to check that the appearance of the printed document is satisfactory. Make any adjustments required and then click on the Print icon on the Print Preview window to print the data. Printing Quick Graphs

The Quick Graph feature allows user to create size distribution graphs for the feed and products of each equipment unit. These graphs are printed by clicking on the print button on the toolbar of the Fast Graph window. Note that the graph prints as a bitmap and therefore text and graphics can appear with jagged edges. A less jagged printout can be obtained by using the Copy to Clipboard button, pasting the graph image into a word processing program (e.g. MS Word) and then printing

To print the graph as shown click on this Print button

Quick Graph window showing Print button

Page 4-74

Section 4.12



Using Report Using Report

JKSimMet provides a Report feature to generate printed reports of the results of mass-balancing, model fitting and simulation work. The Report window is accessed by clicking on the Report button on the main JKSimMet toolbar. Each printed report is fully configurable by the user who must select the data to be printed for any or all of the ports or equipment on a flowsheet. There is no limit on the number of reports which can be created by the user for each flowsheet. A useful aspect of the report tool is the ability to create any number of report configurations which can be used to generate printed outputs as required. Note that unlike the overview tables which present port data only, the Report outputs can include equipment data if required. Each report can be readily viewed in a print preview window and then printed and thus provides the ideal mechanism for producing results in a format suitable for reports or presentations. The data in the reports can also be exported from JKSimMet in a range of formats (e.g. tab-delimited or comma-delimited text files) using the options available in the report Print Preview window.

The first stage in preparing a report configuration is to create a new report.

Create a New Report

To create a new report configuration click on the Create New Report button in the Report window. This brings into view a table which lists all of the ports and equipment items on the current flowsheet. Note that in the default configuration none of the items in the grid are currently selected.


Section 4.13

Page 4-75

Using Report Name a report

JKSimMet Reference To name the new report format double-click in the Name box to highlight the default name of the report configuration and then type in a new name for the report. Press Enter to confirm the name change. The new name will now appear in the Report list and also in the title bar of the report window.

Setting the sizing The user can choose the format which is used to present any size distribution data in the report. To do this click on the Format dropdata format down list and select the required sizing format from the list. Selecting Data for the Report

The user must select the equipment and port items whose data are to be printed in the report. To do this the user can click on the box next to the name of each item to place a tick in the box. Alternatively, if all items listed in the window are to be included in the report, click on the Select All Items button at the top of the report window. To remove an item from the report simply click on the items box again to delete the tick.

Using a Circuit Select list

A shortcut for selecting ports and equipment for inclusion in the report is to use the circuit select list option. If this is ticked the user can choose from the drop-down list one of the Select lists which were defined as part of the simulation, model-fitting or mass balancing procedure. The items from the flowsheet which were included in the select list are automatically ticked for inclusion in the report. This feature is useful when working with large, complex flowsheets.

The Print What list

The report window has a Print What drop-down list which allows users to print port data only, equipment data only or to print both. This list allows users to (temporarily) not print port or equipment data items without having to remove the ticks from all those items in the list.

Selecting Data Types for the Report

To select the type of data to be listed in the report (e.g. Exp, Sim etc.) place a tick in the box next to the name of the required data types in the Data types to print area of the Report window. The user can select as many data types as required for inclusion in the report.

The user can choose to include the data error in a report by placing Selecting Error data for inclusion a tick in the Error box in the Error Type area of the Report window. The user must then select from the adjacent drop-down list the in a report particular error that is to be included in the report. The error data is useful when working on fitting or mass-balancing data.

Page 4-76

Section 4.13


JKSimMet Reference

Using Report

Selecting Port data

If port data have been selected for inclusion in the report the user can choose to print the Totals data and/or the size distribution data for the ports by placing a tick in the appropriate boxes in the Port data to print area of the Report window. Note that if Component data have been entered, these can also be selected for inclusion in the report here. If component data have not been entered, this option is inactive (as shown here).

Previewing a report printout

Once you have configured the report to your satisfaction, click on the Print Preview button to view the report as it will be printed. By default, the Print Preview window opens at Page 1 of the printout with the Zoom setting at 25% of normal size. The user can change the Zoom setting using Zoom drop-down list and if required can resize the Print Preview window by dragging any edge or corner. The Next Page and Previous Page buttons on the Print Preview window toolbar allow the user to view all of the pages in the report.

Printing the report

To print the report simply click on the Print button on the Print Preview window toolbar. Alternatively the report can be printed directly from the Report window by clicking on the Print button on that window’s toolbar.

Preparing a Summary report

The Report window has a box marked Summary. When this box is ticked, the Report feature uses a summary mode to present the port and equipment data in the printed report in a different format to the standard format. The user can choose to use whichever mode suits their requirements. In the case of the port data, the Summary mode prints all of the data of a given type (e.g. Experimental) for all ports in one table. Each data type selected is printed as a separate table, with all ports listed in each table. This compares with the normal report mode which prints the data for each stream on a separate page, with all data types for each stream being listed on this one page for each stream. This difference between the Summary and normal mode is illustrated in the examples of Print Preview windows shown below Equipment summary formats provide a more compact output of key equipment data..


Section 4.13

Page 4-77

Using Report

JKSimMet Reference Print Preview Window showing Summary report data format

Print Preview Window showing normal report data format

Page 4-78

Section 4.13


JKSimMet Reference Exporting data using Report

Using Report

A useful feature of the Report Print Preview window is the ability to export data in report form from the simulator in a variety of formats. Four buttons on the Print Preview window toolbar provide the following data export features: Copy data to Clipboard for pasting into other applications. Save the data as a tab-delimited file* (suitable for importing into a spreadsheet such as MS Excel). Saves the data as a comma-delimited file* (suitable for importing into a spreadsheet such as MS Excel or a word processing application such as MS Word). Saves the data as a text file*. These data export options allow the user to transfer data to other applications for preparation of presentations and reports. Note that once any of these file types has been opened, further saves will append data to it. That is, records of several simulations in sequence can be accumulated for comparison.


Section 4.13

Page 4-79

Using Report

JKSimMet Reference (Blank Page)

Page 4-80

Section 4.13


Model Fitting

Model Fitting

CHAPTER 5

MODEL FITTING


Chapter 5

Page 5-1

Introduction to Model Fitting

Purpose

Model Fitting

5.

MODEL FITTING

5.1

Introduction to Model Fitting

Chapter 5 describes how to use the JKSimMet model-fitting mode. Model fitting allows JKSimMet to be fine-tuned to each specific plant and operating condition, or even to particular ore types. It does so by adjusting selected model parameters on the basis of systematic differences between measured product data and simulation predicted product data. The model fitting procedure can take into account any measured flowrates and estimates of their accuracies.

Overview

For both plant designer and plant operator, model fitting is primarily concerned with the collection of accurate experimental data, at either pilot or full plant scale. The model fitting process provides a powerful means of data examination or assessment as well as the compression of thousands of data points into a few parameters. The parameters characterise how a particular ore behaves in a particular plant. This characterisation can be used to find the optimum plant settings with respect to various criteria, or even to find an optimal plant configuration to achieve stated objectives. As with all data analysis or prediction processes, however, the quality of the output is strongly dependent on the quality of the input. The computer jargon for this phenomenon is GIGO or GARBAGE IN - GARBAGE OUT. A serious difficulty with all realistic simulation systems like JKSimMet is that they will produce very plausible looking nonsense from rubbishy data. Hence, just as the spreadsheet is not a replacement for the accountant, JKSimMet is not a replacement for a metallurgist or process engineer. There is no substitute for professional expertise or experience, especially in the collection and analysis of large quantities of data. JKSimMet provides such a professional with a tool of enormous power. The general procedure is for model fitting is: • • • • •

collect data analyse data optimise plant using models adjust plant collect data to confirm

and start the cycle again.

Page 5-2

Section 5.1


Model Fitting

Data Collection 5.2

Data Collection

This section is not essential for learning how to drive the modelfitting program. However, it is highly relevant to using the model fitting system, and should be studied in detail before gathering data for model fitting. The data entry menus provide a guide to the unit dimensions and operating variables which should be recorded during each test. The stream data or feed stream data menus provide a guide to what should be measured wherever possible.

Flowrates

Flowrate measurements are very useful indeed. Hence, calibration of all flow measurement devices (weightometers, flow meters, etc.) is important. Whenever possible, try for an independent flowrate check. In small or pilot plants, time and weigh a known volume of material.

Sample Analysis

Stream size distributions are crucial characteristics for many of the JKSimMet models. Therefore: • use a set of sieves that you can trust, • use the same set of sieves for sizing all of the samples in each test (sieves can have variations and holes!). • use a 2 sieve series (size fractions can always be combined later for convenience) • sieve to the top of coarse sizes, ie. less than 5% on top screen and as close to the bottom as possible.

Percent Solids

The percent solids of a slurry as measured with a Marcy scale are subject to error, due to solids density variations in the circuit. Such variations are common in cyclone underflow streams. Therefore, percent solids determined from wet and dry sample weights are preferred.

Steady State

JKSimMet is a steady state simulator. Hence, models can most usefully be fitted to data which were taken at steady state. There are two practical approaches to this problem: • Take a series of regular samples (every 15 minutes say) and combine them to make composite samples which cover a period which is long (several hours) compared with circuit fluctuations. • Alternatively, watch the trends and, when you are convinced the circuit is stable, take simultaneous samples of each point. Recheck the trends. If not stable, discard the samples and try again.


Section 5.2

Page 5-3

Data Collection

Model Fitting

If circuit variations are a serious problem, sample and fit one process unit at a time. JKSimMet can be used to combine the units and predict circuit steady state behaviour.

Sampling is a topic in itself. Some useful references are those of Gy (1982) and Lyman (1986).

Sampling

For a detailed ‘How to Do It Guide’ see the Help Files and Chapter 5 of the Monograph Reference. For a simple estimating technique for sampling requirements refer to the paper by Lyman (1986).

Ore Type Characterisation

Ore type characterisation is also a substantial topic. The comminution models in JKSimMet come with a breakage function based on the Rosin-Rammler distribution. This behaviour is typical of a hard, uniform ore. Over the past decade, the JKMRC has researched in some detail how different ores break. The model parameters also list breakage functions for some other ore types. For a really accurate description of breakage behaviour, a breakage test is recommended. JKTech will carry out such tests for a standard feed. The tests require 1000kg of –100 +12mm size ore and can even be carried out on complete (i.e. not split!!) drill core samples. These breakage characteristics can be used to estimate full-scale performance of crushers and mills, and also of SAG or autogenous mills when the JK abrasion test is added. Hence, the results can be very useful either for existing plants or for proposed designs.

Replicate Sampling

Page 5-4

For serious plant testing, where small differences may be worth large sums of money, it is often worth carrying out at least one multiple sample test. That is, instead of taking just one sample set, take 5 to 10 replicate samples. Then process and analyse each replicate separately. These 5 to 10 replicates will provide a mean and standard deviation for every data point. This will provide invaluable information about the accuracy (or lack thereof) of every data point.

Section 5.2


Model Fitting

Data Collection

Concept: Weighted Sum of Squares

If the precision of each data point is measured (or can be estimated from experience), then each difference between experimental data and simulation prediction can be normalized by dividing by its precision. That is, a small difference between an accurate data point and its simulation prediction will make the same contribution to the weighted sum of squares as a large difference from an inaccurate data point.

Concept: Standard Deviation

The usual measure of precision is the standard deviation. If we make repeated measurements of any data point, experimental variations will cause variations in the measured value xi. Then with many repeats, the mean x- of the values will provide an estimate of the true value of x. Subject to a number of assumptions, the expected variations from true x can be characterized by one number - the standard deviation which is defined as: n

∑ (xi

Standard Deviation =

- x-)2

i=1,n (n -1)

If the measurements are normally distributed then, out of 100 measurements, 67 could be expected to lie within plus or minus one standard deviation of the true value (as estimated by the mean), 95 within plus or minus two standard deviations and 97 within plus or minus three standard deviations.

Concept: Estimating Standard Deviation

Experimentally, 5 to 10 complete observations will provide a good estimate of standard deviation. The mean of such a set of measurements should provide a good test of sampling precision - if the test circuit was at steady state.

Concept: Whiten Standard Deviation

For accuracies of size analyses on a weight % retained basis, the Whiten errors often provide a realistic estimate. These are calculated as relative errors: • A standard deviation of 0.1% plus one tenth of the fraction is assumed, up to a maximum weight of 1%. The Select SD Values window lists a wide range of options for setting SD models. Select an option by clicking on it and then click on OK to close this window and return to the port data window.


Section 5.2

Page 5-5

Data Collection

Model Fitting

The Whiten error model is useful for sizings in grinding circuits (other than SAG feed) and acceptable for assays (at percent levels) in mass balancing. The SD model is a generalised two term error model ie it uses a fixed and a proportional term to estimate assay errors. These issues are also discussed in Chapter 6.

Concept: Least Squares Fitting

The simulator takes all of the feed streams as input and uses the models and parameters to predict all of the circuit streams. If some (or all) of these streams are measured (sampled and sized, etc), the experimental measurements can be compared with the simulator predictions. The sum of squares of the differences between measured data and simulated results is taken as a measure of goodness of the model fit. The best estimates of the parameters are expected to be those which MINIMISE the sum of squares. Hence, the model fitting program adjusts user selected model parameters to find a best set of parameter estimates which make the simulator output match the experimental measurements as closely as possible.

Page 5-6

Section 5.2


Model Fitting

Background 5.3

Background

The JKSimMet models are provided with a set of default parameters and, in most cases, a range of parameter values. (See the Supplementary Parameters Manual supplied by JKTech). For any real mineral processing operation, the best-fit parameters will almost certainly be different from the default values provided with the system. There are several classes of parameters used as model inputs: • Machine dependent parameters

Typically dimensions and key operating adjustments.

• Ore dependent parameters

For example, the work index or specific gravity or breakage function for a particular ore at a particular energy.

• Calculated or measured operating parameters

These usually depend on a combination of machine and ore dependent parameters and ore feedrates, etc. Examples are cyclone feed pressure and crusher power draw.

• Circuit flowrates of solids and water

Process instrumentation often provides an estimate of, say, solids mass flowrate to a cyclone classifier. In some cases, such a flow can be treated as data. If it is unmeasured, it may be varied until a best fit to other data is achieved. In this case, the flowrate effectively becomes a parameter.

• Model parameters which can be fitted.

Each model has a list of parameters which can be fitted. Each parameter to be fitted is selected from a menu for that model. These menus are listed with each model description in Appendix A.

.


Section 5.3

Page 5-7

How the Model Fitting Program Works 5.4

Model Fitting

How the Model Fitting Program Works

The model fitting program works by calculating the differences between the predicted and the experimental data, and deriving from these a weighted sum of squares value (WSSQ). On its first iteration (step), the program adjusts each parameter in the parameter list in turn by a small amount, and notes the effect of this adjustment on the weighted sum of squares value after an internally executed simulation. This step is used to estimate the magnitude and direction of the adjustments to the parameters required to minimise the WSSQ. On subsequent iterations, the program varies all the fitted parameters simultaneously, noting the effect of the adjustments. This process is repeated until the program is stopped for one of the following reasons: • a minimum WSSQ has been reached, • the maximum number of steps set by the user has been reached, • the adjustments made to the parameters are having no significant effect on the weighted sum of squares value or • operator intervention. Whereas simulation uses given feed data and given model parameters to predict the product data, the model fitting program uses the sum of the squares of the differences between the predicted and the actual product data to adjust the model parameters.

Page 5-8

Section 5.4


Model Fitting

How the Model Fitting Program Works

Schematically:

SIMULATION Feed Description

MODEL PARAMETERS

Circuit Configuration

Simulator

Predicted Products and Streams

MODEL FITTING

Feed Description

Circuit Simulator

Adjusted Model Parameters

Configuration

Predicted Products and Streams Iterate to Minimum Sum of Squares Measured Products and Stream Data Model Fit MODEL PARAMETER ESTIMATES Sum of Squares


Best Fit Parameters

Section 5.4

Page 5-9

A Simple Example 5.5

Model Fitting A Simple Example

A very simple example has been included in the Learner Flowsheets project of JKSimMet. This example provides a quick guided tour of the fitting menus to get the flavour of the fitting subsystem. You will, however, still need to work through section 5.6 (Learning Fitting) in detail with several real cases in order to become confident with the model-fitting mode. The example is a single Ball Mill in open circuit. There is only one stream predicted – the product. Therefore, there is only one stream that can be fitted. Step 1

Load the Learner Flowsheets project and select the flowsheet called Ball Mill Model Fit.

Step 2

Examine the mill feed and product port data. You will find the raw data in the Ball Mill Feed Feeder equipment unit data and in the Ball Mill Product stream data. Run a simulation by clicking on the Simulate icon and compare the raw and calculated values for the Ball Mill Product. (Use a graph for easier comparison of the size distributions).

Step 3

Now select Model-Fit mode by left-clicking on the Model Fit icon. This will bring up the Model-Fit tabbed dialogue window shown below.

Model Fit Dialogue Window

Step 4

Page 5-10

Section 5.5

Left-click on the Select tab of the Model Fit window to view the list of equipment and streams which the user can select to be used for model fitting. Note that the equipment and streams which have been selected for fitting are highlighted in blue on the flowsheet. This feature is useful for checking that you have selected all of the items on the flowsheet which you want to use in the model-fitting and is particularly useful for complex flowsheets. Version 5.0 December 1999

A Simple Example

Model Fitting

Step 5

Left-click on each item in the list on the Select tab and observe whether or not it has been selected for fitting. If the item is selected for fitting the box labelled Selected will contain a tick. Note also that as you click on each item in the list it is highlighted in red on the flowsheet. This feature is useful for identifying which items you are selecting when the flowsheet is a complex one.

Step 6

Left-click on the Parameters tab to examine the list of unit parameters to be fitted. You will find the list named Ball Mill Parameter List which shows the three spline knots for the ball mill as the parameters to be fitted. The initial values of the knots for the fitting are 1.0, 3.0 and 4.0.

Step 7

Select the tab Data to view a list of the port and equipment data which can be selected for use in the fitting. The list is named Ball Mill Data List. Note that the Data list defines which data (and SDs) the models use in the weighted sum of squares which is minimised in fitting.

Step 8

The final step before running the model fitting is to set the standard deviations (SDs) of the stream data which will be used in the fitting (in this case, the Ball Mill Product). Bring the Ball Mill Product port data window into view and, from the drop-down list under Data Type, select the SDs option. This allows you to view the data SDs and the Error data along with the measured and calculated data values. The SD values are the estimates of the accuracy of the data while Err (Error) data are differences between experimental values and those calculated by the model-fitting. Hint: Experimental, Calculated, SD and Error data can also be examined on the same screen using the overview facility which is available from Overview or on the Data Tab of the Model Fit Window.

Step 9

Make the Model Fit window the active window and click on the Run Fit tab. Click on the Start button to start the model-fitting process. The model fitting program will take these initial estimates provided by the user and search for better ones, given the experimental and calculated streams values. It searches until it finds a minimum residual error (weighted sum of squares of differences). If the program finds what looks like a genuine minimum, it will terminate by providing parameter error estimates (SDs). In this example, the fit is quite good. The Errors SDs value is less than 1. This means


Section 5.5

Page 5-11

A Simple Example

Model Fitting that the data are slightly more accurate than the entered error estimates suggest. Hint: set the scroll bar slider on the Run Fit window to allow you to see the fitted parameters being updated after each iteration.

Step 10

The best fit values for the R/D* knot parameters are listed in the Selected Model Parameters section, along with the SDs of these values. (You may need to scroll across to view these data).

Step 11

Look at the Ball Mill Product port data. Examine the differences between experimental and fitted data by selecting the Abs-Fit option from the Error Type dropdown list and observing these values in the error column. The differences are relatively small.

Step 12

As an exercise, try graphing the experimental and fitted data.

This concludes the short guided tour of the model fitting subsystem. The next step is to work through the tutorial and reference section with a set of real data.

Page 5-12

Section 5.5


A Simple Example 5.6

Model Fitting Learning Fitting

The real power of JKSimMet lies in its ability, through the model fitting sub-system, to tune the JKSimMet simulation models to specific real world operating conditions. To do this, the user collects experimental (stream) data and periodically engages in model fitting to update parameters. Model fitting consists of the adjustment of model parameters on the basis of collected experimental data. The data are collected from the real plant or circuit, and primarily concerns the circuit product. Basically, the situation is as follows. Initially, the one set of data that the engineer has is the plant or circuit feed data. The JKSimMet simulation provides the engineer with a set of predicted or expected product data on the basis of this known feed. The engineer monitors the real circuit or plant product, building up a set of experimental data which can then be compared with the expected or predicted data. The essence of model fitting is to analyse any systematic difference between the predicted and experimental data, and to use it to adjust the selected model parameters.

5.6.1

Preparation for Model Fitting

The subsequent sections of chapter 5 lead the user through the steps necessary in order to execute the model fitting, but there are two essential preliminaries. Simulation

The user must ensure that the circuit or test for which the fitting is to be done has plausible simulation feed and model parameter data. That is to say that it must have run through simulation to convergence. Thus, it is necessary to select an appropriate test and circuit, and to run a simulation before continuing. The simpler the circuit used in model fitting, the better. Indeed, a circuit with a single unit (model) is the ideal for a first fitting with a new ore type. If you enter new data, or in any way alter the flowsheet which you select, you should run a new simulation, even if one has been run before.


Section 5.6

Page 5-13

Learning Fitting 5.6.2

Model Fitting Start Model Fitting

Select the Model-Fit mode by clicking on the Model Fit icon at the top of the screen. This brings the Model Fit window into view.

Model Fit dialogue with Run Fit tab active

The tasks involved in preparation for the execution of model fitting are: • Selection of the appropriate section of the flowsheet ie the select list (which is a feature common to all of the JKSimMet analysis mode dialogues – Model-Fit, Simulate and Mass Balance). • Selection of the model data. This involves both the selection of the data which the models must match, and entering the stream and feed stream data. • Setting up the parameters. This involves both the editing (displaying and recording) of the unit parameters and the selection of the unit parameters to be adjusted.

Page 5-14

Section 5.6


A Simple Example 5.6.3

Model Fitting Selecting Data

Fitting involves the adjustment of parameters and the comparison of data. As has been outlined, there are two data sources for this comparison. They are the data output from the simulation, and the data collected by the plant engineer and entered into the model fitting sub-system. Select items for inclusion in Model-Fitting

Select the Ports for Fitting

In contrast with earlier versions, in JKSimMet V5 the user can choose any items on the flowsheet to be included in the modelfitting process. This is useful if the user wants to model a subsection of a large flowsheet or even one piece of equipment from a flowsheet. So the first task in preparing to model fit data is to select the equipment and ports that will be available for use in the fitting procedure. If an item is selected here, it will be available for selection in the Parameter and Data lists. Step 1

Click on the Select tab in the Model-Fit window.

Step 2

Click on the button marked New to create a new data list. Firstly, you should give a name to the Select list by typing the chosen name into the text box labelled Name and pressing Enter. Any name will do, but we have used Taconite Mill.

Step 3

Click on each of the equipment and port names in the Equipment list in turn and select the items whose data you wish to use in the model fitting. To select an item simply click in the appropriate box to place a tick in it. A glance at the flowsheet shows which parts of the flowsheet have been selected to be included in the model fitting as all selected items are outlined in blue on the flowsheet.

The next task is to define which port data the models must match. This means selecting the ports to be used during the fitting using the Data tab in the Model Fit window. Step 1

Click on the Data tab in the Model-Fit dialogue.

Step 2

Click on the button marked New to create a new data list. Firstly, you should give a name to the port data list by typing the chosen name into the text box labelled Name and pressing Enter. Any name will do, but we have used 'Ball Mill Data Fit List'.

Step 3

Click on each of the port names in the Equipment Port Data list in turn and select the items whose data you wish to use in the model fitting. To select an item simply click in the appropriate box in the column labelled Fit? to place a tick in the box.


Section 5.6

Page 5-15

Learning Fitting

Model Fitting

The maximum number of ports which can be fitted in one fit list is ten . Entering and Editing Port Data

Essentially, this involves entering your data and declaring your confidence about each item in the data set. Step 1

Bring into view the port data window of the stream whose data you wish to edit. Note that you may find it convenient to minimise these windows on screens other than a very large computer display. A minimised window will reopen at the tab and position at which you closed it.

Step 2

Left-click on the Data section and select the SDs option from the drop-down menu. This brings the SD and Error columns into view in the port data window, along with the experimental and calculated data.

STREAM DATA ENTRY (SDs type)

Port Data

The Totals area of the port data window contains data pertaining to the total stream: solids, water and volumetric flowrates, percent solids, pulp SG and solids SG values. Note that numeric characters displayed in blue on a white background can be entered by the user. Numeric fields with a grey background are calculated by JKSimMet and cannot be edited by the user. The Size Distribution tab area contains the list of the sizings from Top Size to Size 30 with the value (%) for each size. Whether the % experimental value refers to % Retained, Cumulative % Retained or Cumulative % Passing depends upon the setting of the stream format field shown at the top left of the screen. This setting can be changed as required by selecting the required sizing format from the drop-down list in the Format box.

Page 5-16

Section 5.6


A Simple Example

Model Fitting

Notice that there are often more size distribution data than will fit in the port data window. If this is the case, scroll bars at the edge of the window will allow you to view all of the data. The Page-Up, Page-Down, Home or End keys or the cursor arrow keys can be used to move around. The user must set the SD values, so we shall deal with these data fields now.

Data Accuracy Entry

The SD (Standard Deviation) column is next to the Experimental data. The SD field must contain a value in each data cell. There are three ways to enter values into these SD fields. • Leave most or all of the entries at the default value of 1.0, simply overtyping the ones you wish to change individually. • Globally change all the SDs to one of the six other available options by: Step 1

Left-click on the button labelled Set SDs which is to be found at the top right-hand corner of the port data window.

Step 2

Select the required option from the Select SD values pop-up window which is displayed.

• The user can change any individual field by overtyping an SD value. The number you enter is an expression of your confidence in the experimental value.

Concept: Ignoring Data

Note that a zero SD means the error, i.e. the difference between this experimental and calculated value, will be ignored in the model fitting process. NB This is different from mass balance where a zero FIXES the result at the measured value!


Section 5.6

Page 5-17

Learning Fitting

Model Fitting

Concept: High Accuracy Data

If you have high confidence in an experimental value, set the SD to a small value.

Error Display

Error values can be expressed in one of several ways: Absolute Error, Percentage Error, or Weighted Error. The user can further choose whether the error displayed is related to the mass-balancing, model-fitting or simulation mode of JKSimMet. The user can determine which of these forms is displayed by the following procedure: Step 3

Position the cursor over the Error cell at the top of the data window and left-click on the black inverted triangle to make the drop-down list appear. Error type drop-down list

Step 4

Select the error type required from the drop-down list which is displayed.

Absolute Error

Tells you the actual difference between the calculated and the experimental values.

Percentage Error

Tells you the percentage difference between the calculated and the experimental values.

Weighted Error

Tells you the number that the parameter-fitting program will use in its weighted error sum of squares. You will probably find this the most useful setting.

Page 5-18

Section 5.6


A Simple Example 5.6.4

Model Fitting Setting Up the Parameters

The second task in preparing for model fitting is to define which equipment parameters are to be fitted Unit Specific Comments

Appendix A contains model descriptions and default parameter values. It also contains a section of specific comments on fitting of each type of model and the parameters which can be selected for fitting for each model.

Equipment Parameter Selection

The Parameter tab data in the Model-Fit window is used to define which equipment parameters are adjusted in the model fitting. Initial estimates of the values of these parameters are entered in the Guessed Value column. These initial estimates of the parameter values are necessary for the first iteration of the model fitting process. In subsequent runs of model fitting for the same model, the user can use the values output from the previous model fitting run. The task is to select the equipment (ie model) parameters you want to adjust in the fitting process.

Parameter Selection

Step 1

With the Model-Fit window as the active window, select the Parameters tab. Firstly you should create a new parameter list by clicking on the New button. Type a name for your list in the Name box and press Enter. Using the same name that you gave the data list is a good option, but anything will do. The example shown here is called Ball Mill Parameter List.

Step 2

Place the cursor in the first data cell of the equipment column and press Enter to bring into view the dropdown list of equipment on the flowsheet


Section 5.6

Page 5-19

Learning Fitting

Model Fitting

Step 3

Select the item of equipment which you want to modelfit and press Enter to make the selection appear in the cell. In this example, Ball Mill is the only item in the list.

Step 4

Left-click on the Parameter cell and select the required parameter from the drop-down list which appears. The list of parameters changes with each equipment type, only showing those parameters which can be fitted for that particular equipment. In this case select parameter LnR/D1.

Step 5

Note that JKSimMet automatically inserts your initial estimate of the parameter value from the equipment data window in the Guessed Value column. The Scale Factor is also automatically set at 10% of the initial estimate. If you wish, these values can be changed by highlighting the existing value and over-typing with a new value.

Step 6

By default, JKSimMet places a tick in the Fit? column for each parameter as it is entered to indicate that the parameter will be adjusted in the fitting procedure. If you do not want a parameter to be fitted, click on the item’s check box to remove the tick. Note that the guessed value will be copied into the model whether it is checked for fit or not.

This entry completes the parameter tab data entry. Cancel Entry

To delete a row of data from the parameter list, select the equipment name in the row you wish to delete and press Enter to bring the drop-down list into view. Select the option None from the list to clear the data from the row. Note: Being able to decide whether a parameter is adjusted in the fitting is useful because it allows you to try a fit without certain of the parameters by not selecting them for fitting and then to fit using those parameters by simply changing the flag selecting them again. This saves deleting and re-typing all the details. Slaved units will use the same scale factors, guessed values and fit modes. (See section 5.6.5 for a description of Master/Slave fitting). Repeat the above steps for each of the parameters you wish to include in the model fitting. The maximum number of parameters is 10. You may, however, define as many parameter lists as you wish.

Page 5-20

Section 5.6


A Simple Example 5.6.5 Master/Slave Fitting

Model Fitting Master/Slave Fitting

Master/slave model fitting allows the same parameters to be fitted to two or more (up to a maximum of ten) units in a single flowsheet. The parameters fitted will have the same values for all the slave units. Master/Slave fitting can be used when fitting survey data collected simultaneously from parallel units with the same operating conditions. Alternatively, it can be used for survey data collected sequentially from a single process unit, where it is expected that model parameters will not be affected by any change in operating conditions. The circumstances that indicate whether master/slave model fitting can be used are therefore dictated by the type of data and the type of model to be fitted. Note that not all models are suitable for Master/Slave Fitting. Slave units are entered on the right-hand side of the Parameters tab. Place the cursor in the slave column, and press ENTER to view the pop-up list of available units. Up to 10 master units are available, with up to 10 slave units per master. If slave fitting is used, ensure that the appropriate slave stream SD's are set. It is necessary to select the streams to be model fitted for the slave units in the Select tab. Note that the fitting statistics displayed (eg. Data SD, Residual Error) will include the slave units.


Section 5.6

Page 5-21

Learning Fitting 5.6.6

Model Fitting Fit the Model Parameters

Before running the model fitting procedure you may wish to change the maximum number of steps to be executed in fitting. To do so: Step 1

Left-click on the Control tab in the Model Fit window and check that the required parameter list is selected in the Parameter Fit List drop-down list. Use the cursor to highlight the number in the Maximum Iterations box. Overtype with the value required, and press Enter to register the change.

The default number of steps is 100. You may well feel that this is too few, particularly if there is more than one item of equipment. A value of 200 to 300 is probably better. Having collected together the circuit simulation data and your experimental data, and nominated which model parameters you wish to fit, you are now ready to execute the model-fitting program. Step 2

Left-click on the Run Fit tab and then click on the button marked Start to begin the model fitting. The model-fitting program updates the unit (model) parameters, effectively running a simulation. During execution, the program fills in the result values, but it will update the SDs if it reaches a satisfactory fit. For interpretation of the model fitting results, refer to section 5.7 (Checking the Fit).

Page 5-22

Section 5.6


Learning Fitting

Model Fitting

Stopping Execution of the Program

The maximum number of steps field can be set to stop the iterations of the fitting program when required. Alternatively, the fitting program can be stopped at any time, simply by clicking on the button marked Stop on the Run Fit tab.

Concept: Data Standard Deviations

At the best-fit point, an estimate of the goodness of fit is calculated by dividing the weighted sum of squares (Residual Error) by the number of points less the number of parameters, and taking the square root. If the data and the error estimates are in agreement, and if the model is appropriate, this number will tend towards one.

Concept: Stream Data SDs

The same approach can be used for each stream point. These values are reported for each fitted stream in the Data tab of the Model Fit window. A small stream data SD, i.e. where SD approaches a value of one, indicates a good match between experimental and calculated data for that stream.

Concept: Parameter Standard Deviations

The solution of the minimisation also provides estimates of parameter accuracy. The mathematical proof of this estimate of accuracy is complex. Intuitively, if the parameter is well defined, the sum of squares will vary more rapidly as the parameter is adjusted. For a more detailed explanation, see Lynch (1977), chapter 7. If the program finds small variations in a parameter make NO apparent difference to the sum of squares at the minimum, it sets the parameter SD to 1E20. Such parameter fits should be treated with CAUTION and the data examined for problems.


Section 5.6

Page 5-23

Checking the Fit

Model Fitting

5.7

Checking the Fit

During the execution of the fitting program, the Model-Fit window is displayed. As the fitting program goes through each iteration the values in the results section of the window are updated. Assuming that the fitting reached a satisfactory conclusion, the standard deviations (SDs) of the parameters are updated when the fitting program stops. There are various ways in which the user can judge whether the results are good or bad: • Compare the size or order of magnitude of the SDs with that of the associated value. When the SD is small compared with the value as a ratio, it is a good fit, when large, it is a poor fit. • The summary values in the lower half of the Model Fit window also indicate the success of the fit. Low values in the Residual, Error Sum, and Errors SD fields indicate a good fit; large values, a poor fit. Moreover, in the case of these fields, cross comparisons between fittings can be made. If these values are smaller in the most recent run of the fitting than they were in the previous run, the fit is getting better. If they are getting larger, you are going in the wrong direction. • The engineer can also judge the relative success of the fitting by looking at the stream data windows. Examine the Error column. Weighted Error and Percentage Error versions of the difference between calculated and experimental data are most useful. These are displayed by selecting the appropriate item from the Error drop-down list. • The graph plotting facility of JKSimMet allows the engineer to plot raw and fitted data on the same graph, as detailed in section 5.8 (Presentation of Model Fitting Results). •

Page 5-24

The overview facility of JKSimMet allows key experimental and calculated data for multiple streams to viewed in a summary table. These overviews are configurable by the user (see section 3.10 for details).

Section 5.7

Version 5.0 June 1999

Model Fitting

Presentation of Model Fitting & Results 5.8

Presentation of Model Fitting Results

There are two main ways to present the results of model fitting: • printing data • plotting graphs . We shall deal with these in turn. Printing Model Fit Results

Given that model fitting concerns the experimental (raw) data and the predicted (fitted) data for streams, our task is to print these two types of data for the streams concerned. To easiest method to print the data for individual ports is simply to print the data in the relevant port data window as follows. Step 1

Bring into view the data window for the port whose data you want to print.

Step 2

Left-click on the Print icon on the main JKSimMet toolbar to view the Print Preview window for this item.

Step 3

If the Print Preview shows that the layout is to your satisfaction, click on the Print icon at the top, righthand corner of the Print Preview window (you may need to resize this window to see the Print icon)

Step 4

Repeat Steps 1 to 3 for all the other ports whose data you want to print.

These steps also apply to any other window which has data that you want to print, such as equipment data. The best way to produce a printed copy of the error and SD information on the Parameters and Data tabs in the Model Fit window is simply to print this window. Hint: The Overview window provides a convenient means of looking at experimental and model fitted data on the screen. This overview can also be printed, using the Print icon. The Report feature provides a means of printing both port and equipment data. The user can configure the report to show experimental and fitted data, SDs and errors for any ports. (See section 3.11 for more information on the Report feature).


Section 5.8

Page 5-25

Problems & Solutions Related to Model Fitting Plotting Graphs of the Model Fitting Results

Model Fitting

The graphs presenting model fitting results are, once again, of stream data. They involve experimental (raw) data, and predicted (fitted) data. The simplest way to begin is to configure a graph and simply nominate the data to be plotted. You can then edit the graph format and annotation as required. Step 1

Left-click on the Generic Graph Config button on the main JKSimMet toolbar to bring the Graph Definition window into view.

Step 2

For this exercise, you will create a new graph so click on the Port Data tab.

Note that the default setting for the graphing facility already has some data pre-selected so you must now define which data you want to plot on the graph.

Page 5-26

Step 3

Specify a new Port Data list by left-clicking the New button and typing a name for your data set into the Name box and then pressing Enter.

Step 4

Move the highlight to the row labelled Port in the first column and press Enter.

Step 5

Select the name of the required port from the dropdown list which appears.

Step 6

Position the highlight on the first cell in the Format row and press Enter.

Step 7

Select the required graph format from the Format dropdown list. Cum % Passing is a good choice.

Step 8

Select the option Exp & Fit from the drop-down list in the row labelled Data. Note that the list allows the user to plot single data types (e.g. Experimental data only) for the port or pairs of data types (Exp and Fit or Exp and Sim). Where a pair of data types is the selected option, JKSimMet represents the experimental data with data markers and the calculated data with a line.

Step 9

Move to the Line row and select the required style of line from the drop-down list.

Step 10

Move to the Point row and select the required symbol for the data marker from the drop-down list.

Step 11

Move to the Colour row and choose the colour with which the line and data markers will be drawn on the graph.

Step 12

If a spline interpolation is required between the data points on the graph click on the box in the Spline row to place a tick in the box.

Section 5.9


Model Fitting

Presentation of Model Fitting & Results Step 13

Set the minimum value of x to be plotted for this data set by typing the value in the X Min cell. Place the highlight in the cell, double-click and then type the new value.

Step 14

Repeat step 13 for the maximum value of x in the X Max cell.

Step 15

Repeat Steps 4 - 14 for each of the streams you want to plot on the graph.

Step 16

Left-click on the Display Graph button at the top of the Graph Definition window. Your new graph will now be displayed.

You can now refine the format of the plot and print the plot, etc, as outlined in the section 3.9 (Learning Graphing). Repeat the above steps for each of the streams for which you wish to compare the raw and fitted data. The quality of fit is represented by the closeness of the points to the line, (the closer the better). Overview

This facility provides an excellent summary. Set the % passing size properties from the Flowsheet Icon on the tool bar, e.g. P80 and % -75 µm. Overview can summarise flows and these key sizes for experimental and fitted data.

5.9

Problems Related to Model Fitting and Possible Solutions

There are, of course, many problems that may be encountered during model fitting. It is possible, however, to point out some of the more common mistakes, so that you are aware of them. Errors, Warnings, Some problems detected by JKSimMet produce error messages. ERRORS 140-163 are relevant to the Model Fitting module. Faults Please refer to the expanded descriptions of these errors in Appendix B.

Skill versus Practice

Model fitting is not a cut and dried procedure. The only way to acquire a useful skill level is to practice on a wide range of real data. JKSimMet offers a user-friendly environment for what are really very complex and powerful mathematical techniques.


Section 5.8

Page 5-27

Problems & Solutions Related to Model Fitting

Model Fitting

Initial Parameter As with all non-linear least squares programs, Model Fitting is sensitive to initial parameter estimates. The default values and the Estimates supplementary information provide a useful guide. However, trial and error may be necessary to find the best estimates to use with a new circuit or new data. Graphical Analysis

The graph capability of JKSimMet is the most powerful way to examine your data fit. Discontinuities in size distributions highlight poor data or a change in measurement technique. Graphical analysis also highlights any bias in the data fit.

Different Size Measurement Techniques

Be very careful of changes in size measurement technique, such as from sieves to Cyclosizer.

No Apparent Progress

When nothing much seems to be happening in model fitting, a simple first check is to ensure that you have a reasonable Maximum Number of Steps setting, and that the streams and parameters that you intend to include in the fitting are selected with a tick in the Parameters section of the Model Fit window.

Data

Note that it is necessary to have as much feed and product data as possible for each of the unit Models to be tuned. Simulation requires only feed data, but fitting must have some product data as well.

Not Enough Data

Even when you have the necessary data to perform model fitting, it is essential to ensure that there are enough readings to be useful for fitting; in general terms, the more data the better.

SDs and Emphasis

The SD settings in the stream data window may be set so that they can cause such an over-emphasis on one parameter that the potential of the fitting is compromised. Always try to make the SDs as good an estimate as possible.

Page 5-28

Section 5.9


Model Fitting

Problems & Solutions Related to Model Fitting

Scale Factors

The Scale Factor in the Parameters section of the Model-Fit window can also be a source of problems. If the scale factor is too big the fitting may stop, because any adjustment in the parameter produces such a large change that it steps over the minimum of the sum of squares. On the other hand, however, if the scale factor is too small, the fitting may stop because any adjustment produces a change of so small a scale as to be judged insignificant, even though you may not be close to a minimum point. So, be very careful with scale factors. As a guide, perhaps a scale factor onetenth of the magnitude of the parameter estimate would be a reasonable place to start.

Parameter Problems

Appendix A contains model descriptions, default values and a section on fitting for each specific model. These comments may help to overcome problems with parameters.

Large Weighted Errors

Examine the weighted errors carefully. These often indicate suspicious data points. A typical example is a screen top size which contains several times the predicted weight, because the laboratory screen stack did not extend to a large enough top size. Set the error to zero for this fraction to fix the problem.

Knot Positions

Where spline functions are used, the knot values can usually be fitted, but not the knot positions. These models provide a fairly smooth response because of the use of spline functions. A simple guide to knot positioning is that knots should be selected wherever a bend is needed. After all, the spline function is a mathematical model of a draftsman’s spline curve - a thin strip of steel with screw positions which are equivalent to spline knots.

Slave/Master Model Fitting

If problems are encountered when model fitting slave units, try fitting them individually. Despite all good intentions, all data sets in a survey may not have the same operating conditions and therefore may require different model fitting parameter values. Examine raw and calculated data for each unit to identify poor fits. One set of poor data, or data with inappropriate operating conditions, can prevent a good model fit solution being reached.


Section 5.9

Page 5-29

Model Fitting

References 5.10

References

GY, P.M., 1982. Sampling of Particulate Materials: Theory and Practice, 2nd Ed. Elsevier, Amsterdam. LYMAN, G.J., 1986. Application of Gy's Sampling Theory to Coal, International Journal of Mineral Processing, 17, pp 1-22. LYNCH, A.J., 1977. Mineral Crushing and Grinding Circuits, (Elsevier, Amsterdam). NAPIER-MUNN, T.J., MORRELL, S., MORRISON, R.D., & KOJOVIC, T. 1996. Mineral Comminution Circuits – Their Operation and Optimisation. JKMRC Monograph Series in Mining and Mineral Processing 2. Series Editor T.J. NapierMunn, Julius Kruttschnitt Mineral Research Centre, University of Queensland.

Page 5-30

Section 5.10

Version 5.0 June 1999

Mass Balancing

Mass Balancing

CHAPTER 6

MASS BALANCING


Section 6

Page 6-1

Introduction to Mass Balancing

Mass Balancing

6.

MASS BALANCING

6.1

Introduction to Mass Balancing

Purpose

Chapter 6 describes how to use the JKSimMet mass balancing sub-system.

Overview

Even the most carefully collected plant survey data are subject to many sources of variation. Some of these errors are due to: • • • • •

statistical effects sampling procedures or design assaying procedures sizing procedures fluctuations in plant flowrates.

As with all data improvement processes, the usefulness of the massaged data will be strongly dependent on the quality of the input data. The mass balancing module can help you to assess data efficiently and to refine your experimental technique when problems are detected. Mass Balancing will make good quality data better. It will not fix poor quality data or do anything more than highlight inadequate experimental technique. The module is used to mass balance sizing data, assay data and flowrate data collected at steady state. The balancing process produces best fit estimates of flowrates and a set of adjusted size and assay data which is consistent with those flowrates. As with model fitting, the overall process is: • • • •

Page 6-2

collect data, analyse data, check accuracy of data fit and refine experimental technique and instrumentation until desired level of accuracy is obtained.

Section 6.1


Mass Balancing 6.2

Data Collection Data Collection

The comments in section 5.2 are just as relevant for mass balancing as for model fitting. Some additional comments about assay measurements and techniques are appropriate here. There are well established rules for calculating the accuracy of a sampling and assay process (Gy, 1982). These can be used to establish an error model which can then be used to provide estimates of standard deviation for each point. Alternatively, 5 to 10 replicate samples can be taken and processed. If these input accuracies are established, then the program estimates of accuracy for flowrates will be real estimates and not relative estimates. If replicate sampling is carried out for assays on a number of streams (ie. a range of assay values), a simple two term error model can be generated by plotting relative standard deviation against average assay values from each stream. The intercept and slope of this plot will provide fixed (minimum) and relative (%) error components which can be used in the generalised version of the Whiten model. You also need to s pecify a sensible maximum (absolute) error.


Section 6.2

Page 6-3

Background

Mass Balancing 6.3 Background Mass Balancing can be thought of as a type of model fitting. The models in this case are quite fundamental. Hence, they do not impose the experience knowledge (which is built into other mathematical process models) onto the data. These mass balancing models are: •

a mixer

(for example, a pump sump),

•

a general classifier (for example, a hydrocyclone),

•

a unit which conserves some properties but not others (for example, a grinding mill will preserve total assays and flowrates but not size fractions.

The basis of the mass balancing algorithms is the differences in composition of various streams, that is, the differences generated by the process equipment. Consider a process with these streams having assays a, b, c: a

b c

If the flowrate in stream of assay a is 100 tph, then: 100 a = x*b + (100-x)*c where x is the flowrate in stream of assay b and then: x = 100 (a-c)/(b-c) This is the basis of the traditional three-product solution, where a, b and c may be assays for size, Cu or any other conserved property. It does not matter what kind of assays a, b and c are, as long as there is some difference in their values. If the process is just a splitter and the assays are all the same: a=b=c and therefore x = 0/0 which is undefined.

Page 6-4

Section 6.3


Mass Balancing

Background

Expressed another way, the flowrates can be estimated only if a process imposes a difference on its products, that is, the information is imparted by the process. If no information is imposed, as with a splitter, then the information cannot be used to make estimates, as it is not there to begin with. If this program produces a good balance around a splitter, then the splitter is behaving as a classifier and should probably be re-engineered. It follows that the most useful properties to use for mass balancing around a process unit will be those which have the largest difference in the product streams. This means that size assays will work well around a size classifier such as a screen or a hydrocyclone, and copper assays will work well around a copper flotation circuit. The reverse will generally not be true, with some notable exceptions. For example, gold and/or lead assays are often very useful around a hydrocyclone classifier because its density-separating characteristic will usually produce a large difference in these assays. The power of this program lies in its ability to use a wide range of assays across a large flowsheet. The program algorithm is driven by the assays with large differences but still takes account of those with small differences.

Concept: Mass Balancing

The mass balancing module takes all selected streams and calculates the smallest set of data adjustments which will make the data consistent. If some (or all) of these streams are measured (sampled and sized, etc), the experimental measurements can be compared with the data. The sum of squares of the differences between measured data and adjusted data is taken as a measure of goodness of fit of the model. Hence, the mass balancing program adjusts user selected flowrates to find a best set of flowrates which make the balance output match the experimental measurements as closely as possible.

Concept: Weighted Sum of Squares

If the precision of each data point is measured (or can be estimated from experience), then each difference between experimental data and simulation prediction can be normalized by dividing by its precision. That is, a small difference (or adjustment) between an accurate data point and its simulation prediction will make the same contribution to the weighted sum of squares as a large difference from an inaccurate data point.


Section 6.3

Page 6-5

Background Concept: Standard Deviation

Mass Balancing The usual measure of precision is the standard deviation. If we make repeated measurements of any data point, experimental variations will cause variations in the measured value xi. Then with many repeats, the mean x- of the values will provide an estimate of the true value of x. Subject to a number of assumptions, the expected variations from true x can be characterized by one number - the standard deviation defined as: n

∑(xi - x-)2

Standard Deviation =

(i=1,n) (n-1)

If the measurements are normally distributed then, out of 100 measurements, 67 could be expected to lie within plus or minus one standard deviation of the true value (as estimated by the mean), 95 within plus or minus two standard deviations and 97 within plus or minus three standard deviations.

Concept: Estimating Standard Deviation

Experimentally, 5 to 10 complete observations, that is, sampling plus analysis, will provide a good estimate of standard deviation. The mean of such a set of measurements should provide a good test of sampling precision - if the test circuit was at steady state.

Concept: Whiten Standard Deviation

For accuracies of retained size analyses, the Whiten errors often provide a realistic estimate. These are calculated as relative errors: • For fractions greater than 10%, a standard deviation of 1.0% is

assumed.

• For fractions less than 1%, a standard deviation of 0.1% is

assumed.

• For fractions between 1% and 10%, a standard deviation of

0.1% plus one tenth of the fraction is assumed.

Page 6-6

Section 6.3


Mass Balancing

How the Mass Balancing Program Works 6.4

How the Mass Balancing Program Works

As noted earlier, the mass balancing problem is a special case of the non-linear least squares fitting problem. The mass balancing program used by JKSimMet is a program called MBal written by Dr Bill Whiten and based on an algorithm developed by Dr Rob Morrison. The balancing algorithm uses special assumptions about data accuracy to linearise the problem. This allows for an initial flowrate solution which is analogous to the multiple linear regression solution, that is, a solution which is computationally rapid and does not require initial estimates of flowrates other than one flowrate to use as a basis for all others. The mass balancing program refers to this algorithm as the Morrison solution. If the data are accurate, these flowrates will be indistinguishable from those produced by the correctly weighted solution. The Morrison solution provides the initial flowrate estimates for what becomes essentially a constrained non-linear least squares fitting. A minimum set of flowrates is adjusted to minimise a true weighted sum of squares of data adjustments. However, the key difference between mass balancing and model fitting is that all data streams are adjusted, that is, the imbalances in the mass balance are distributed over both feed and product streams. For the model fitting minimisation, all of the errors are allocated over the product streams. That is, the feed streams are assumed to be accurate. This difference is important where aspects of the feed stream are more difficult to measure than those of the products. This is especially true with streams of coarse particles encountered in crushing and screening plants. For these plants, sampling error becomes critical and the mass balanced feed stream will usually be more useful than the experimental data as a basis for assessment of operation and for simulation.


Section 6.4

Page 6-7

How the Mass Balancing Program Works

Mass Balancing

Schematically:

Mass Balancing Product 1

Feed

Product 2

Mass Balance Adjusted Data

Feed (+

δ)

Product 1

(+ δ)

Product 2

(+ δ)

(minimize adjustments)

(minimize adjustment)

Model Fitting Feed

SIMULATION

Product 1 Product 2

Parameter Adjustments

Feed

Product 1 (Observed - Calculated) Product 2 (Observed - Calculated) Minimize the difference between observed and calculated

Page 6-8

Section 6.4


Mass Balancing 6.5

A Simple Example A Simple Example

The simplest, non-trivial case for mass balancing is a separator of some type which receives one feed stream and separates the feed stream into two products. Interestingly, this is also the most common application of mass balancing. This example provides a quick guided tour of the mass balancing module to get the feel of the system. To use it effectively, you will need to work through Learning Mass Balancing (Section 6.6).

The example which is included in the Learner Flowsheets project is called Example Cyclone Mass Balance. This example is a single hydrocyclone in open circuit. Step 1

Load the Learner Flowsheets project. Select the flowsheet named Example Cyclone Mass Balance

Step 2

Left-click on the Mass Balance icon on the toolbar to activate the mass balancing mode and to bring the Mass Balance window into view.

Step 3

Click on the Select tab to view the list of units and streams. Note that the current list is called Select-1 and that the user can set up more than one list of selected items. Click on each stream or unit name in turn to see which experimental data have been selected for use in the mass balance. The presence of a tick in the boxes marked Selected, Water, Feed etc. indicates that the item will be included in the mass balance. You will find the unit named Cyclone has three ports selected.


Section 6.5

Page 6-9

A Simple Example

Mass Balancing

You will find that all the units and water additions and streams are selected initially. You may turn these on and off with by left-clicking on the box to make the tick appear or disappear as required.

Data Entry

Step 4

Click on the Run Balance tab and then select the GSIM option on the check box on the top right hand corner of the Run Balance tab window. Also ensure that Select-1 is the option chosen in the drop-down list for the Select list.

Step 5

Bring the Cyclone Overflow data window into view.

Step 6

From the Data drop-down list select the SDs option and from the Error drop-down list select the Abs-Bal option. You will see the stream data in a format which is almost exactly like that in Model Fitting.

The experimental stream data and the related SDs are displayed as well as the balanced data and its related errors. Page 6-10

Section 6.5


Mass Balancing

A Simple Example

Stream Data

The Totals tab section of the window contains the experimental solids and water mass flow values and related data for the stream. The Size Distribution tab contains the list of the sizings from Top Size to Size 30 with the value (%) for each size fraction. Whether the % experimental value refers to % Retained, % Passing, or Cumulative % Passing depends upon the choice of stream format selected in the Format drop-down list at the top left of the screen. The Components tab section of the window contains any assay data for the stream.

Scrolling

Notice that the Size Distribution tab section contains too much data to display all of it in the window at one time. You can scroll through the data by using the Page-Up, Page-Down, Home or End keys, or the cursor up and down control keys. You may also click on the Print icon on the JKSimMet tool bar for a printout of the window you are working on.

Data Accuracy Entry

The user must set the data standard deviation (SD) values in the column labelled SD. This column must contain a value in each cell where corresponding experimental data are entered. Note that this standard deviation is your estimate of data accuracy obtained from repeat samples or from experience. There are three ways to enter values into these SD fields. •

Leave most or all of the entries at the default value of 1.0 and simply over-typing the ones you wish to change individually.

•

Globally change all the SDs to one of the three other available options by: Step 1


Click on the Set SDs button at the top, right-hand corner of the stream data window to bring the Select SD Values window into view.

Section 6.5

Page 6-11

A Simple Example

Mass Balancing

Step 2

•

Select the required option from the Select SD Values window which is displayed and click on the OK button to change the SDs for the stream to the option which you have chosen.

The third option is that you can change the individual fields by over-typing an SD value. The number which you enter is an expression of your confidence in the experimental value.

Concept: Ignoring Data in Mass Balancing

Note that in mass balancing mode a large SD means the error will be largely ignored. This is different from Model Fitting where a zero SD switches an error off completely. In mass balancing mode a zero value for the SD will make the mass balancer hold the experimental value constant, ie. it will not be adjusted.

Concepts: High Accuracy Data

If you have high confidence in an experimental value to be used in mass balancing, set the SD to a small value.

Concepts: Calculating Missing Data

If both the experimental value and SD are set to zero, the mass balancer will treat this datum as unknown, and estimate a value, if there are sufficient other data provided. This is useful when flow data cannot be obtained in the stream sample survey. Now that we know about setting SDs, we can continue our tour.

Page 6-12

Step 7

Look at the data window for each port. For this example you should examine the Feeder called Cyclone Feed and the Cyclone Underflow and Cyclone Overflow port data windows.

Step 8

Bring the Mass Balance window into view and select the Run Balance tab. Left-click on the button marked Start to run the mass balance algorithm. The program will execute and when it is completed the results will be displayed.

Step 9

Bring into view the port data windows and examine the raw and adjusted data in each stream.

Step 10

Compare the raw and adjusted data graphically by selecting Graph from the Cyclone properties list (Rightclick on Cyclone Icon). Select experimental then calculated for a quick comparison.

Section 6.5


Mass Balancing

A Simple Example

For a numerical comparison of the experimental and calculated data select the absolute difference option on the Error drop-down list. This completes our brief tour through Mass Balancing.


Section 6.5

Page 6-13

Learning Mass Balancing 6.6

Mass Balancing

Learning Mass Balancing

The mass balancing module of JKSimMet is useful in two areas. Firstly, it provides a check on data accuracy which is not model dependent. The mass balancing models are correct (that is, they contain no built in experience). Hence, if the data balance well but the model fitting does not fit well, it indicates that the model is not appropriate. Where coarsely sized samples are used, as in crushing and screening circuits, the mass balanced data may be more useful for model fitting than the raw data. Secondly, mass balancing is useful for determining flowrates and recoveries around complex circuits. The example which we will use in this section, Learning Mass Balancing, is concerned with flowrates and recoveries in a copper flotation circuit.

6.6.1

Preparation for Mass Balancing

For our tutorial, mass balancing is performed on a circuit flowsheet that has already been established. Ensure that you have either selected an existing project, or you have input a new flowsheet (see section 3.7 on Creating a New Project if you are unfamiliar with the steps necessary to establish a project). A tutorial example called Copper Flotation has been provided for this section.

Page 6-14

Step 1

Load the Learner Flowsheets project and select the flowsheet named Copper Flotation from the drop-down list. If necessary, resize the flowsheet window to view the entire flowsheet. Ensure that the flowsheet is locked.

Step 2

Click on the Mass Balance icon on the toolbar to bring the Mass Balance window into view.

Section 6.6


Mass Balancing


Notice that the Mass Balance window has a four selectable tabs for the user to enter the information required for mass balancing. The items in the Select and Component sections need to be defined before running the mass balancing. If you have not defined these items, JKSimMet will provide error messages to indicate what information is missing.

6.6.2

Model Types for Mass Balancing

In Version 5 of JKSimMet the flowsheet drawing for mass balancing is the same one used for simulation and model-fitting, with the full range of equipment icons available to draw a circuit diagram. However, no matter what equipment icon is visible, there are only two model types in mass balancing. These are: •

classifier or mixer unit This unit either selects particles to go to different product ports of the unit (classifier) or adds particles from different feeds (mixer). That is, particles are sorted or mixed in this type of unit, not broken down or altered.

•

transform unit In this unit assays are preserved but size structures are destroyed. In mass balancing all comminution devices are transform units.

The mass balance algorithm decides which type of mass balance unit is required according to the flowsheet icon selected by the user.

6.6.3

Selecting Data

As is the case in the Simulation and Model-Fitting modules you may select a single unit or a cluster of units on your flowsheet to mass balance. This allows you to check small parts of a circuit for data consistency. Step 1

Bring the Mass Balance window into view.

Step 2

Left-click on the Select tab to bring the Select section into view.


Section 6.6

Page 6-15


Mass Balancing

For the Copper Flotation example the selection list is called Mass Balance Select List 1. The default selection for a new select list is for none of the units and streams to be selected. Therefore the first stage in defining a select list is to examine the list of equipment and streams and to select the required items by clicking on the box next to the item name to enter a tick. A Select All and a Select None button have been provided to help users to configure select lists quickly. Note that as you click on each item on the list its flowsheet icon is highlighted in red. Also note that items which have been selected for inclusion in the mass balancing are highlighted in blue on the flowsheet. These visual cues help users to identify the equipment and streams on complex flowsheets. Step 3

Work through the Select list and ensure that: • • •

all equipment units are selected all streams are selected all water additions are not selected

Note that for GSIM, percent solids and internal water flows are always enabled. Because each Select list has a name, you may set up several different lists to examine different sections of a circuit. You can select every stream and flow to balance or any single unit or selection of streams. Note: in V5.0 stream data are stored in equipment ports. To balance a subset of the data, you need to choose both equipment and ports. The “water” check box, applies to Water Feeders. These should only be used with GSIM or when “% solids as a component” is checked on the component tab.

Page 6-16

Section 6.6


Mass Balancing 6.6.4

Learning Mass Balancing Component

The mass balancing module can analyse two types of data, namely components or size distributions. The model-fitting and simulation modes in JKSimMet only use size distributions. The size format is called GSIM for Grinding Simulation. JKSimMet uses GSIM as the default component type. If GSIM is selected via the GSIM Mode check box on the Run Balance tab or the Components tab, no further data entry is required.

To use GSIM mode click in this box to select it. No further component data entry is required.

However, it is possible to define your own labels for other measurements of stream characteristics, such as assays, which can be used to mass-balance the flows around a circuit. The user must specify the component list names before running mass balancing. Note that while the mass balance module can handle stream components other than size e.g. assays, these cannot be combined with balancing by size distribution. Therefore a circuit can be balanced based on size distributions only or assays only. To perform a mass balance using data other than size the user must select a Component list and give it a name. The next step is to define each of the components. Step 1


Left-click on the Component tab to view the component list. For the Copper Flotation example, the list is called CuFe and the components are copper and iron assays, %Cu and %Fe.

Section 6.6

Page 6-17


Mass Balancing

Step 2

Ensure that both the %Cu and %Fe assays are selected for use (i.e. each has a tick in the box in the Use column which is beside the Component Name column).

Step 3

Relative SDs may be specified as automatically calculated from here. However, their use is not recommended as a balance using relative SDs takes most note of the smallest assay values which are often the least well defined.

Step 4

The Control area of the Component section has a box marked %Solids as a component. If this box does not have a tick in it, all %Solids, water flows etc. are ignored i.e. adjustment differences are absorbed in the unspecified components and will not be shown on the screen or printouts. For the Copper Flotation example we will leave the box empty. Typically you would use % solids as a component when balancing a set of specific gravity fractions. If you use % solids as a component you must specify appropriate water additions. For what happens when % solids are included as a component see section 6.6.5 on Water.

Entering Component Data

Once a Component list has been defined in the Component tab of the Mass Balance window, JKSimMet sets up the correct number of data cells for the component data to be entered in each of the port data windows. The component data can be accessed by clicking on the Component tab of the port data window. The flowsheet is now set up to mass balance the data using component data, in this case assay data. All that remains to be done is to enter the assay data into the port data windows.

Page 6-18

Step 1

To enter (or examine) stream assay data, open a port data window and click on the Component tab. This window will now contain as many rows of components as the user has defined in the Mass Balance window Component tab. The user enters new assay data (or edits existing data) by typing over the values in blue text in the column marked Exp. In the Copper Flotation example the %Cu and %Fe assay data have already been entered as shown in the example below.

Step 2

Select the SD’s error display type from the Data dropdown list.

Section 6.6


Mass Balancing

Error Display


Step 3

Select the data standard deviation value by clicking on the Set SDs button and selecting the required SD from the choices presented in the Select SD Values pop-up window. Alternatively the user can type in their own values for the SDs. In the Copper Flotation example the assay SDs are set to 10%. However, for less well defined data, the Whiten Error provides a more realistic error model.

Step 4

Repeat steps 2 and 3 above for each port in turn.

Step 5

Finally, open the Feed unit equipment window to examine the feed stream data. Ensure that the measured feed flowrate has been entered (and the % solids by weight if available).

The right-most column under the Components tab in the stream data window is the Error column, and the values in it can be expressed in one of three ways; Absolute Error, Percentage Error or Weighted Error. The user can select which of these forms is displayed by the following procedure:

Step 1

Click on the Error box to view the drop-down list.

Step 2

Select the required mass balance error type from the list (either Abs-Bal for absolute error, Pct-Bal for percentage error or Wtd-Bal for weighted error).

Absolute Error

Tells you the actual difference between the calculated and the experimental values.

Percentage Error

Tells you the percentage difference between the calculated and the experimental values.


Section 6.6

Page 6-19

Learning Mass Balancing Weighted Error

Mass Balancing

Tells you the number that the program will use in its sum of squares. You will probably find it the most useful setting. The value of this weighted error is (exp - adj)2  S.D.   

6.6.5

Water

If you have selected %Solids as a component on the current Mass Balance window Component tab you can also mass balance any water additions to the circuit. In Version 5, mass balance water additions are made by selecting the appropriate water feeder and including it on the Select list. For this example, you will need to add two water feeders to the flowsheet. Measured data and estimated SDs are entered in the water addition data window. This removes the need for the water addition list used in Version 4. See Appendix A1.2 for a detailed description of the Water Feeder.

Some typical water addition and % solids data are tabled below. Select % Solids as a component on the Component tab (see section 6.6.2 on Components) and also select water additions on the Select tab (see section 6.6.4 on Selecting Data) to use this facility

Stream

FEED COMB SCAV CONC RGH 1 CONC RGH 1 TAIL RGH 2 CONC RGH 2 TAIL SCAV CONC FINAL TAIL CLNR SCAV CONC CLNR FEED CLNR SCAV TAIL CLNR 2 TAIL CLNR 1 CONC CLNR 1 TAIL FINAL CONC Page 6-20

Section 6.6

% Solids Exp

% Solids SD

30.0 28.0 45.0 29.0 40.0 28.0 35.0 27.0 40.0 28.0 28.0 40.0 45.0 30.0 50.0

1.00 3.00 2.00 2.00 2.00 2.00 2.00 2.00 4.00 3.00 3.00 4.00 3.00 5.00 5.00 Version 5.1 November 2001

Mass Balancing


Water Feeders: Clnr Feed Sump Scav Conc Sump

20 15

SD 1.0 SD 1.0

Remember: Select the Water Feeders and tick % solids as a component in the Mass Balance dialogue window.

6.6.6

Solution Controls

With the Mass Balance window as the active window, click on the Control tab to bring the control section into view.

Note that it is not necessary to understand this section to use the mass balance module. The following comments are for users with a mathematical background.

The mass balancing algorithm runs in several stages. The first is the simple solution which is analogous to multiple linear regression. Unless the data has serious problems it will converge in one step; that is, the second solution will be the same as the first. If small negative values occur, increase the number of steps to eliminate these values. However, recheck your data carefully. Negative values indicate measurement bias. For higher numerical accuracy you may increase the iteration limits. However, there will be no gain in the balance accuracy because data accuracy will be the usual limit.


Section 6.6

Page 6-21


Mass Balancing

Hint: Read section 6.9 on Problems relating to Mass balancing before adjusting these settings. The values shown above are the default values. If the adjusted data show unacceptable inconsistencies (for example, Au assays in ppm or 1.0 E-06 will not work too well with a convergence criterion of 1.0 E-05) then you must either reduce the limit or, more sensibly, re-scale the assay. For example, express your gold assays as Au ppm and do not constrain the assay total to 100%.

6.6.7

Carrying out the Mass Balance

This is the simplest step. Once the components have been specified, the desired equipment and streams selected and the data have been input, the mass balancing can begin.

Page 6-22

Step 1

Click on the Run Balance tab of the Mass Balance window.

Step 2

Ensure that the correct Select and Component lists are selected in the cells above the main data area. For the Copper Flotation example we will use the existing Select list Mass Balance Select List 1 and the Component list CuFe.

Step 3

Left-click on the Start button to start the mass balancing program.

Section 6.6


Mass Balancing


The mass balancing program will run and when it is complete the results will be summarised in the Mass Balance window as shown below. The user can also examine the detailed data in the port data windows or using the Overview or graphing features.


Section 6.6

Page 6-23

Checking the Balance 6.7

Mass Balancing Checking the Balance

During the execution of the balance program, the Mass Balance window is displayed. Once execution has stopped, the values in the results section of the window are updated. Assuming that the balance has reached a satisfactory conclusion, the calculated standard deviations of the solid flowrates are also updated. The standard deviations calculated by the mass balancing program for each solids flowrate are analogous to the Model Fitting estimates of parameter accuracy, that is, solids stream flowrates are the parameters of Mass Balancing. There are various ways in which the user can assess the results:

Page 6-24

•

The overview window is probably the most useful way to check data and results. It also allows recovery of any component to be displayed for all streams. See Section 6.8.1 for details of the overview facility.

•

Compare the size or order of magnitude of the SDs with that of the associated value. When the SD is small compared with the value as a ratio, it is a good fit; and when large, a poor fit.

•

The summary values in the Sum of Squares section at the foot of the Run Balance tab also indicate the overall success of the fit. Low values indicate a good balance while large values of these items indicate a poor balance. Moreover, in the case of these fields, cross comparisons between mass balances can be made. If these values are smaller in the most recent run of the balance than they were in the previous run, the balance is getting better. If they are getting larger, your mass balancing is going in the wrong direction.

•

The engineer can also judge the relative success of the mass balancing by looking at the port data windows. Examine the values in the Error column. The Weighted Error and Percentage Error versions of the difference between balanced and experimental data for sizings are most useful.

•

The graph plotting facility of JKSimMet allows the user to plot raw and balanced size distribution data (GSIM) on the same screen, as detailed in section 6.8 (Presentation of Mass Balancing Results).

•

Mass Balancing can be carried out one unit (or a small set of units) at a time. This allows you to put the test data under a microscope. If circuit conditions were changing as you did your test work, unstable sections will give unusable results and varying conditions will usually produce nonsense.

Section 6.7


Mass Balancing

Checking the Balance

Concept: Data Standard Deviations

At the best-fit point, an estimate of the goodness of fit is calculated by dividing the weighted sum of squares (Residual Error) by the number of points less the number of parameters, and taking the square root. If the data and the error estimates are in agreement, and if the model is appropriate, this number will tend towards one. With Whiten SDs, good data achieve values in the range 1 - 4.

Concept: Stream Data SDs

The same approach can be used for each stream point. These values are reported for each fitted stream in the Mass Balance window and the stream data windows. The solution of the mass balancing minimisation also provides estimates of parameter accuracy. The parameters in this case are the stream flowrates. The mathematical proof of this estimate of accuracy is complex. Intuitively, if the parameter is well defined, the sum of squares will vary more rapidly as the parameter is adjusted. For a more detailed explanation, see LYNCH (1977), chapter 7. If the program finds that small variations in a parameter make NO apparent difference to the sum of squares at the minimum, it sets the parameter SD to 1E18 Such mass balance results should be TREATED WITH CAUTION. Note also that such a result may mean you are trying to balance around a splitter or a classifier which is not classifying.


Section 6.7

Page 6-25

Presentation of Mass Balancing Results 6.8

Mass Balancing

Presentation of Mass Balancing Results

There are two main ways to present the results of mass balancing: • •

the overview window and printing

We shall deal with these in turn. For mass balanced data, graph plotting is limited to GSIM format.

6.8.1

Overview

The overview window gives you a powerful means of summarising your data and checking it for adjustment problems. Each overview data set defined by the user displays a list of data from all selected streams. The user can select the types of data which are displayed in the overview window. The best way to use the overview feature is to compare experimental and calculated values for each assay (or size fraction) across the complete circuit. This will give a very useful picture of the accuracy of the data and the mass balance. Note that the overview window can be configured to show either data or calculated Recovery information.

Page 6-26

Step 1

Left-click on the Overview Config button on the main JKSimMet toolbar. This brings the Overview window into view.

Step 2

Select the existing overview.

Section 6.8


Mass Balancing

Recovery Selection


Step 3

In order to make it easier to view the data in the overview window, resize the window by clicking and dragging the bottom, right-hand corner of the window. Also widen the Equipment and Port columns by clicking and dragging the right-hand border of the title cell in each column.

Step 4

You can now add a column to view the Fe assay SD data by clicking on the Insert Column icon at the top of the overview window.

Step 5

Place the cursor in the top title cell of the new column and press Enter to bring a drop-down list of options into view. Select Components from the list.

Step 6

Place the cursor in the middle title cell of the new column and press Enter to bring a drop-down list of component options into view. Select %Fe from the list.

Step 7

Place the cursor in the lowermost title cell of the new column and press Enter to bring a drop-down list of options into view. Select Calc Bal SD from the list of options. The overview window should now look like the picture below.

To examine recovery data for the components in the streams select Recovery by placing a tick in the Recovery box. Note: The balanced recovery selection will calculate recoveries based on mass balanced assays and flowrates. By default, the recovery is calculated with respect to the circuit feed stream. This reference stream is labelled in bold text in the Overview table. To change the stream which is the reference for


Section 6.8

Page 6-27


Mass Balancing

recovery calculations, move the cursor to the row in the overview window which has the named stream in and right-click in the equipment column. This brings up a dialogue window as shown below which allows you to define the selected stream as the reference for the recovery calculations.

6.8.2 Printing Mass Balance Results

Printing the Mass Balance Results

Printing can be selected from any window by clicking on the Print icon on the JKSimMet toolbar. When this is done, the current window will be printed. Given that mass balancing concerns the experimental (raw) data and the adjusted (mass balanced) data for streams, our task is to print these two types of data for the streams concerned. One way to do this is to print individual port data windows. In this case ensure that the port data window Data type is set to SD’s. An alternative method for printing the experimental and adjusted data is to configure a Report. This allows the user to select any of the port data types for printing and includes a Summary format which is useful for comparing data. To print recovery data, use the overview table with the Recovery option selected. Remember to select a stream to use as the recovery basis. (If this stream is the feed stream, this will produce an element distribution which is often the objective of mass balancing).

Page 6-28

Section 6.8


Mass Balancing 6.8.3

Presentation of Mass Balancing Results Plotting Graphs

Plotting Graphs The graphs presenting mass balance results are, once again, of stream data. They involve experimental (raw) data and adjusted of the Mass Balancing Results data. The simplest way to begin is to select the default format options available in the graphing sub-system and simply nominate the data to be plotted. You can then edit the format and axes as required. At present, graphing is available only for GSIM format. Therefore, to examine graphing for mass balancing, leave the Copper Flotation flowsheet and select the flowsheet named Example Cyclone Mass Balance. For this exercise, you will create a new graph.

Step 1

Left-click on the Generic Graph Config button on the main toolbar to open the Graph Definition window

Step 2

Left-click on the Format tab to make this the active tab.

Step 3

Left-click on the New button at the top, right corner of the Graph Definition window to create a new graph format.

Step 4

Place the cursor in the Name text box and double-click to highlight the default graph format name. Now type in a new format name and press Enter. Any new name will do.

Step 5

Change the labels and the information in the Axes and Data Interpretation area of the Format tab, using the picture below as a guide.


Section 6.8

Page 6-29


Mass Balancing

The next step in configuring the graph is to tell JKSimMet where to find the data to be plotted.

Page 6-30

Step 6

Left-click on the Port Data tab to make this the active tab and click on the New Data icon to create a new graph data set.

Step 7

Name your data set, following the procedure described in Step 4.

Step 8

Move the cursor across to column 1 of the row labelled Port in the Data Selection - Ports area of the window and press Enter to view the drop-down list of ports whose data can be graphed. Select the Cyclone Underflow by highlighting its name and pressing Enter.

Step 9

Move the cursor to the Format cell and press Enter to view the drop-down list of format options. For this plot select the Cum. % Passing option.

Step 10

Move the cursor to the Data cell and press Enter to view the drop-down list of data which can be plotted. Note that individual data types (e.g. Simulated) or pairs of data types (Experimental and Simulated) can be selected. In the latter case the Experimental data are

Section 6.8


Mass Balancing

Presentation of Mass Balancing Results represented by the data marker and the calculated data are represented by the line. For this graph select the Exp & Bal option.

Step 11

If you would like to change the style of line or data marker or the colour used to display the data on the graph select the required items in the Line Point and Colour cells respectively.

Step 12

Ensure that the box in the Spline cell is not ticked.

Step 13

Move the cursor to the X Min cell and enter appropriate values in the minimum graph range for the lines you want to plot. This is a type-over field. In this case enter the value 0.01 for the minimum value of X to be plotted.

Step 14

Repeat Step 13 for the X Max cell, in this case entering the value 10 for the maximum value of X to be plotted.

Step 15

Repeat Steps 8 - 14 for all streams required, placing each in a new column.

Step 18

Left-click on the Display Graph icon at the top righthand corner of the Graph Definition window to view your graph. The plot for the Cyclone Mass Balance Example looks like the picture below.

You can now refine the format of the graph and print it etc., as outlined in the section 3.8 (Learning Graphing). Repeat the above steps for each of the streams for which you wish to compare the raw and calculated data. The goodness of fit is represented by the closeness of the points to the line; the closer the lines and points, the better the fit.


Section 6.8

Page 6-31

Problems and Possible Solutions 6.9

Mass Balancing

Problems Related to Mass Balancing and Possible Solutions

There are, of course, many problems that may be encountered during mass balancing. It is possible, however, to point out some of the more common mistakes, in order to alert you to some of the major pitfalls.

Errors, Warnings, Some problems detected by JKSimMet produce error messages. See Appendix B for such problems. Faults ERRORS 120-139 are relevant to the Mass Balancing module. Please refer to the expanded descriptions in Appendix B.

Skill versus Practice

Mass Balancing is not a cut and dried procedure. The only way to acquire a useful skill level is to practise on a wide range of real data. JKSimMet offers a user-friendly environment for what are really very complex and powerful mathematical techniques.

Graphical Analysis

The graph capability of JKSimMet is the most powerful way to examine your data fit (in GSIM stream format only). Discontinuities in size data highlight poor data or a change in size measurement technique. Graphical analysis also highlights any bias in the data fit.

Different Sizing Techniques

Be very wary of changes in size measurement technique e.g. from screens to Cyclosizer.

Different Assay Techniques

Where assay techniques change between stream samples, as they sometimes do for different assay ranges, there may be inherent biases within the assay techniques. These will lead to biases within the mass balance.

Data

Note that it is necessary to have enough feed and product data to achieve a useful mass balance.

Some Common Mass Balancing Pitfalls

There are a couple of simple traps which can appear in many guises. If you become aware of these now you may recognize them more easily when you encounter them.

Page 6-32

Section 6.9


Mass Balancing

Problems and Possible Solutions

6.9.1

The Middlings Problem

If we return to our one unit flow diagram and add on a middling stream of assay m:

b a

m c

It is easy to see that there are not enough assays to go around. However, if we have two assays in each stream, we would write them out as simple equations and solve for two unknowns. However, as m really is a middlings stream, it will be close to a in composition and very often recycled back to it. In this case, no matter how accurately we can sample and assay the streams, we can only find out: •

the ratio between flows b & c (if m goes elsewhere)

or •

the flows in b and c if a is recycled.

However, the actual flowrate in m can be either zero or infinity. There is a straightforward solution. Measure (or estimate) the flowrate in stream m and input this flowrate as data. The mass balancing module allows you to do this.


Section 6.9

Page 6-33

Problems and Possible Solutions 6.9.2

Mass Balancing

The Infinite Division Problem

If one wishes to extract maximum information from a survey, it is The Infinite Division Problem not unusual to assay on a two (or even three) dimensional matrix, for example, assay by size or assay by size by specific gravity. This subdivides the stream into even smaller sub-groups. Each sub-group has an extra step of processing and an increased relative error. Hence, we tend towards trying to solve for (0 - 0) / (0 - 0). This is not a useful numerical exercise. Once again, the solution is straightforward. Use the total assays with large differences to calculate the Mass Balancing flowrate solutions. Once you have these flowrates, fix them by entering them as experimental flowrates with low standard error estimates and add all of the small assays into the problems. Now that the flowrates are defined, the Mass Balancing module can allocate the minimum adjustments required to make all of the fractional assays consistent. (Note this balancing module does not balance across the matrix for more than one component at a time - this component is usually size.)

Page 6-34

Section 6.9


Mass Balancing

Metallurgical Accounting

6.10

Metallurgical Accounting

The day to day data collected from a mineral processing plant are rarely consistent and will almost always contain redundant information. In general, any two methods of calculation will yield different results. The challenge for metallurgical accounting is to produce adjusted data which are both self-consistent and as accurate a representation of plant performance as possible. Consider a typical base metal concentrator with several products from several circuits,

Feed

x

Copper Au Circuit

x

x

Lead Circuit

Zinc Circuit

x

x

x

Cu Au Conc

Pb Conc

Zn Conc

x

Tailings

At each point marked ⊗, we have Au, Cu, Fe, Pb and Zn Assays. For the feed, we have weightometer readings and for the concentrates we have load out weights with stockpile surveys. If we select an accounting period which is large compared with the circuit residence time, we can carry out a mass balance over this complete data set. If large adjustments are required, these may be measurement problems in sampling or assay techniques. Select smaller circuits to mass balance to isolate these problems. Once a consistent set of adjusted data is produced for each accounting period, the sums of these sets will also be consistent. If assays and flowrates are available on a short time scale, eg. several times per shift, these data can be balanced for each time period, printed to file or exported to most Windows spreadsheet and word processing packages by copying and pasting. JKMetAccount For users with a serious interest in metallurgical accounting, the JKMetAccount program was created to enable the Metallurgist or Plant Manager to track the performance of a mineral processing plant over time. It's major strength comes from harnessing the power of the JKMBal mass balancing engine within a rigorous data management environment. Changes to your plant flowsheet, which can cause major problems for a spreadsheet based accounting system, are handled with ease by JKMetAccount. Combine these features with a graphical flowsheet drawer and the ability to use the full formatting power of Excel in your reports and you have a tool that we believe you will soon come to regard as indispensable. Further details are available from JKTech or at www.metaccount.com


Section 6.10

Page 6-35

References

Mass Balancing 6.11

References

LYNCH, A.J., 1977. Mineral Crushing and Grinding Circuits, (Elsevier, Amsterdam), Chapter 7. LYMAN, G.J., 1986. Application of Gy's sampling theory to coal, International Journal of Mineral Processing, Vol 17:1-22. GY, P.M., 1982. Sampling of particulate materials: theory and practice, 2nd Ed, (Elsevier, Amsterdam). MORRISON, R.D., 1976. A two stage least squares technique for the general material balance problem, JKMRC Internal Report No 61 (unpublished).

Page 6-36

Section 6.11


Appendix A

Model Descriptions

APPENDIX A

Model Descriptions


Appendix A

Page A-1

Introduction

Appendix A A1

Introduction

This appendix of model descriptions contains: • • • • •

a description of each model available in JKSimMet key equations which are the mathematical basis of the models known limitations and restrictions some guidance and restrictions for parameter fitting typical model parameter values, where appropriate

There are a number of generic models included in JKSimMet, which can be used to describe the behaviour of a wide range of processes. For example, the simple efficiency curve model can be used to describe any sort of classification device, such as a cyclone, or a spiral classifier. Selection or fitting of parameters for these models will depend entirely on the type of process being modelled. Most of the process units available to the user when drawing the flowsheet can be described by a number of models. Typically, a process unit will have a specific model, developed for that particular device, and a number of generic models. Selection of the appropriate model is at the user's discretion and will often depend on available test data.

A1.1

Parameter Defaults and Range Limits

Model parameters in V5 have default values and a permitted range. The default value and range can be viewed by double clicking on the parameter value. These values are not currently editable by the User.

A1.2

Model Differences in JKSimMet V5.0 and 5.1

To provide a more ‘obvious’ structure for Version 5, a class of feeder models has been added. These provide: • A source for ore • A source for water Later modules will provide access to configuration data. For the long term option of a full dynamic simulator, the feeder models will provide a way of inputting variation with time.

Page A-2

Appendix A1


Appendix A

Introduction A1.2.1

Ore Feeder

Ore Feeder

The ore feeder (called Feed) is a specialised piece of equipment which has a single ‘product’. The Feed unit allows you to set up the flowsheet ore SG and the default size distribution. The size markers, i.e. Percent passing a particular size and size at a particular percent passing can be set by double clicking on those fields on the Totals tab. Note that while the flowsheet properties dialogue allows you to set global properties for Data Information blocks and tools such as simulation and model fit, these properties for the feeder and ports may be set at different values for each.

A1.2.2

Water Feeder

Water Feeder

The water feeder replaces the ‘Unit Feed Density’ section of each model in JKSimMet Version 4. The three models provided with the Water Feeder are functionally identical to the three options for ‘Unit Feed Density’.

Option 1 - Feed Streams

No water is added. The model reports on flow rates of solids and water added to the piece of equipment to which it is connected. This information is redundant as it is also contained in the feed port of that piece of equipment. This model is provided for compatibility with Version 4.


Appendix A1

Page A-3

Introduction

Option 2 – Required % Solids

Appendix A

This option allows the user to set a maximum percent solids for the total feed to the connected equipment. If the feed percent solids is higher than ‘Required % Solids’ the water feeder adds additional water to achieve the required percent solids. If the percent solids value is already lower than required, the water feeder adds no water. It does NOT remove water to achieve the required value.

Page A-4

Appendix A1


Appendix A Option 3 – Water Addition

Introduction Water Addition is the recommended mode for common use. The user specifies the required water addition in cubic metres per hour. This option has two more uses. The experimental water addition may be used as a parameter in Model Fitting. That is, a model fit may use water addition as a parameter when water flows were unmeasured or the measurement is dubious. The ‘exp Water Addition’ is subject to optional update after a model fit as are all other parameters. Note that percent solids or water flow from the circuit should be constrained by a small SD value to provide a constraint on total water addition. The third use of this option is for mass balancing of water additions. The User provides the ‘exp New Water Addition’ and an ‘sd’ estimate on this model. The other requirement is that the Water Feeder and Water are selected on the Select Tab of the Mass Balance tool. The balanced water addition is returned to the calc* field of the Water Feeder. If you wish to use this value for fitting or simulation, copy it into the Exp value.


Appendix A1

Page A-5

Introduction

Appendix A A1.2.3

Variable Rates SAG Model

The Variable Rates SAG model also has some differences – detailed in Appendix 11.

A1.2.4 Splitters

Page A-6

Variable Rates SAG Mill Model

Splitters

The range of splitter models has been increased. discussed in Appendix 14.

Appendix A1

These are


Appendix A

Hydrocyclone (Model 200, 201) A2

Hydrocyclone (Model 200, 201)

A2.1

Model Description

The model is based on the concept of a reduced efficiency curve, which in turn is developed from the actual efficiency curve and the corrected efficiency curve for the classifier treating a particular ore. The important concept is that the reduced efficiency curve is a characteristic function of an ore and is independent of the dimension or operating conditions of the cyclone. A typical set of efficiency curves for a cyclone is shown in Figure A2.1.

The model consists of a series of equations which are described below. At least one cyclone test on a particular ore is required to provide data for the calculation of constants in the equations.

A2.2

Model Equations

The model consists of a series of equations which are described below.

PressureThroughput Relationship

The pressure-throughput relationship can be expressed as:

Q = KQ2 Dc2 (P/ρp)0.5 (Do/Dc)0.68

(A2.1)

where KQ2=KQ1 (Di/Dc)0.45 (θ)-0.1 (Lc/Dc)0.2

(A2.2)

The proportionality constant, KQ1, is a function of the feed material and the diameter of the cyclone. For cyclones of Krebs design, treating identical feed solids, the dependence on cyclone diameter may be empirically represented by the equation KQ1=KQ0 Dc-0.1

(A2.3)

where KQ0 depends on feed solids characteristics (eg. specific gravity) only.


Appendix A2

Page A-7


Appendix A

For normal industrial operation, the classification size can be Classification Size Relationship related to the variables according to the equation d50c/Dc=KD2(Do/Dc)0.52 (Du/Dc)-0.47 λ0.93(P/{ρp g Dc})-0.22 . . . (A2.4)

where KD2 is related to the minor design variables Di, Lc and θ by KD2=KD1 (Di/Dc)-0.5(Lc/Dc)0.2 (θ)0.15

(A2.5)

and KD1 may be written as KD1=KD0 (Dc)-0.65

(A2.6)

KD0 depends on feed solids characteristics only (such as size distribution and specific gravity). (Note that the classification sizes for specific minerals within the feed stream can be estimated using the following formula: d 50c ( m ) =

FeedSG -1 * d 50c MineralSG -1

where FeedSG is the mean feed solids density, d50c is the overall corrected d50, MineralSG is the density of the specific mineral of interest, and d50c(m) is the corrected d50 of the mineral of interest.) Recovery to Underflow Relationships

Water recovery (Rf) and volume pulp recovery (Rv) to underflow are related to the major variables by: Rf=Kw2(Do/Dc)-1.19 (Du/Dc)2.40 (P/{ρp g Dc})-0.53 (λ)0.27 . . .(A2.7) and Rv=Kv2 (Do/Dc)-0.94 (Du/Dc)1.83 (P/{ρp g Dc})-0.31

(A2.8)

Further, the effects of inlet diameter, cone angle and cylinder length have been evaluated as Kw2=Kw1 (Di /Dc)-0.50 (θ)-0.24 (Lc/Dc)0.22

(A2.9)

and Kv2=Kv1 (Di/Dc)-0.25 (θ)-0.24 (Lc/Dc)0.22 Page A-8

Appendix A2

(A2.10)


Appendix A


Here Kw1 and Kv1 are constants also depending on feed solids characteristics. The current data indicate that Kw1 and Kv1 are independent of cyclone diameter for geometrically similar cyclones treating identical feed solids. Small quantities of viscosity modifiers such as clay, can have a marked effect on these variables.

Efficiency Curve Relationship

The efficiency curve used in this model is given below:

Eo(d/d50c)=C⋅(1+β⋅β*⋅d/d50c) (exp(α) - 1)/(exp(α⋅β*⋅d/d50c) + exp(α) - 2)

(2.11)

When β is 0, β* is 1 the above equation reduces to Eo(d/d50c)=C⋅(exp(α) - 1)/(exp(α⋅d/d50c) + exp(α) - 2)

(A2.12)

The shape parameter β determines the initial rise, while α determines the slope at larger values of d (d≈d50c). Both α and β are normally constant for given feed solids, while C and d50c vary with cyclone dimensions and operating conditions. The parameter β* is determined, for given values of α and β, by the condition that Eo(1) = C/2

(A2.13)

β* is calculated iteratively in the model. Figures A2.1 and A2.2 show the effects of α and β on the shape of the efficiency curve. Modified Efficiency Curve

An alternative to the standard efficiency curve is available with the Nageswararao Fines hydrocyclone model. With this model the user can specify the value of the reduced efficiency curve (ie. fraction reporting to overflow) at 33% and 66% of the d50c size. The curve is fixed (by definition) at the 100% point for zero size and at the d50c. A cubic spline curve is used to describe the efficiency curve for sizes below the d50c point. For sizes larger than the d50, a log-normal distribution curve is used. The lognormal curve is determined so that there is no discontinuity in slope at the d50c point. Figure A2.3 below shows how the modified efficiency curve works. The user needs to specify (or model fit) the values of the curve at 33% and 66% of the curve only.


Appendix A2

Page A-9


Appendix A

The other parameters used by the model are used in the same way as the standard Nageswararao model. The Nageswararao-Fines model is useful for describing asymmetric efficiency curves where a long 'tail' exists for either coarse or fine material.

Interactions

The interactions of variables within a cyclone are complex. Refer to section A2.7 (Summary Table) for a summary of interaction dependencies.

Scaling

Facilities for scaling the operation of the hydrocyclone are built into the model.

100

% of Feed to Overflow (corrected)

Increasing Alpha 80

60

40

20

0 0.00

0.50

1.00

1.50

2.00

2.50

d/d50 (corrected)

Figure A2.1: Effect of α on Reduced Efficiency Curve

Page A-10

Appendix A2


Appendix A


180


160

Increasing Beta

140 120 100 80 60 40 20 0 0.00

0.50

1.00

1.50

2.00

2.50

d/d50 (corrected)

Figure A2.2: Effect of β on Reduced Efficiency Curve

180


160 140

Efficy. curve at 0.33xd50c

120 100

Efficy. curve at 0.66xd50c

80 60 Efficy. curve at d50c 40 20 0 0.00

0.50

1.00

1.50

2.00

2.50

d/d50(corrected) Figure A2.3:


Efficiency curve used in the Nageswararao-Fines Model

Appendix A2

Page A-11

Hydrocyclone (Model 200, 201) A2.3

Appendix A

Hydrocyclone Model Printout (Nageswararao) (Model 200)

Hydrocyclone Model Printout (Nageswararao - Fines) (Model 201)

Page A-12

Appendix A2


Appendix A

Hydrocyclone (Model 200, 201) A2.4 Symbol

Symbols Meaning

α

reduced efficiency curve sharpness parameter

β

reduced efficiency curve hook parameter

β*

reduced efficiency curve calculated parameter

C

100 - Rf or recovery of water to overflow, %

Dc

cyclone diameter, m

Di

diameter of circle with the same area as cyclone inlet, m

Do

diameter of circle with the same area as vortex finder, m

Du

diameter of circle with the same area as spigot, m

Eo(d) percentage of feed material of size d reporting to overflow g

gravitational acceleration

KD

constant in the classification size relationship

KQ

constant in the volume pulp recovery relationship

Kv

constant in the volume pulp recovery relationship

Kw

constant in the water recovery relationship

Lc

length of cylindrical section, m

P

feed pressure at inlet, kPa

Q

cyclone throughput, m3/hr

Rf

recovery of water to underflow, %

Rv

volumetric recovery of feed pulp to underflow, %

d

mean size of particle, mm

d50c

size of a particle in feed which has equal probability of going to underflow or overflow, due to centrifugal action, mm

Cv

volumetric fraction of solids in feed slurry

λ

101.82Cv/ (8.05 ∗ (1.0 − Cv)2)

ρp

density of feed pulp, tonnes/m3

θ

cone full angle, degrees


Appendix A2

Page A-13


Appendix A

Known Restrictions

•

As the feed becomes coarser, d50c tends to decrease even when all the other variables are kept constant. The effect of size distribution of the feed material becomes insignificant when the feed consists of mainly –53 µm particles, and also when the proportion of –53 µm particles is less than 25% of the feed solids.

•

The analytic form used does not provide a perfect representation for the reduced efficiency curve. As a result the model often tends to predict fewer coarse particles in the overflow than occur in real operation, however, the magnitude of the error is considered to be small.

•

Viscosity variations due to changes in pulp density are largely accounted for by the model. Viscosity variations caused by variable quantities of slimes affect the parameters in quite a systematic way.

•

As viscosity (or slimes fraction) increases, the cut size becomes coarser, the water split to overflow is reduced, and the cyclone pressure drop becomes larger. However, the reduced efficiency curve remains relatively constant until the onset of roping.

•

The model may be used to estimate operation during roping:

•

–

the cut size will become 5 to 10 times larger (ie. multiply KD0 by 5 to 10 times

–

the efficiency curve will become an “inefficiency” curve with an α value typically of 0.1 - 0.2.

–

water split and pressure drop are relatively unaffected although a small drop in pressure is often claimed. This may result from a reduced volume of solids to overflow.

The onset of cyclone roping is difficult to predict. In general 50% solids by volume is a practical underflow limit. However, very coarse underflow may achieve higher density and finer ones somewhat lower density as detailed below. JKSimMet will warn you that roping is likely if either of the density limits (detailed below) are exceeded.

Page A-14

Appendix A2


Appendix A

Cyclone Roping Constraint


If the cyclone feed density is less than 35% solids by volume, the SPOC constraint (Laguitton 1985) is claimed to predict onset of roping. Vol % solids in U/F = Limiting Vol % solids (~56) + 0.2 (Vol % Solids in Feed -20) The limiting % solids is defined as the onset of roping at a volumetric feed density of 20%. In tabular form: Feed Underflow Density Density % by Volume 5 10 15 20 25 30 35

Empirical Constraint

53 54 55 56 57 58 59

at sg 2.7 Feed Underflow Density Density % by Weight 12.4 23.1 32.3 40.3 47.4 53.6 59.2

75.3 76.0 76.7 77.5 78.2 78.8 79.5

at sg 4.0 Feed Underflow Density Density % by Weight 17.4 30.8 41.4 50.0 57.1 63.1 68.3

81.8 82.4 83.0 83.6 84.1 84.7 85.2

Industrial experience demonstrates that a coarse underflow will remain in spray discharge at a higher density than a fine underflow. This is intuitively reasonable in terms of slurry viscosity but difficult to predict. Plitt et al (1987) have developed an empirical relationship based on Lynch (1965) data and others. - 50% passing U/F size µm   Vol % Solids in U/F = 62.3 1 - exp ( ) 60   This approach puts a 50% solids by volume limit on an underflow with 50% passing 100 µm and 60% at a P50 of around 200 µm. This function decreases sharply with size dropping to 45% solids by volume at a P50 of 80 µm and 40% at a P50 of 60 µm.


Appendix A2

Page A-15


Appendix A

In tabular form: Roping onset Underflow % Solids by Vol. 50% passing (µm) 35.2 50 39.0 60 45.9 80 50.5 100 53.9 120 58.6 170 60.0 200 61.3 250

% Solids at sg 2.7 59.4 63.3 69.6 73.4 75.9 79.3 80.2 81.0

% Solids at sg 4.0 68.5 71.9 77.2 80.3 82.4 85.0 85.7 86.4

The two effects are probably competitive to some degree. Further, each operation has a 'comfort limit' on cyclone underflow density which may be a good deal lower than the above limits.

A2.6

Summary Table SUMMARY OF THE EFFECTS OF VARIABLES ON CYCLONE OPERATION

Variable

Resultant effect on parameter

Increased

Q

d50c

Rf

Rv

Dc

increase

(.57) increase

(.82)

decrease

(-.4)

decrease

(-.55)

Di

increase

(.45) decrease

(0.5)

decrease

(-.5)

decrease

(.25)

Do

increase

(.68) increase

(.52)

decrease (-1/19)

decrease

(-.94)

Du

--

(-.47)

increase

(2.4)

increase

(1.83)

Lc

increase

(.2) increase

(.2)

increase

(.22)

increase

(.22)

p

increase

(.5) decrease

(-.22)

decrease

(-.53)

decrease

(-.31)

λ

--

increase

(.93)

increase

(.27)

--

ρp

decrease

(-.5) increase

(.22)

increase

(.53)

increase

(.31)

θ

decrease

(-.1) increase

(.15)

decrease

(-.24)

decrease

(-.24)

decrease

Note: The numbers listed in brackets are exponents for dependence of the parameter on the variable.

Examples of the effects of α and β on reduced efficiency curves are given in the attached Figures A2.1 and A2.2. The β* parameters used in the model are calculated.

Page A-16

Appendix A2


Appendix A

Hydrocyclone (Model 200, 201) A2.7.1

Fitting the Cyclone Model (200) PARAMETER MENU

Pressure Data

If you wish to predict cyclone pressure accurately at other conditions you will need at least one accurate pressure measurement and a set of at least two out of three of the feed, underflow and overflow samples. If pressure data are not available, an approximate pressure can be estimated from the manufacturers published data. The calculated pressure is used in the equations for classification size and recovery to underflow. Hence, the cyclone pressure is an important measurement. The measured or assumed pressure data must be entered on the Performance Data tab of the cyclone equipment data window. If an accuracy estimate is available, use it to calculate the standard deviation. If not, use 10% of the pressure value. The capacity constant KQO can be calculated from the cyclone flowrate and the cyclone dimensions. (Refer to equations A2.1A2.3). Typical values of KQO are in the range 300-600. The scale factor for fitting should be 100. To make the pressure observation available to the fitting calculation, it must be selected with a tick on the Equipment Data tab of the Model Fit dialogue window.

Classification Size (KDO)

Equations A2.4 to A2.6 define the cut size. KDO is typically a small number - say 0.001 to .00001. Therefore, a scale factor of 0.0001 is usually suitable.

Water Split % to The actual water split to overflow (Cal WS) is fitted rather than the two parameters, KV1 and KW1, which are defined by a single O/F (Cal WS) water split. When model fitting a single set of cyclone data, ALWAYS fit Cal WS. A good starting point is 50% with a scale factor of 5. After fitting, the calculated values of KV1 and KW1 are displayed on the cyclone equipment data window (Model Parameters tab). Version 5.1 November 2001

Appendix A2

Page A-17

Hydrocyclone (Model 200, 201) Efficiency Curve (α α and β)

Appendix A

The reduced efficiency curve is an "S" shaped function as shown in Figure A2.1. Typical values of a α range from 0.5 to 4. Beyond 5, the efficiency curves become very sharp and larger numbers are not significant. A good initial estimate is 2.0. The β factor modifies the "S" curve to add an additional "hook" - or a negative portion to the actual efficiency curve. A typical value is zero. However, a poor fit at fine sizes can be tested by trying values of β of 0.01 to 0.5. Fitting of β is available but not recommended. A scale factor of 0.1 is suitable once a good initial estimate has been found by trial. If the efficiency curve is a poor fit at coarse sizes, try the alternative fines modified or spline efficiency curve models.

Master/Slave Fitting

Multiple sets of cyclone data can be model-fitted using the Master/Slave facility, with one important provision. The water split (Cal WS) cannot be fitted using Master/Slave fitting. Fit KD0, KQ0, α and Cal WS for each data set independently, and determine the average values of KV1 and KW1 for each cyclone data set from the fit. Use the average values of KV1 and KW1 in each cyclone data set. Use Master/Slave to fit KD0, KQ0, α and (if required) β, over all data sets.

A2.7.1

Fitting the Nageswararao Fines Model (201) PARAMETER MENU

The comments in A2.7.1 above apply equally to Model 201 except for the Efficiency Curve parameters α and β which are replaced by Eff @ 0.33 (of d50c) and Eff @ 0.66 (of d50c). Typical values are 0.85 and 0.65 respectively.

Page A-18

Appendix A2


Appendix A


References

DE KOOK, S.K., 1956, Symposium on recent developments in the use of hydrocyclones - a review J. Chem. Metal. Min. Soc. S.Afr., Vol. 56:281-294. KAVETSKY, A., 1979. Hydrocyclone modelling and scaling. JKMRC report to AMIRA, November. KELSALL, D.F., 1953. A further study of the hydraulic cyclone. Chem. Eng., Sci., Vol. 2:254-273. LAGUITTON, D. (Ed), 1985. The SPOC Manual Simulated Processing of Ore and Coal, CANMET EMR Canada, Ch. 5.1 (Part B). LYNCH, A.J. 1965. The characteristics of hydrocyclones and their application as control units in comminution circuits, AMIRA Progress Report No. 6, University of Queensland (unpublished). LYNCH, A.J. and RAO, T.C., 1965. Digital computer simulation of comminution systems. Proc. 8th Comm. Min. Metall. Congr., Aust., N.Z., Vol. 6:597-606. NAGESWARARAO, K., 1978. Further developments in the modelling and scale-up of industrial hydrocyclones. Ph.D. Thesis (unpublished). University of Queensland. PLITT, L.R., FLINTOFF, B.C. and STUFFCO T.J., 1987. Roping in hydrocyclones. 3rd International Conference on Hydrocyclones, Oxford England, Elseveir, pp21-23. YOSHIOKA, N. and HOTTA, Y., 1955. Liquid cyclone as a hydraulic classifier. Chem. Eng. Jpn., Vol. 19:632-640.


Appendix A2

Page A-19


Appendix A

(Blank Page)

Page A-20

Appendix A2


Appendix A

Single Deck Screen (Model 230) A3

Single Deck Screen (Model 230)

A3.1

Model Description

Mechanistically a screening process can be regarded as a series of trials, as a result of which particles of a particular size have a probability of entering the fine product. This concept of defining the screening efficiency in terms of a number of trials (or bounces) is the basis for a screen model. A typical efficiency curve for a vibrating screen is shown in Figure A3.1. There are three regions on the curve:

A

B C

Particle Size Figure A3.1 :A Typical Efficiency Curve for a Vibrating Screen

the region describing the above-aperture size material (region A), • the region describing the below but near aperture size material in which the probability of passing through the aperture is directly dependent on particle size (region B), • the region describing the ultra-fines that adhere to the coarse particles (region C). •

Region B of the efficiency curve is the important region for modelling purposes, and it can be described by the equation (Whiten and White 1977). E(x) = exp[-TRN.fo.(1-x/d)k]

(A3.1)

where E(x) is the fraction of particles in the feed of size x which enter the coarse product, d is the screen aperture; fo the fraction open area, TRN is the efficiency parameter and k is a minor parameter used for precise fitting purposes. Typically, the value of k is about 2. The performance of the screen in region C can only be determined experimentally since it will be dependent on local Version 5.0 December 1999

Appendix A3

Page A-21


Appendix A

conditions such as the moisture content of the ore which causes small particles to adhere to large particles. For design purposes it is necessary to make a reasonable assumption about the shape of the curve in region C and this assumption is made by the design engineer based on knowledge of local conditions. The typical dependence of the efficiency parameter, TRN, which is analogous to the number of trials, on the feed rate is shown in Figure A3.2 for different materials used for the screen deck.

100

Steel 10

Rubber 1.0 0

F W1

FW2

High

Feed Rate/Unit Width Figure A3.2: The dependence of the screen efficiency parameters on the feed rate for rubber and steel decks.

The explanation of Figure A3.2 is that when the feed rate to screens with rubber decks is low the particles move independently, accumulate energy, take large bounces and have little opportunity to pass through the screen aperture. An increase in feed rate causes an increase in inter-particle collisions, reduction in particle energy and bounce lengths, and an increase in number of trials. Hence, the screen efficiency increases. A further increase in feed rate causes more particle interference, a decrease in the number of trials due to particles not reaching the screen surface, and a decrease in screening efficiency. With steel screens, however, the coefficient of restitution is low and particles do not accumulate energy. Particle bounces are small and high efficiencies occur at low feed rates. As the feed rate increases the inter-particle interference increases and this reduces the number of trials and the screening efficiency.

Page A-22

Appendix A3


Appendix A Model Limitations

Single Deck Screen (Model 230) A better understanding is required of the relationship between particle shape, aperture shape and screen efficiency, and also of screening performance in the difficult area between dry and wet screening. The first is a problem of optimization of existing screens, the second is a problem of plant operation.

A3.2

Model Equations

Region B (Figure A.3.1) is described by equation 1. E(x) = exp (- TRN * P/T)

(A3.2)

where P = fo*((1-fs) (1 - x/d)2 + fS*(1 - x/d))T

(A3.3)

and fS = 1 - (W/L)

(A3.4)

In region A E(x) = 1.0

(A3.5)

In region C an adjustment is made using the submesh factor (SF). This adjustment transfers some of the submesh material in the undersize stream to the submesh fraction of the oversize stream, that is to account for the small particles that adhere to the larger ones. The important operating parameter is feed rate per unit screen width (FW) and this function is approximated by several straight lines as shown in Figure A3.2. The number of trials TRN is related to operating parameters by a set of regression equations of the following form. Ln(TRN) = A + B * FW + U * P1 + V * P2 FW
(A3.6)

Ln(TRN) = C + D * FW + U * P1 + V * P2 FW1
(A3.8)

and Ln(TRN) = C + D * FW2 + U * P1 + V * P2 FW>FW2

(A3.9)

SF is also related to operating parameters by a regression equation SF = E + F * PSF + G * TSF


(A3.10)

Appendix A3

Page A-23

Single Deck Screen (Model 230) Fines Factor

Appendix A

The fines factor is used to describe the "piggyback" effect of fines on coarse material. The material coarser than the "fines critical size" is considered in terms of its notional surface area. n

Vol i Area of particles α ∑ (x i + x i+1 ) / 2 i and SF* Area is the t/h of fines which are carried into the oversize product.

Moisture Behaviour

For damp ores, the behaviour of moisture can be very important. There are sometimes several kinds of moisture. The only one of interest to this model is in the fines, that is, fractions finer than the "Moisture Split Critical Size XM". All of the feed moisture is assumed to be carried in material finer than this size. It is then allocated across the coarse and fine products in proportion with how the material finer than XM is allocated.

Scaling

The model allows scaling of screen length by linear scaling of the number of trials parameter, TRN. Scaling of screen width is accomplished within the normal model structure as FW is feed rate per unit width. Aperture, fraction open area and slot shape are also included as normal model parameters.

Page A-24

Appendix A3


Appendix A

Single Deck Screen (Model 230) A3.3


Single Deck Model Printout showing Default Parameter Values

Appendix A3

Page A-25

Single Deck Screen (Model 230) A3.4 Symbol

Appendix A

Symbols Meaning

xi

size of particles in the ith size fraction

E(x)

fraction of particles in the feed of size x which enter the coarse product

X1,X2

lower and upper screen sizes at fraction being considered

X3

a critical size - if required - close to screen aperture. However V is usually zero

X4

sub-mesh screen size, i.e., the smallest sieve in the series

TRN

efficiency parameter (number of bounces or trials)

fo

fraction open area

T

total area of screen

W

width of apertures

L

length of apertures

fs

fraction slot = 1-(W/L)

d

maximum size of particle than can pass through the screen, ie. aperture size

FW

solids feed rate/unit width of screen

P1

% of feed of size x such that X1
P2

% of feed < size X3

SF

submesh factor

PSF

% of feed < size X4

TSF

tonnes/hour feed of size , X4

XF

fines factor critical size

XM

moisture split critical size

A

Regression constant

B

"

C

"

D

"

E

Page A-26

Regression constant

F

"

G

"

U

"

V

"

Appendix A3


Appendix A


Known Restrictions

Accurate application of the screen model requires data from the screen to be simulated for parameter fitting. For simulation of screens for which data are not available, data for a similar screen type with similar feed may be used. Using data from operations with markedly different screens or feeds will not provide useful results. The same square root of two series of screen sizes should be used for both fitting and simulation. The regression equations of the screen model make it quite complex and more difficult to handle than most JKSimMet models. For most processing plants only the tonnage dependence is required. That is the values of U and V can be left at zero. For wire mesh screens often equation A3.5 is adequate on its own. Where there are large variations in the fitted submesh factor (SF) try the dependencies of equation A3.9 as detailed in Sub Mesh Factor Modelling. However, a constant SF is often adequate. In a situation where you really want to tune a screen and are prepared to collect a lot of accurate data, contact JKTech for assistance with the parameter and regression fitting.


Appendix A3

Page A-27


Appendix A

Parameter Fitting the Screen Model

PARAMETER MENU Ap Length Ap Width OA % A int (TRN) B*FW (TRN) D*FW (TRN) U*P1 (TRN) U*P2 (TRN) E int (FF) F*PSF (FF) G*PSF (FF) XF XM

The basic concept of a number of trials is quite simple. However, the extensive correction factors and sectionalised curves make this quite a difficult model to fit. The Model Fitting program can process only one set of flowsheet data at a time. However, one flowsheet may contain many measured sets of screen data. Clearly, the flowrate and near size dependencies require several sets of data to define the curves shown in Figure 2. To describe any particular set of screen data, only a number of trials TRN (parameter 22) and a submesh factor SF (parameter 23) need to be found. Good initial estimates for these parameters are 5 and 0.1 respectively. However, both TRN and SF are calculated variables in this model. Therefore, we need to fit them as regression parameter A (Ln TRN) and regression parameter E with FW1 set to a larger value than any anticipated screen feed rates per unit of width and with B, V, U, D, F and G all set to zero.


Master/Slave model fitting allows the secondary dependencies on the parameter menu to be established when multiple sets of data are available. Setting up Master /Slave fitting is detailed in section 5.6.5. Parameter dependencies are discussed in A3.7. However, fitting of multiple data sets is complex and assistance from JKTech consultants is strongly recommended if you intend to tackle this aspect of the fitting process.

Aperture Length and Width

Where screen data do not provide precise aperture and wire dimensions, the screen aperture can be fitted to the data. Note that for slotted screens, effective aperture length depends on the shape of the particle because the size data are measured using square mesh screens.

Page A-28

Appendix A3


Appendix A Selection of feed size parameters X1 to X4

Single Deck Screen (Model 230) Screen performance can be affected by the feed size distribution. This is usually a secondary dependence compared with feed rate. However the model does allow it to be incorporated. X1 and X2 are the upper and lower sizes of a critical size fraction (or fractions). If a particular range of sizes in your feed data is highly variable use X1 and X2 to bracket it. Set X3 to the screen aperture; or the average screen aperture, if you are going to fit several screen mesh sizes. Set X4 to say - 2 or 3 times the submesh top size. The finer part of a size distribution has most of the surface area and will tend to dominate surface carryover. Traditional screen design techniques relate a different “fines factor” to half of the screen aperture. You can use X3 set to half the screen aperture to approximate this dependence if there are large variations in fines in the feed. Similarly, a traditional approach would use a “near size” dependence of aperture size to half aperture size and X1-X2 can be set to estimate this dependence.

A3.7 Trials versus Feedrate

Regression Model Parameters

This is the important dependence. Fit each of the data sets available. This will give you a set of TRN values at each fitted feed rate. You may also have a set of fractions between P1 and P2 at each TRN value. The next step is to plot up (TRN) versus feedrate. Any graphing package eg MS Excel, can be used. Select FW1 and FW2 to let you describe the curve accurately in three sections. An alternative method is to print out your graph (with a full grid) and rule on several line sections to suit. Their slopes and intercepts will provide B and A and D and C respectively. A multiple linear regression program can also be used - if you are adept with such programs. Most spreadsheet programs (eg. Lotus, MS Excel) have built-in multiple linear regression functions).

Critical Size Dependencies

If your Trials (TRN) versus feedrate data are erratic and your data are a good fit (less than 2 stream SD with Whiten weights), then it is worth trying P1 and P2 dependencies. Use a multiple linear regression program to fit ln (TRN) against feedrate, P1 and P2 and divide into separate data sets using your estimates of FW1 and FW2.


Appendix A3

Page A-29


Appendix A

You can impose the continuity constraint by correcting equations 6 and 8 Ln(TRN) values by equation 7. If you have a constrained non-linear fitting program which can handle multiple equations, you can fit FW1 and FW2 as well. However, you will need lots of good data. Submesh Factor Modelling

This is the other important dependence. For many operations, SF is small and more or less constant. However, for operations with damp ore, it can be crucial to a good model. Once again, plot your best fit SF values against the calculated PSF and TSF values from the parameter screens and draw a linear regression line against any one variable. Print out the graph with a fine grid for this slope (for G) and the intercept E. points.

Running the Screen Model

Input your estimated values back into the screen menu and import to each of your data sets. Try a simulation and check agreement on product streams. Expect to make errors in this procedure the first few times.


For up to 10 data sets, Master/Slave fitting provides an excellent way of estimating these dependencies for good data. You can add secondary dependencies one at a time to test for a significant reduction in the sum of squares. Hint : Only the undersize and a flowrate is needed for a full screen fit.

A3.8

References

WHITEN, W.J. and WHITE, M.E., 1977. Modelling and simulation of high tonnage crushing plants, XII International Mineral Processing Congress, Brazil, Volume II, 148-158. WHITEN, W.J., 1984. Models and control techniques for crushing plants, Control 84, Mineral/Metallurgical Processing, (Editor, J A Herbst), Publishers - AIME, New York, 217225.

Page A-30

Appendix A3


Appendix A

Efficiency Curves (210, 610, 211, 611, 203) A4

Efficiency Curves (Models 210, 610, 211, 611, 203) (General Classifier Models)

A4.1

General Model Description

These models (210, 211, 203) use simple efficiency curves to describe the operation of any classification device. They are also provided as some of the optional models for the flotation cell and flotation column (610, 611). For these two flotation devices, the concentrate is the coarse stream.

A4.2

Simple Efficiency Curve (210, 610)

A4.2.1

Model Description

The model is simply an efficiency curve with a fixed d50c and a fixed water split to fine product. Refer to Figures A2.1 and A2.2 of the Hydrocyclone model for efficiency curve shapes. A typical DSM screen has an α value of 4 and a β value of 0. The model can be used to approximate many classifiers. Therefore the default parameter values should be used with caution.

A4.2.2 Efficiency Curve Relationship

Model Equations

The efficiency curve used in this model is given below: Eo(d/d50c) = C⋅(1+(β⋅β*⋅d/d50c)) (exp(α) - 1) / (exp(α⋅β*⋅d/d50c) + exp(α) - 2) When β is 0, β* is 1 and the above equation reduces to: Eo(d/d50c) = C⋅(exp(α) - 1) / (exp(α⋅d/d50c) + exp(α) - 2) The shape parameter β determines the initial rise, while α determines the slope at larger values of d (d ≈ d50c). Both α and β are normally constant for given feed solids. The parameter β* is determined, for given values of α and β, by the condition that: Eo(1) = C/2 β* is calculated iteratively in the model. C is the fractional water split to the fine product.

Scaling

This form of the model does not permit scaling.


Appendix A4

Page A-31

Efficiency Curves (210, 610, 211, 611, 203) A4.2.3

Appendix A

Efficiency Curve Model (210) Printout (with default values)

A4.3

Simple Efficiency Curve - Water and Fine (Model 211, 611)

A4.3.1

Model Description

The model is also a simply an efficiency curve with a fixed d50c as described above for Model 210 with the added feature of allowing the fines and water splits to be different.


Model Equations

The efficiency curve used in this model is the same as that described in A4.2.2 above except that C (fractional water split to fine product) is replaced in the equations with a separate parameter F (fractional split of fines to fine product): Eo(d/d50c) = F⋅(1+(β⋅β*⋅d/d50c)) (exp(α) - 1) / (exp(α⋅β*⋅d/d50c) + exp(α) - 2) When β is 0, β* is 1 and the above equation reduces to: Eo(d/d50c) = F⋅(exp(α) - 1) / (exp(α⋅d/d50c) + exp(α) - 2) The shape parameter β determines the initial rise, while α determines the slope at larger values of d (d ≈ d50c). Both α and β are normally constant for given feed solids. The parameter β* is determined, for given values of α and β, by the condition that: Eo(1) = F/2 β* is calculated iteratively in the model. F is the fractional fines split to the fine product. The water split is calculated directly from C, the fractional water split to fines product.

Page A-32

Appendix A4


Appendix A

Scaling

Efficiency Curves (210, 610, 211, 611, 203)


A4.3.3


A4.4

Splined Efficiency Curve (Model 203)

A4.4.1

Model Description

The model is also a simply an efficiency curve but the analytic form of the curve used in Models 210 and 211 is replaced by a four knot spline curve.


Scaling

Model Equations

The efficiency curve in this model is provided by specifying four pairs of coordinates through which a smooth curve (piecewise cubic spline function) is constructed. Fine end of the curve is specified by the water split as in Model 210.



Appendix A4

Page A-33

Efficiency Curves (210, 610, 211, 611, 203) A4.4.3

Appendix A


A4.5

Symbol

Symbols Equivalent JKSimMet parameter

Meaning

α

Reduced efficiency curve sharpness Alpha parameter.

β

Reduced efficiency parameter.

curve

dip

β*

Parameter for describing reduced efficiency curve.

the

C

Water split to fines product.

F

Fines split to fines product FI%Fines Size of particle in the feed which has equal probability of going to D50c fine or coarse product.

d50c

A4.6

Beta Beta* WS%Fines

Known Restrictions

Range of Validity The highly simplified form of these models means that extrapolation away from the conditions at which the parameters were determined will significantly decrease the accuracy. If a wide range of data is available, it may be possible to use Model 251 (see Appendix A5) which has a variable cut point. Page A-34

Appendix A4


Appendix A

Efficiency Curves (210, 610, 211, 611, 203) A4.7

Fitting the Efficiency Curve Models

A4.7.1

Fitting the Simple Efficiency Curve Model (210, 610)

PARAMETER MENU

This is a simple model to fit as it has no scaling capabilities. Fit the water split, alpha and d50c. See the comments regarding fitting Beta in the cyclone model description (Appendix A2). For DSM Screens, initial estimates of 4 for alpha and 50% for the water split should be adequate for most data sets. An initial d50c estimate of half of the actual screen aperture is appropriate.

A4.7.2

Fitting the Simple Efficiency Curve Model – Water and Fine (211, 611)

PARAMETER MENU

This also is a simple model to fit as it has no scaling capabilities. Fit the water split, the fines split, alpha and d50c. See the comments regarding fitting Beta in the cyclone model description (Appendix A2).

A4.7.3

Fitting the Splined Efficiency Curve Model (203)

PARAMETER MENU

This also is a simple model to fit as it has no scaling capabilities. Fit the water split and the four efficiency values at the knots on the Version 5.1 November 2001

Appendix A4

Page A-35

Efficiency Curves (210, 610, 211, 611, 203)

Appendix A

spline curve. It is important to remember to set the size values for the knots before attempting model fitting. Even though it seems incorrect, it is possible for the fitted efficiency values to be greater than 1 or less than 0. Sometimes, model fitting arrives at values at the ends of the curve which are outside the 0 – 1 range in order to achieve the best shape for the curve inside the 0 – 1 range. This is due to the properties of the spline curve for which the values at the ends of the curve have an effect on the shape of the curve in the centre region. The simulation model code truncates the efficiency values to be less than 1 and greaster than 0. The combination of these two features, control of the shape of the centre of the curve and truncation at 0 and 1 ensures that the model predictions are sensible.

A4.8

References

LYNCH, A.J., 1977, Mineral Crushing and Grinding Circuits. (Elsevier, Amsterdam) pp. 124-126.

Page A-36

Appendix A4


Appendix A

Efficiency Curve Variable D50c (Model 251) A5 A5.1

Efficiency Curve Variable D50c (Model 251) Model Description

This model is an extension of the Efficiency curve (Fixed D50c) model to include a regression relationship for d50c. The water split to the fine product remains fixed.

A5.2 d50c Relationship

Model Equations

For normal operation the classification size d50c can be related to the operating variables according to the equation: Log10 (d50c) = W * log10 (SW) + X * FW * C / 100 + Y * FPS + Z . . .(A5.1)

Efficiency Curve Relationship

The efficiency curve used in this model is given below: Eo(d / d50c) = 100.C.(1+(β.β*.d / d50c)) (exp(α) - 1) / (exp(α.β*.d/ d50c) + exp(α) - 2)

(A5.2)

When β is 0, β* is 1 and the above equation reduces to: Eo(d/d50c) = 100.C.(exp(α) - 1) / (exp(α.d / d50c) + exp(α) - 2) . . . (A5.3) The shape parameter β determines the initial rise, while α determines the slope at larger values of d (d close to d50c). Both α and β are normally constant for given feed solids. The parameter β * is determined, for given values of α and β, by the condition that: Eo(1) = 100⋅C / 2 β* is calculated iteratively in the model.

Scaling



Appendix A5

Page A-37

Efficiency Curve Variable D50c (Model 251) A5.3

Efficiency Curve Variable D50c Model Showing Default Values

A5.4

Symbols

Symbol

Page A-38

Appendix A

Meaning

α

reduced efficiency curve sharpness parameter

β

reduced efficiency curve dip parameter

β*

reduced efficiency curve calculated parameter

W,X,Y,Z

regression constants in the d50c equation

d50c

size of particle in the feed which has equal probability of going to fine or coarse product

C

% water split to fine product

SW

slot width (mm)

FW

volume flow rate of water in the feed (m3)

FPS

% solids in the feed

Appendix A5


Appendix A

Efficiency Curve Variable D50c (Model 251) A5.5

Known Restrictions

As Model 251 is based on a regression equation, extrapolation beyond the scope of the data used in the regression will decrease accuracy significantly. Effect of the log relationship

The relationship between D50c and Slot Width is defined in Log space. This means that the multiplier coefficient W will have a different effect for slot widths less than and greater than 1.0 mm. For slot widths less than 1.0 mm a multiplier greater than 1 will make the calculated D50c value smaller than the slot width. However, for slot widths greater than 1.0 mm, the effect is reversed.This can cause unexpected results when changing slot width.

Screen Wear

DSM screens are sensitive to wire wear condition. The screens are usually reversed on a regular basis. If possible, test data should record the wear condition. If this is not possible, test at both new and worn to obtain a range of likely operation.

A5.6

Fitting

PARAMETER MENU W * Slot X * FPS Y * FdWater Z (int) Sharpness α Dip β C

This is a simple model to fit as it has no scaling capabilities. Fit the water split, α and d50c. See the comments regarding fitting β in the cyclone model description (Appendix A2). Initial estimates of 4 for α and 50% for the water split should be adequate for most data sets. An initial d50c estimate of half of the actual screen aperture is appropriate.

Multiple Data Sets

If the data cover a range of feed rates, feed percent solids, slot widths and screen widths, proceed as follows: •

Fit each data set for α, C and d50.

•

Refit with average α and C set constant. That is, force all the variation into the cut size.

•

Use Master/Slave fitting to fit the separation size equation (A5.1) for W, X, Y and Z.


Appendix A5

Page A-39

Efficiency Curve Variable D50c (Model 251)

Appendix A

Note: If the slot width does not have a strong effect on d50c, then the data are very questionable.

A5.7

References

LYNCH, A. J., 1977, Mineral crushing and grinding circuits, (Elsevier, Amsterdam), pp 124-126.

Page A-40

Appendix A5


Appendix A

Crusher (Model 400/405) A6

Crusher (Models 400 and 405)

A6.1 Model Description (Andersen/Awachie/Whiten) The crusher model considers the crushing process as two components: • •

Selection

the selection of particles for breakage, and the breakage of the particles so selected.

Clearly, whether or not a particle is selected will depend principally upon its size relative to the closed-side setting (CSS) of the crusher and the extent of choke feeding. The size distribution of the daughter products of breakage will depend principally upon the initial size of the particle and upon its physical properties. New feed entering the crusher is classified (or selected). Some material, predominantly the finer fraction, bypasses the breakage process entirely and reports directly to the product. The remainder is broken, and the daughter fragments are then recycled to the classification step. The new fine fraction exits via the product, and the coarser material is rebroken.

Perfect Mixing Model

If we think of a crusher as a stagewise breakage process, then we can model it in terms of a steady state balance.

f

x

Classification Function

p

Appearance

A*C*x

Function

C*x

Figure A6.1: Schematic representation of the crusher model

A schematic representation of the crusher model is given in the above figure. Mass balance equations may be written about each node as: x = f + ACx (A6.1) x = p + Cx Version 5.1 February 2003

(A6.2) Appendix A6

Page A-41

Crusher (Model 400/405) where

Appendix A

x

is a vector representing the amount in each size fraction in the crusher

f

is the feed size distribution vector

p

is the product size distribution vector

C

is the classification function, a diagonal matrix describing the proportion of particles in each size interval entering the crushing zone

A

is the appearance function, a lower triangular matrix giving the relative distribution of each size fraction after breakage.

Combining (A6.1) and (A6.2) results in the Whiten crusher model equation: p = ( I - C ) * ( I - AC ) -1 * f

(A6.3)

where I is the unit matrix.

Since the feed and product are expressed as size distributions, and the properties of the internal classification and breakage mechanisms are expressed with respect to particle size intervals or mean sizes, it is convenient to represent these quantities as vectors and matrices respectively. Since f is known and p is the desired output, the problem resolves itself into obtaining estimates of C and A for a particular machine and feed material. These values can then be manipulated by simulation to explore the effects of changing machine parameters, material characteristics or operating conditions upon the product size distribution. An important limiting factor in crusher operation is the power drawn by the machine. This model permits estimates of power draw to be made for a given condition, so that the simulations can be constrained by power requirements (by the user). The power draw can be normalised to experimental data or estimated from data for similar crushers in the Supplementary Parameters Manual. Note: a single particle breakage test of the ore is required for either type of power estimate.

Page A-42

Appendix A6


Appendix A

Crusher (Model 400/405) A6.2

Model Equations

p = (I - C) * (I - A * C)-1 * f Selection

Where C is the classification function (a diagonal matrix) and where C(x) is the probability of selection for breakage of a particle of size x and is defined as: C(x) = 1 (A6.4) for x > K2 i.e. all particles are broken  K2 - x K3 C (x) = 1 -  K - K   2 1

(A6.5) for K1 < x < K2

C(x) = 0 (A6.6) for x < K1 i.e. no particles are broken (x = mean particle size) An example of the classification functions is given in Figure A6.2. 1.0 K3

0.0 K1

K2 Particle Size x

Figure A6.2 - Classification function, C

The model equations are developed by non-linear regression analysis of survey data collected over a wide range of operating conditions, followed by multiple linear regression of the fitted parameters against the operating conditions. The general form of these relationships is: K1 = A0* Crusher gap - A1 * Throughput + A2* Feed coarseness K2 = B0* Crusher gap - B1 * Throughput + B2* Feed coarseness K3 = C0 (generally held constant at a value of 2.3) Version 5.1 February 2003

Appendix A6

Page A-43

Crusher (Model 400/405)

First Approximation

Appendix A

For many crusher types performance can be estimated by setting K1 to the closed side setting, K2 to the open side setting (or K1 plus eccentric throw). Both K1 and K2 will decrease with particle interference as the crusher throughput increases to choke feeding. The breakage severity (t10) will also increase (see A6.6 and equation A6.11). The model allows for inclusion of minor variables where more detailed data are available The equations in the model are of the form: K1 = A0* CSS + A1 *TPH + A2 * F80 + A3 LLen + A4

(A6.7)

K2 = B0* CSS - B1 * TPH + B2 * F80 + B3 * LHr + B4 * ET + B5 (A6.8) K3 = C0 (usually 2.3) Where

(A6.9)

Closed side setting Liner Length Eccentric Throw Liner Hours Crusher Feed Rate Crusher Feed 80% passing size Crusher Product 80% passing size

CSS LLen ET LHr TPH F80 P80

Note that only closed side setting and crusher throw will normally be used. The other relationships require a very detailed experimental database.

Page A-44

Appendix A6


Appendix A


Andersen Breakage Model

Ore Breakage Characterisation

The Andersen model uses the results of JK breakage testing of coarse particles to predict both breakage and crusher power consumption. This model has been extensively tested on cone crushers (mostly operating as secondary crushers) over a broad range of ore types. When the model was developed, only the pendulum device was available for single particle breakage tests. However, the JK Drop Weight test is now used as it provides for a wider range of energies and particle sizes. The first step is to use the JK breakage test to characterise ore breakage over a range of input and absorbed energies. The absorbed energy (per unit mass of particle) is referred to as the specific comminution energy. For details of the testing procedure, see Appendix 13.

A6.4

Breakage Distribution Parameter t10

A typical size distribution of product from the JK breakage tester is given in the figure below. This product size distribution may be adequately described by a one parameter (t) family of curves (Awachie (1983); Narayanan and Whiten (1983)). The parameter t10 is defined as the cumulative percent passing one tenth of the geometric mean size, Y, of the test particle. The parameter is shown in the figure below, together with other tn values - t2 and t4,which are defined in a similar manner to t10. Using the tn values (n= 10, 2, 4, 25, 50 and 75), the whole of the size distribution may be fully described. Y = Test Particle Size t

t t

2

4 10 Y/10

Y/4

Y/2

Y

Particle size mm Figure A6.3 - Typical pendulum product size distribution


Appendix A6

Page A-45


Appendix A

The tn values (n = 10, 2, 4, 25, 50 and 75) for the product size distributions for nine pendulum tests on hard rock ores from four major crushing operations at different sites were determined and a 'best-fit' spline curve was drawn through all of the tn data using a JKMRC multiple spline regression package, MSR. This breakage distribution information may be conveniently stored as a three dimensional spline relationship between the breakage distribution parameter, t10 ( a measure of the amount of breakage or reduction), the cumulative percent passing a particular relative size, and the relative size, tn, of the particle being broken. Using the t10 spline knots 10.0, 20.0 and 30.0, Table A.6.1 gives the cumulative percent passing the relative sizes t75, t50, t25, t4, and t2 i.e. the cumulative percent passing the Y/75 size (etc), where Y is the size of the original particle being broken as shown in Figure A6.4. The distribution for any intermediate value of t10 is determined by spline interpolation.

Table A6.1: Appearance Function Data

SIZE RELATIVE TO INITIAL SIZE T75 Breakage Parameter t10

Page A-46

Appendix A6

T50

T25

T4

T2

CUMULATIVE PERCENT PASSING

10.0

2.8

4.0

5.5

22.2

51.4

20.0

5.6

7.2

10.7

43.4

80.8

30.0

8.9

11.3

16.4

60.7

93.0


Appendix A


Figure A6.4: The relationship between t10 and the remainder of the product size distribution

A6.5

Breakage Parameters

Breakage parameters can be established from regression analysis of the same data as the classification equations.

t10 = D0*Crusher gap + D1*Throughput – D2* Feed coarseness (F80) + D3 (A6.10)

This equation shows the intuitively expected dependence on the crusher gap, throughput and feed size distribution.

The "feed coarseness" factor is somewhat application dependent. That is, it will be influenced by crusher liner profile and effective slope as well as closed side setting and gap.

First Approximation

Typical cone crusher operation for secondary and tertiary crushers will be at a t10 of 15 to 20. For a lightly loaded crusher (size control on a primary jaw crusher) will operate at a t10 of 5-10. A high reduction crusher (toothed roll or choke fed tertiary) may achieve a t10 up to 25.


Appendix A6

Page A-47

Crusher (Model 400/405) A6.6 Energy - Size Reduction Relationship

Appendix A

Crusher Power Predictions

The JK breakage test also provides important information on the specific comminution energy (kWh/t) required for a fixed size reduction, quantified by the breakage distribution parameter t10, for each particle size broken. The specific comminution energy, Ecs, defined as the amount of energy available for breakage, is derived as the energy absorbed from the drop weight on impact. This energy has been found to have a linear relationship with the breakage distribution parameter, t10, but is also dependent on the test particle size. This relationship is ore-specific and is used to characterise ores and compare the crushing energy requirements of different ores.

Figure A6.5 shows the energy - size - size reduction relationship derived from a JK breakage test for a fine-grained, siliceous copper ore.

1.5

t10 = 30.0 t10 = 20.0 t10 = 10.0

1.2 0.9 0.6 0.3 0.0 10

14

18 22 Size mm

26

30

Figure A6.5 - Energy size reduction relationship

This information as used in the crusher model program in the spline form is tabulated below. The energy required for a given reduction increases with a decrease in particle size. In Model 400, provision is made for data for three particle sizes. In Model 405, the matrix is extended to accept data for five particle sizes to match the data available from the JKTech Drop Weight Test.

Page A-48

Appendix A6


Appendix A

Crusher (Model 400/405) Table A6.2 - Energy-Size Reduction Relationship (Spline Form) – Model 400

Reduction parameter

Particle size mm

t10

14.50

20.63

28.89

Specific comminution energy kWh/t

% 10.0

0.35

0.30

0.25

20.0

0.80

0.70

0.50

30.0

1.2

1.0

0.80

Table A6.2 - Energy-Size Reduction Relationship (Spline Form) – Model 405

Reduction parameter t10 %

Particle size mm 14.50

20.63

28.89

41.10

57.80

Specific comminution energy kWh/t

10.0

0.35

0.30

0.25

0.20

0.15

20.0

0.80

0.70

0.50

0.40

0.30

30.0

1.2

1.0

0.80

0.60

0.40

Power Prediction A power prediction method has been developed using energy – size-reduction information from the pendulum test (Andersen & Method Napier-Munn, 1988) and is also applicable to the Drop Weight test. Using the ore-specific energy-size-reduction relationship from the pendulum test, the breakage function, B the classification values Ci (from the parameter fitting or model regression equations, the model calculates the total energy required to reduce the feed size distribution to the product size distribution as if all the feed was broken in the pendulum or drop weight testing device, i.e. it defines the energy which would have been used by the breakage device to achieve the same degree of breakage observed in the crusher. The sum of the products of the amount of material selected for breakage in each size fraction, Ci*xi (tonnes) (from equation (A6.3)), and the Ecs (kWh/t) for each size at the breakage parameter value t10 (determined from the parameter fitting or model regression equation (A6.11)), is the total comminution energy calculated by the model, Pcalc (kWh).


Appendix A6

Page A-49


Appendix A

This total model-calculated energy is then regressed against the actual power draw observed during the plant surveys on a particular crusher using multiple linear regression analysis, resulting in a simple equation of the form given below. Pobs =

E1 * Pcalc + E2

(A6.11)

where Pobs is the observed crusher power draw (kW) Pcalc is the model calculated comminution energy(kWh) E1

is a constant dependent on the efficiency of the crusher

E2

is a constant of similar value to the 'no-load' power draw

The constant included in the regression equation adequately accounts for the crusher machine power draw (the power required to overcome machine frictional losses), or 'no-load' power draw as it is commonly termed. This 'no-load' power appears to vary slightly with throughput and is a function of both plant power factor and drive motor efficiency. Feed rate (t/h) and feed coarseness are usually less significant variables and a satisfactory model can be obtained by absorbing these effects into the constant term. These variables are implicitly included in the pendulum power calculation. The power regressions developed may be used to predict the power requirements of crushers operating on different ores after determining the relationship between the breakage parameter, t10, test particle size, and the specific comminution energy, Ecs, for the ore under investigation. The pendulum test should be conducted on representative ore particles over the range of the crusher feed size. Where a specific mathematical performance model of the form of equations A6.7 to A6.10 has been developed from extensive plant surveys, the power draw may then be predicted for different operating conditions. In a design situation, given the feed and the desired product size distributions, the t10-size-Ecs relationship for the ore to be processed must be obtained from the pendulum test and this information used in the model to calculate the total comminution energy required. The crushing power requirements can then be determined for a similar crusher from a power regression of the form of equation A6.11 obtained from another site.

Page A-50

Appendix A6


Appendix A


Crusher Model (400/405) Showing Default Values

Printout

Model 400

Model 405


Appendix A6

Page A-51


Page A-52

Appendix A

A6.8

Symbols

Symbol

Meaning

f

feed size distribution (vector)

p

product size distribution (vector)

A

appearance function (matrix)

C

classification function (diagonal matrix)

I

unit matrix

K1

size below which C = O

K2

size above which C = 1

K3

exponent in the equation for C

CSS

closed side setting (mm)

TPH

tonnes/hour feed

F80

coarseness of feed, e.g. 80% - 25.4mm

t10

breakage distribution factor total power consumed in size reduction using the pendulum (from laboratory tests results)

Ai

regression constants

Bi

"

Ci

"

Di

"

Ei

"

Appendix A6


Appendix A


Known Restrictions

This is the most general of the crusher models developed at the JKMRC. It has been extensively tested for large (7ft) cone crushers. The model provides an excellent description for individual results for many types of crusher, e.g., jaw, roll, toothed roll, hammer mill etc., but has not been extensively tested on these other crusher types. The feed coarseness relationships are usually based on scalped feed oversize variations. They could well be different from variations in scalping screen aperture. This interaction is a subject for continuing investigation. For power calculations large particles are apparently softer (see Table A6.2). The drop weight test is not suitable for particles of diameter larger than 63mm. Hence, using specific comminution energies derived on smaller particles will tend to overestimate required pendulum power. There is also a physical flow limit for most types of crushers. For crushers which cause a considerable increase in volume, this limit is important. Hence for cone or 'Gyra disk' types, check the simulated flowrates against the design tables for that type of crusher and the corresponding bowl and mantle. Typical flowrates are available from standard references such as Mular and Bhappu (1978), Chapter 11.


Appendix A6

Page A-53


Appendix A

Fitting the Crusher Model

The model fitting subsystem only analyses one data set at a time. Hence the actual parameters adjusted are the constant terms in each of the equations A6.7, A6.8, A6.9 and A6.10.

That is, A4

for

K1

B5

for

K2

D3

for

t10

and

PARAMETER MENU

There are two distinct levels of use of the crusher model. The different uses require different fitting strategies.

Limited Data

One data set allows a (somewhat approximate) estimate of product size for small variations in closed side setting. For one data set: fit A4 and B5 with A0 = 1.0, and B0 = 2.0 and (for cone crushers) K3 = 2.3. Set other A and B values to zero. Similarly for the breakage function: fit D3 D0, D1 and D2 are set to zero. Note that one data set does not provide useful information about power dependencies.

Page A-54

Appendix A6


Appendix A


Extensive Data

The model is much more useful with a range of data. This means 5 to 10 data sets covering a range of crusher settings, feed rates and (if possible) feed sizes. JKTech can undertake breakage tests to characterize an ore as shown in Figure A6.3 and Table A6.1 and to determine the size single particle breakage/power as shown in Figure A6.5 and Table A6.2.

HP Grinding Rolls (and others)

Note that the value of K3 is generally 2.3 for cone, jaw and gyratory crushers only. For other types of crushers, such as grinding rolls and hammer mills, it is advisable to fit K3 also, with 2.3 as a good initial estimate


Master/Slave model fitting is available for the crusher model in the general release version of JKSimMet. Model fitting of multiple data sets is complex; assistance from JKTech consultants is strongly recommended if you intend to tackle this aspect of the fitting process. Setting up Master/Slave fitting is detailed in Section 5.6.5


Appendix A6

Page A-55


Appendix A

Regression Modelling

The procedure is very similar to that for the screen model. Hence, an efficient test program can be designed to gather screen and crusher data together. Fit each test using only constant terms, A1, with all of the other regression terms set to zero. Use the ore Specific Appearance and Power Data measured by JKTech, or use the defaults (average of 4 ore types). Measured oretype data should give more accurate results for breakage and are essential for realistic power estimates. Each data set produces estimates of K1, K2, K3 and A and B. Set K3 = 2.3 Use a multiple linear regression package to fit each estimate to the measured variables. If any coefficients plus or minus their estimated errors bracket zero, try a refit without that variable included. If the error of prediction improves (i.e., gets smaller), omit the variable by setting its model coefficient to zero.

A6.12

Model Testing

Import each feed and product into the model and simulate to check each set. This is quite a complex model and it is not difficult to make errors. If any data sets are seriously in error, try to track down the reason. Check the calculated K1, K2, and t10 against your fitted estimates. When all else fails (or much earlier, if you prefer), ask JKTech, who will be happy to assist. As soon as you have reasonable parameter estimates, you may use Master/Slave fitting on up to ten data sets at a time to test secondary crusher model dependencies.

Page A-56

Appendix A6


Appendix A


References

ANDERSEN, J. A., 1989. M.Sc. Thesis, University of Queensland, (unpublished). ANDERSEN, J.A. and NAPIER-MUNN, T.J., 1988. Power prediction for cone crushers, Mill Operators' Conference, Cobar. AWACHIE, S.F.A., 1983, Development of crusher models using laboratory breakage data, PhD Thesis, University of Queensland. MULAR A. L. & BHAPPU, R. B. 1978, Mineral Processing Plant Design. WHITEN, W.J., 1984, Models and control techniques for crushing plants, Control 84, Minl./ Metall.Process (Am.Inst.Min.Engrs. Annual Meet., Los Angeles, USA, February), 217-225.


Appendix A6

Page A-57


Appendix A

(Blank Page)

Page A-58

Appendix A6


Appendix A

Rod Mill (Model 410) A7

Rod Mill (Model 410)

A7.1

Model Description

The rod mill model is based on the concept of stages of breakage. A stage of breakage has three components: selection • appearance • classification. •

That is, each stage is equivalent to breakage, screening and recirculation. The mill is considered as a number of segments in order. Each segment is a stage of breakage.

A7.2

Model Equations

Diagrammatically a stage of breakage may be considered as: fj feed vector to stage j

m=C.q+f (I-S).m

ONE

S

Selection

Diagonal Matrix S

Appearance

A

Lower Triangular Matrix A

Contents

q

Segment contents Vector q

STAGE OF BREAKAGE

C.q

C

Classification

pj

Figure A7.1


Diagonal Matrix C

product vector from stage j

A representation of the breakage process in a rod mill

Appendix A7

Page A-59


Appendix A

Eliminating m and q by matrix algebra yields pj = (I-C) . (A.S +I-S) . [I-C⋅(AS+I-S)]-1 . fj or pj = X . fj since AS and C are assumed constant for all stages.

Stages of Breakage

If there are v stages of breakage in the mill then:

p = (X)v ⋅ f

(A7.1)

or p = X⋅X⋅X ... ⋅ f

for v times

Non-integer numbers of stages can only be calculated by interpolation. Once A, S and C are known, any particular operating condition can be represented by a value of v.

Feed Rate

The key dependence is the variation of stages of breakage v with mill feed rate F. Experimentally: F (v)1.5 = MC where MC is the mill constant. The mill constant can also be scaled as detailed later.

Appearance Function

The default Appearance Function is the modified Rosin-Rammler equation: A(x,y) = (1-e-x/y)/(1-e-1) Where A(x,y) is the proportion after breakage of particles of initial size y which are smaller than size x. The appearance A is made up of vectors of the differences in x for the specified screen interval. For specific ores, JKTech can measure the appearance function. A range of appearance functions for various ores is given with the ball mill model description in Appendix A8.

Page A-60

Appendix A7


Appendix A Classification Function

Rod Mill (Model 410) The classification function C is a diagonal matrix which provides a simple classifier. Each diagonal element gives the proportion of that size fraction returned to the breakage stage for rebreakage. The usual values are (for a √2 size distribution) 1.0, 0.5, 0.25, 0.125, 0.063 and so on. Hence, each stage of breakage in a rod mill will eliminate the top size fraction from the product.

Selection Function

The selection function, S is a diagonal matrix. It gives the proportions of each size fractions which are selected for breakage. S is represented by three parameters XC, SL and IN as shown in the figure below, and is calculated by: Si = SL ⋅ Size + IN

for Size i > XC

Si = SL ⋅ XC + IN

for Size i < XC

and limited if Si > 1.0 then Si = 1.0 and if Si < 0.0 then Si = 0.0 An example of a selection function is given in the figure below.

1.0

SL Selection Function

IN 0.0

XC Size

Figure A7.2


Graph of a rod mill selection function

Appendix A7

Page A-61


Appendix A

Scaling

The rod mill model is scaled by modifying the mill constant according to dimensions and operating conditions described below:

Mill Size

DSIM2.5 LSIM FACTA =   ⋅L FIT  DFIT  These scale factors only apply for rod mills with normal length to diameter ratios, that is, 1.2 < simulated L/D < 1.6 and L ≤ 7m.

Media Load

Load Fraction (i.e. volume of mill occupied by charge and media at rest after grinding out) FACTB =

(1 - LFSIM ) ⋅ LFSIM (1 - LFFIT ) ⋅ LFFIT

Note 30% < LF < 45%

Critical Speed

Fraction Critical Speed FACTC =

CSSIM CSFIT

Note 50% < CS < 80%

These factors are applied to the Mill Constant MC of the original mill to estimate the mill constant of the simulated mill. MCSIM = MC ⋅ FACTA ⋅ FACTB ⋅ FACTC The required number of stages of breakage is MCSIM2/3 vSIM =  F   SIM  Feed Size

Coarseness of feed (90% passing size)  F90FIT  FACTD = ln F90  / ln 2 SIM  MCSIM2/3 vSIM =   + FACTD  FRSIM 

Page A-62

Appendix A7


Appendix A Ore Hardness

Rod Mill (Model 410) Work Index WISIM FACTE = - 0.8 ln  WI   FIT   S(I)FIT  FACTF = ln 1-S(I)  + FACTE FIT  FACTG = exp (FACTF)  FACTG  S(I)SIM = 1+FACTG  


Appendix A7

Page A-63

Rod Mill (Model 410) A7.3

Page A-64

Appendix A7

Appendix A Rod Mill Model Printout Showing Default Values


Appendix A


Symbols

Symbol

Meaning

f

feed size distribution (vector)

p

product size distribution (vector)

A

appearance function (step matrix)

C

classification function (diagonal matrix)

S

selection function (diagonal matrix)

Si

element of selection function S from size i

v

number of stages of breakage of original mill

vSIM

v for simulated mill

F90FIT

90% passing size for fitted mill feed

F90SIM

90% passing size for simulated mill feed

MCSIM

mill constant for simulated mill

MC

mill constant for original or fitted mill

SL

slope of selection function

IN

intercept of selection function

XC

Size below which selection function is constant

DSIM

diameter of simulated mill

DFIT

diameter of fitted mill

LSIM

length of simulated mill

LFIT

length of fitted mill

LFSIM

load fraction of simulated mill

LFFIT

load fraction of fitted mill

CSSIM

fraction critical speed of simulated mill

CSFIT

fraction critical speed of fitted mill

WISIM

work index of ore for simulated mill

WIFIT

Work index of ore for fitted mill

Note:


The fitted mill is the rod mill which provided the experimental data.

Appendix A7

Page A-65


Appendix A Known Restrictions

Scaling

Note the restrictions for scaling in the section on Model Equations.

Change in Feed Pulp Density

The number of stages of breakage is calculated from the feed solids mass flow. No account is taken of water in the feed. It is assumed that rod mills operate at 75 to 85 percent solids in the feed.

Effect of Feed Size

There is some doubt about the adjustment of number of stages of breakage according to feed coarseness. Data from some operations exhibit an effect while data from others do not. If the particles are large enough and strong enough to resist a rod impact, the dependence is reasonable. The scaling effect can be eliminated from open circuit operation by setting F90FIT (parameter 16) equal to F90SIM (parameter 80).

Mill Speed

This dependence is reasonable from 50-80% of critical speed at industrial mill feed rates.

A7.6

Fitting the Rod Mill Model

PARAMETER MENU

Because the rod mill model is dependent on feed conditions, it is difficult to fit in closed circuit until the parameters are very good estimates. Therefore, mass balance a closed circuit rod mill first. Then fit the discharge using the mass balanced feed rate and sizing. (Use Whiten SDs for the product size distribution). If an ore specific breakage function is available, it should be used. The mill constant (MC) and the three selection function parameters can be fitted. For fitting, set the simulated and original mill dimensions etc. to the same values.

Page A-66

Appendix A7


Appendix A

Rod Mill (Model 410) Check the experimental feed 90% passing size and input it. Use a measured work index if available - an approximate one if not. This model is fussy about initial estimates and some trial and error may be needed. These guidelines will help for many cases. If you are new to the rod mill model use the rod mill example in Chapter 3 and graph the output to get a feel for how XC, SL and IN interact and change the shape of the product curve. Set XC to about half of the top size of the mill feed and MC to 2000. Assume a selection value of 0.1 at XC and 1.0 at the feed top size. Calculate slope and intercept to suit. Try a simulation with these values. If the product distribution is approximately the right shape, (plot as cumulative percent passing both simulated and experimental products) fit the rod mill constant. If the shape is very different, increase the assumed selection value for a steeper product slope and proceed when the slope is similar. If the fitting program finds a reasonable minimum, - that is, the mill constant error is less than 20% - change the MC estimate to the new value and fit the slope. If the sum of squares decreases, update the SL guess to the fitted value and fit XC and IN also.

A7.7

Reference

LYNCH, A.J., 1977. Mineral crushing and grinding circuits, (Elsevier, Amsterdam), 51-60.


Appendix A7

Page A-67


Appendix A

(Blank Page)

Page A-68

Appendix A7


Appendix A

Perfect Mixing Ball Mill (Model 420) A8

Perfect Mixing Ball Mill (Model 420)

A8.1

Model Description

This model considers a ball mill as a perfectly mixed tank with contents described by a vector size distribution s. The product vector p is produced by a discharge rate di for each size fraction, where D is a diagonal matrix of rates, that is: p = D•s

(A8.1)

Within the mill, two factors control breakage. The first is the rate of selection of each size for breakage. The second is the way in which the selected particles are broken (or appear) in the mill contents. Selected = R•s where R is a diagonal matrix of rates. Appearance = A•s where A is a triangular matrix of breakage (appearance) functions (distributions). At steady state, the mill feed minus the material selected for breakage plus the material from breakage minus the material discharged must equal zero. This can be written as: f - R•s + A •R•s - D•s = 0 Discharge Rates

(A8.2)

For overflow mills and most of the operational range of grate discharge mills, the discharge elements can be approximated by: Di = Di* 4 v / (d2 l)

(A8.3)

where Di* is close to unity v is the total volumetric mill feed rate d and l are mill diameter and length A typical discharge function is given in Figure A8.1.


Appendix A8

Page A-69

Appendix A


1

* D

i

0. Discharge Screen Size

Log (size)

Figure A8.1 - Typical graph of mill discharge function

Breakage Rates

Breakage rates tend to increase rapidly with particle size, with the increase tapering off at the feed top size.

Log (R ) i

Log (size) Figure A8.2 - Typical graph of breakage rate factor

Appearance Function

Page A-70

The appearance function A is ore dependent, and can be measured using the drop-weight testing technique developed at the JKMRC. A table of appearance functions for a variety of ore types and the associated operating work indices is given in section A8.7. The standard Broadbent-Calcott appearance function is also included.

Appendix A8


Appendix A

Perfect Mixing Ball Mill (Model 420) A8.2

Model Equations

Considering equation 8.1 as the elements of each vector and matrix yields: i

fi - Risi +

∑ A ij R js j -

D is i = 0

(A8.4)

j=1

and: pi = Disi

(A8.5)

Substituting for si yields: i Rj Ri fi - D pi + ∑ A ij pj- pi = 0 i Dj

(A8.6)

j=1

where feed and product are related by R/D for a particular breakage function. Equation A8.3 can be used to scale for feed rate and mill dimensions. In general, the mill contents s is not known and it is not possible to separate the R/D* ratio into its components. The R/D* function is represented internally by a cubic spline function (that is, by a smooth curve). A number of spline knots (generally between 2 and 4) on the 1n(R/D*) function are fitted. Scaling

Scaling of the ball mill model is achieved by modifying the fitted R/D* function according to dimensions and operating conditions as described below.

Mill Diameter

The mill diameter d is scaled.

FACTA =

dSIM d   FIT 

Note: This factor is in addition to a direct volume effect which is built into the model. Load Fraction

The load fraction LF is the volume of mill occupied by charge and media at rest when the load is ground out.

 (1 - LFSIM ) . LFSIM   FACTB =   (1 - LFFIT ) . LFFIT  Version 5.1 February 2003

Appendix A8

Page A-71

Appendix A


Fraction Critical Speed

Fraction critical speed is scaled by:  CS FACTC =  SIM  CS FIT

  

55%
The Work Index is scaled by:

Work Index

WISIM0.8 FACTD =  WI   FIT 

Ball Size Scaling

By assuming that the reduction mechanisms of impact and attrition occur in a ball mill, the following relationships can be derived from theoretical considerations. Impact breakage

∝

Db3

Attrition breakage

∝

1/Db

where Db = ball top size diameter. Impact breakage is assumed to predominate above a certain size xm whilst attrition is the main reduction mechanism at sizes below xm. The size xm is assumed to be equivalent to that at which maximum breakage occurs. Size xm can be related to ball diameter as follows: xm

=

K . Db2

where K is the maximum breakage rate factor. The value of K has been found to be of the order of 4.4 E-04. K can be calculated from the formula above if the value of xm is known. The graphing facility within JKSimMet allows easy graphing of the breakage rates to determine this value. xm (fit) and xm (sim) are both calculated. The smaller of the two is denoted xm (small) and the larger as xm (large) . The above relationships are used to scale R/D* values at each spline knot to account for ball size effects. The scaling factor for ball size effects depends on the knot position size. for knot position size < xm (small) 1 ( ) = Db FACTE = Db (1Db ) Db SIM

FIT SIM

FIT

Page A-72

Appendix A8


Appendix A

Perfect Mixing Ball Mill (Model 420) for knot position size≥ xm (large)

 Db SIM  FACTE =    Db FIT 

2

For knot positions between xm (small) and xm (large) linear interpolation is used.

The effect of ball size is shown in the diagram below.

New xm

Old x m

Ball size decreasing

Knot 1

Knot 2

xm

Knot 3

Knot 4

Particle Size

Figure A8.3: R/D* Relationship with Ball and Particle Size

Scaling Calculation

These factors are applied to each fitted 1n (R/D*) knot as follows: R/D*SIM=R/D*FIT•FACTA•FACTB•FACTC/FACTD•FACTE

Scaling Using Breakage Functions

Where characteristic breakage functions have been measured (i.e. pendulum tested) for both ores, these breakage functions may be used to predict performance. Note that it is not valid to scale this way from the default breakage function.


Appendix A8

Page A-73

Appendix A


Page A-74

Appendix A8

Ball Mill Model Printout Showing Default Values


Appendix A


Symbols

Symbol

Meaning

f

feed size distribution vector

p

product size distribution vector

s

mill contents size distribution vector

A

appearance function lower matrix

R

breakage rate function diagonal matrix

D

breakage discharge function diagonal matrix

D*

normalised discharge function

R/D*SIM

normalised R/D ratio for simulated mill

R/D*FIT

normalised R/D ratio for fitted mill

dSIM

diameter of simulated mill

dFIT

diameter of fitted mill

LSIM

length of simulated mill

v

volume flow rate of feed

LFSIM

load fraction of simulated mill

LFFIT

load fraction of fitted mill

CSSIM

fraction critical speed of simulated mill

CSFIT

fraction critical speed of fitted mill

WISIM

work index of ore for simulated mill

WIFIT

work index of ore for fitted mill

Db

ball diameter (top size)

DbSIM

ball diameter for simulated mill (top size)

DbFIT

ball diameter for fitted mill (top size)

K

maximum breakage rate factor

xm

maximum breakage size.


Appendix A8

Page A-75

Appendix A


Known Restrictions

Change in Coarseness of Feed

It is known that the coarse end of the R/D* function does vary with gross changes in the amount of coarse material in the feed stream. As the amount of coarse material in the feed is decreased, the relevant R/D* values increase. This limitation is not considered significant for changes of less than plus or minus 50% in the amount of coarse material in the feed.

Critical Speed Range

The critical speed dependence is approximately valid for 55-78% of critical speed and incorrect outside of that range.

Predicting Rates If the ball mill model does not produce any of a coarse fraction (i.e. at 'Missing Sizes' none in the mill discharge) then the effective rate of grinding is 'infinite'. One way to overcome this problem is to size the mill contents and expand to the perfect mixing model used for the SAG mill model.

This is usually not experimentally convenient. practical approaches are to:

Some more

•

test the mill at maximum tonnage with coarse feed. If there is any coarse material in the discharge, the actual rates can be estimated.

•

use a set of rates and knot values from the supplementary information for a similar mill feed sizing and fit with Work Index alone the first time. Transfer the coarse rate values from calc to exp, return the Work Index to its original value and refit the two smaller rates. This procedure should give reasonable answers with a coarser feed. Work is proceeding on improving the ball mill model in this area.

High Mill Viscosity or Pulp Density

The perfect mixing mill model only takes account of pulp density variations as variations in mill volume. Therefore, higher pulp density will always predict higher grinding rates. In practice, the rates do improve until pulp viscosity begins to interfere with ball action and rates decrease rapidly. This onset is difficult to predict as it is highly ore type dependent. However, effective mill operation of greater than 50% solids by volume is unlikely and improbable at greater than 60% solids by volume.

Ball Size Scaling

The ball size scaling relies on the R/D* function exhibiting a maximum. If there is no maximum in the fitted R/D* function, increasing the ball size will give optimistic results.

Page A-76

Appendix A8


Appendix A Wide Range Size Data

Perfect Mixing Ball Mill (Model 420) The mill model assumes a constant breakage function for all size fractions. This assumption simplifies the model but experimental evidence suggest strongly that partial breakage increases in severity with decreasing size - down to some limiting size. Therefore, if more than (say) twenty size fractions are considered, an apparent minimum rate may be produced in the finer ranges. This phenomenon is more likely to be an artefact of an incorrect assumption than to have any physical significance. Research work continues in this area.

A8.6

Fitting the Perfect Mixing Ball Mill Model

PARAMETER MENU

The ball mill model is well-behaved for model fitting. It can be fitted in closed circuit with the cyclone model with generally better results than by fitting each model to mass balanced data. Hence a good closed circuit fit will also provide a good mass balance estimate of circulating load.

R/D* Spline Knots

Use three knots for normal grinding conditions and four knots for a wider than usual size range (such as SAG mill discharge or a very fine product).

Knot Positions

To determine an appropriate set of knot positions divide the number of size fractions covering the feed size distribution by the number of knots plus one. This will give about equal log size spaces from both ends and between knots.

Knot Estimates

Estimates for the function values at the knot positions are provided as ln(R/D*) values. A simple ascending series provides a good first estimate, for example: 0.5

1.5


2.5

Appendix A8

Page A-77

Appendix A

Perfect Mixing Ball Mill (Model 420) If you have several sets of data, use an operating Work Index for each (calculated from mill feed rate, mill power, feed and product 80% passing sizes). If the major variation is hardness only, then the average knots can be used.

Work Index, Load Fraction

The calculated R/D* values are displayed on the unit data entry screen. There should be a smooth increase with size. Sometimes the curve will have a maximum at the coarse end. If there are any sudden changes or ups and downs, try adjusting the knot positions. There will often be a bump at a change in size measurement technique, such as the transition from screen sizing to Cyclosizer sizing. Systematic deviations can sometimes be removed by adjusting a knot towards the largest deviation. Graph Cumulative Simulated and Experimental Product

When nothing else works, plot the experimental feed and product on a coarse scale (say 0-30%) percent retained against log size. If there are any large discontinuities, check your data very carefully, and repeat your sampling if possible.


The perfect mixing ball mill model is well suited to fitting of multiple data sets. The ln(R/D*) knot values can be fitted simultaneously for a number of surveys. Ensure that you use the same knot positions, and number of knots, for each mill in your master/slave fitting test.

Page A-78

Appendix A8


Appendix A


Table of Appearance Functions

This table shows ore-specific appearance function values determined from single particle breakage tests using JK breakage testers –pendulum or drop-weight.

Size Interval Ball milling circuits from which the samples were collected: Massive Massive Porphyry Porphyry Massive Sulphide Sulphide Hard Soft Sulphide (Ni) Coarse (Cu) (Cu) Fine (Pb-Zn) (Pb-Zn) 1 0.000 0.000 0.000 0.000 0.000 2 0.0591 0.0505 0.08586 0.05220 0.1128 3 0.1052 0.0974 0.1248 0.09919 0.1490 4 0.1318 0.1276 0.1387 0.1288 0.1497 5 0.1295 0.1278 0.1278 0.1284 0.1250 6 0.1127 0.1128 0.1076 0.1129 0.09885 7 0.0927 0.09469 0.08722 0.09423 0.07866 8 0.07486 0.07810 0.06960 0.07727 0.06289 9 0.06082 0.06428 0.05540 0.06339 0.04943 10 0.05005 0.05316 0.04428 0.05239 0.03842 11 0.04166 0.04424 0.03574 0.04364 0.03003 12 0.03462 0.03666 0.02899 0.03623 0.02376 13 0.02723 0.02880 0.02278 0.02847 0.01865 14 0.02054 0.02171 0.01743 0.02146 0.01448 15 0.01537 0.01623 0.01325 0.01604 0.01120 16 0.01144 0.01207 0.01004 0.01192 0.00864 17 0.00849 0.00894 0.007581 0.00883 0.00664 Operating Work Index 12.8 9.0 13.6 12.2 15.9 Size Interval Ball milling circuits from which the samples were collected: Quartzite Porphyry Massive Massive Standard Sulphide Soft Sulphide Sulphide Function Low Grade USA (Cu,Pb,Zn) (Pb, Zn, Cu) (Cu) (Cu) 1 0.000 0.000 0.000 0.000 0.000 2 0.09514 0.05013 0.1171 0.1081 0.193 3 0.1322 0.0970 0.1537 0.1442 0.157 4 0.1417 0.1273 0.1522 0.1472 0.126 5 0.1267 0.1276 0.1247 0.1253 0.101 6 0.1049 0.1128 0.09723 0.1006 0.082 7 0.08477 0.09481 0.07685 0.08050 0.066 8 0.06778 0.07832 0.06131 0.06444 0.053 9 0.05371 0.06451 0.04810 0.05076 0.043 10 0.04244 0.05336 0.03729 0.03958 0.035 11 0.03379 0.04438 0.02911 0.03103 0.028 12 0.02709 0.03677 0.02303 0.02459 0.022 13 0.02127 0.02888 0.01810 0.01929 0.018 14 0.01637 0.02177 0.01407 0.01496 0.015 15 0.01254 0.01628 0.01089 0.01155 0.012 16 0.009565 0.01211 0.008413 0.008888 0.010 17 0.007279 0.008968 0.006483 0.006825 0.008 Operating Work Index: 14.1 10.2 14.1 13.5


Appendix A8

Page A-79

Appendix A


A8.8

References

LYNCH, A.J., 1977. Mineral crushing and grinding circuits, (Elsevier, Amsterdam), 309-312. WHITEN, W.J., 1976. Ball mill simulation using small calculators, Proc. Australas. Inst. Min. Metall., 258, 4753. MORRELL, S. 1992. Ball size effects in ball mills. Chapter 2, End of project report, AMIRA/JKMRC Project P9J. "Simulation and Automatic Control of Mineral Treatment Processes".

Page A-80

Appendix A8


Appendix A

Autogenous & SAG Mill Model (Model 430-431) A9

Autogenous Mill Model (Model 430) and Semi-Autogenous Mill Model (Model 431)

A9.1 Model Description The JKMRC has been involved in the development of a model of autogenous and semi-autogenous grinding for many years. The first model to provide useful predictions was the Leung model (Leung, 1987). It used ore-specific breakage functions obtained off-line using a laboratory test procedure. It has largely been superseded by the Variable Rates model( see Appendix 11). However, because of its relative simplicity, the Leung model provides a good introduction to SAG mill modelling. Caution: The Leung model scales on volume. This is irrelevant for optimisation but is important for scale up from pilot to full scale mills of more than 8 to 9m in diameter. The power model (Morrell, 1991) was added in 1992. The Leung model has the general structure shown in Figure A9.1. The appearance function has two components: •

high energy corresponding to impact breakage, determined from the twin pendulum single particle breakage apparatus, and

•

low energy corresponding to an abrasion mechanism, determined from laboratory tumbling tests.

In both cases the functions are obtained off-line on representative samples of ore and do not rely on being simultaneously back-fitted to operating data. The energy levels at which the high energy appearance function is determined are based on the mean energy in the mill, which is related to mill diameter. Discharge rates are determined as the product of the rate at which the load is presented to the grate, dmax, and the classification at the grate (which is represented by a simple classification function). The model iterates to select a value of dmax equal to the fraction of mill occupied by material of a size less than the grate size, which in turn is assumed to be a simple power function of feed rate expressed as a proportion of mill volume. The model predicts product size distributions and mill loads from a known feed size and tonnage for a given mill and feed ore. Ball charge is incorporated through the assumption that balls are equivalent to mill load particles of equal mass. Average breakage rates are provided as defaults for both the autogenous and SAG mill models. Note that these rates are different and are based on a limited data set. Usually, breakage rates will be model fitted to plant data.


Appendix A9

Page A-81

Autogenous & SAG Mill (Model 430-431)

Limitations /Caution

Appendix A

This model is a significant development of earlier models, and has been shown to be successful in describing operating data on full scale autogenous and SAG mills. Its scale-up capability is limited to mills up to 8 to 9m in diameter from pilot mills of up to 2m. The dependency of the model parameters on operating conditions such as mill speed, percent solids, grate open area, liner characteristics and pulp rheology was not well established when this model was developed. Most of these issues are addressed in the Variable Rates model(A13) The Leung model is based on data from mills operating at approximately 70% of critical speed and 60-70% solids by weight in the feed.

Load

Feed

Product

Mass Transfer and Discharge

Breakage

Breakage Rate

Appearance Function

High Energy (impact)

Mass Transfer Function

Classification Function

Low Energy (abrasion)

Figure A9.1: Autogenous Mill Model Structure

Page A-82

Appendix 9


Appendix A

Autogenous & SAG Mill Model (Model 430-431) A9.2

Model Equations- Particle Breakage

Particle Breakage This description follows the structure shown in Figure A9.1. The model assumes that each size fraction experiences only one energy level of breakage. (The reality will certainly be a distribution of energy levels).

High Energy Breakage

The relationship between the amount of breakage and the input energy is described by t10= A (l - e - b Ecs )

(A9.1)

where t10 is the percentage of the broken particle which will pass through a screen of one tenth the size of the original particle, and Ecs is the energy absorbed per unit mass during breakage measured in kWh/t. A and b are the parameters which characterize this equation for a particular ore. A is usually taken as 50. Parameter b is derived from a drop-weight breakage test of closely sized ore particles. Required sample size varies according to ore variability. However, as a guide, about 50 kg of 50 mm material is needed.

Low Energy Breakage

One or more 3 kg samples of 50 mm natural ore are tumbled for 10 minutes in a small dry mill at 70% of critical speed. The products of each run are sized and t10 is measured for each run. Where 50mm material is not available, other sizes are used and adjusted using a simple linear model. The t10 data are fitted to t10 = a0 + a1 * mean size + a2 * sample mass + a3 * time.

(A9.2)

The actual value of the abrasion parameter ta is one tenth (scale factor only) of t10: based on top size of 55*38 mm, mass 3 kg and time 10 minutes.


Appendix A9

Page A-83

Autogenous & SAG Mill (Model 430-431) Low Energy Appearance Function Abrasion

Appendix A

The size distributions produced by ores tested to date have a similar shape. This shape can be scaled to the ta factor that is the percentage passing one tenth of the original particle size. A cubic spline function is used for smooth interpolation. A 100mm particle is chosen as an example as particles of this size will typically undergo abrasion rather than crushing breakage. Parameter ta is taken as 1.0 to make the scaling obvious. size (mm)

% passing

t value

scale*

100

100

t1.25 t1.5 t10 t100 t250 t500

2.687*ta 1.631*ta 1.0*ta 0.9372*ta 0.8070*ta 0.6365*ta

80 67 10 1 0.4 0.2

2.687 1.631 1.0 0.9372 0.8070 0.6365

The example shows that most of a 100 mm particle remains unbroken. This value of t is assumed to be equal for all size fractions.

Breakage Energy As the charge provides the grinding media, the level of available energy is related to the coarse fraction of the mill charge. The average size of the top 20% of the charge is used as the highest energy reference level. S20 = (p100 * p98 * p96 ... p80) 1/11

(A9.3)

and the potential energy at the full height of the mill 4 E1 = 3 π (S20)3 ρ g D

(A9.4)

where D is mill diameter in metres. An assumption due to Austin et al (1984) is used to relate other energy levels to E1. Austin et al provided a rationale for energy levels in mills to be related by E particle α 1/(x)1.5

(A9.5)

where x is particle diameter. Hence, the energies experienced by smaller sizes are scaled using this relationship. This allows an Ecs to be calculated for each size and t calculated from equation (A9.1).

Page A-84

Appendix 9


Appendix A High Energy Appearance Function (Crushing Breakage)

Autogenous & SAG Mill Model (Model 430-431) Once the energy of breakage is known, the distribution the particle breaks into can be described by a cubic spline surface.

spline knots t =

0.0

10.0

30.0

50.0

function values for t2 t4 t10 t25 t50 t75

0.0 0.0 0.0 0.0 0.0 0.0

50.53 23.33 10.00 4.975 3.064 2.325

92.49 61.58 30.00 15.62 9.412 6.893

96.47 82.86 50.00 25.88 14.71 10.32

For example, for a 50 mm particle, a t of 30 would produce this distribution.

t2 t4 t10 t25 t50 t75

Combined Appearance Function

Size (mm)

% passing

50 25 12.5 5 2 1 0.67

100 92.49 61.58 30.00 15.62 9.412 6.893

As noted earlier, the abrasion distribution does not vary with particle size while the crushing breakage is highly dependent on particle size. Hence, abrasion will tend to dominate for coarse particles and impact for fine particles (from equation (A9.5)). To generate an appearance function for each size fraction, the high and low energy appearance functions are combined proportionally.

a=

tLE * a

LE + t HE * a HE tLE + t HE

(A9.6)

where, aLE' aHE = low and high energy appearance functions tLE' tHE


= low and high energy t values

Appendix A9

Page A-85


Appendix A

Equations (A9.1) to (A9.6) combined with the two tables of spline knots yield a complete appearance function (that is how each component will break) for each size in the mill load.

Breakage Rates

To predict a product from the mill contents and the appearance function requires only a rate of selection for breakage for each size fraction of the mill load. These rates will be inherently scaled because the mill load will be constrained by mill dimensions and the mill diameter (if the energy versus breakage assumptions are correct). These rates will certainly vary if mill speed is changed but this dependence is not included in the Leung model. To describe these rates, a five knot spline function is used. Best fit values to data are tabulated. Spline knots (mm) 0.250 4.00 16.0 44.8 128

ln (Rate of Breakage) Autogenous

ln (Rate of Breakage) SAG

2.63 4.04 3.32 1.98 3.37

2.176 4.444 3.577 2.753 4.082

These are the default values in each model. These rates are fitted to customize the model to any particular operating mill.

SAG Mill Modification

The ball charge is approximated by a distribution of equivalent weight particles added to the mill load for the high energy breakage calculation (equation (A9.3)). That is, only the appearance function will be varied by the addition of balls. This completes the description of the Breakage area of the model.

Page A-86

Appendix 9


Appendix A


Classification

Model Equations (Mass Transfer and Discharge)

The mill grate is modelled as a very simple classifier. When this model was developed the relationship between the classification, discharge and the operating conditions was not well defined. Hence, the classifier/discharge is assumed to be constant- for other than minus grate size hold up. A simple form is used. D=1

x < xm

1n(x) - 1n(xg) D = 1n(x - 1n(x ) m)

(A9.7)

xg > x > xm

g

where xm is the particle size below which it will always pass through the grate if presented to it - that is, behave like water. xg is the size of the grate through which the largest particles will pass through.

Pebble Port Modification

Pebble port allows a small discharge rate of substantially coarser particles. This modification affects the classification curve as shown below.

1.0

fp x

m

Size

x

g

x

p

xp is the notional size of the pebble port fp is the notional fraction open area of the pebble ports compared with the fraction of grate open area. Typical values for fp are 2 to 5% ie. 0.02-0.05. While this modification gives a good description of pebble product, the areas are notional only and in fact reflect relative discharge rates. Discharge Rate

The quantity of pulp discharged will depend on the quantity per unit time presented to the grate multiplied by the classification function. d = dmax * D


(A9.8) Appendix A9

Page A-87


Appendix A

where dmax is the fraction of the load presented to the grate per unit time and D is the classification function. The water is assumed to follow the sub mesh particles. The actual value of D is found iteratively. The required value satisfies the following empirical mass transfer law (Austin, 1976).

Mass Transfer "Law"

The value of dmax is adjusted until the model prediction matches the required one. That is, until it lies on the operating line of L = m1 Fm2 where m1 = 0.37

(A9.9)

m2 = 0.37 L is the fraction of the active volume of the mill occupied by minus grate size material and F is the total volumetric feed rate per minute divided by the active volume of the mill.

Perfect Mixing Mill Model

The perfect mixing model at steady state provides the structure to combine the various components of the model. It relates the different parts in the following manner. i fi - ri si + ∑ rj s j a ij - disi = 0 j=1

(A9.10)

pi = di * si

(A9.11)

where fi, si, ri, di and pi are feed rate, contents, breakage rates, discharge rates and product rate vectors and aij is the combined appearance function. The form of equations (A9.10) and (A9.11) allows both the mill load and the product to be calculated for any mill load and discharge rate adjusted until equation (A9.9) is satisfied.

Page A-88

Appendix 9


Appendix A

Autogenous & SAG Mill Model (Model 430-431)

Calculation sequence

↓ Calculate breakage rates

↓ Calculate volume of below grate size material in the mill, L

↓ Calculate discharge rate

↓ If error is acceptable exit else make correction to Dmax

Mill Load

This model is unusual because it uses an internal port to describe the mill contents. This port is accessible from the model properties drop down or from the model window. It does not appear as stream equipment.

Scaling

This model is inherently scaled for mill diameter and volume. This scaling optimistic in capacity as mill diameter is increased. It is reasonable for mills of up to 8 to 9m diameter.

A9.4

The Grinding Mill Power

Prediction of AG/SAG Mill Power Draw

The gross power draw of the mill is that drawn by the mill motor(s), ie metered power. It is assumed that this has two components, viz •

net power, ie. the power delivered to the charge

•

no-load power, ie. the power to overcome drive train and bearing losses.

The gross power can, therefore, be represented by the following equation Gross Power Draw = No-Load Power + Net Power


Appendix A9

(A9.12)

Page A-89


Appendix A

The gross power draw is calculated from the fraction critical speed, ball SG and ball and rock porosity. These data are provided by the user. The calculations use pulp load data generated by the model calculations. The model data entry screen section for the power calculations include the 'net power adjustment factor'. This is a calibration constant which varies slightly from mill to mill depending on mill liner configuration and other factors. Users are strongly recommended to leave this value set at 1.21. Other values should not be used unless a comprehensive range of load vs power data are available.

Net Power Draw

From photographic evidence, the charge shapes shown in Figure A9.2 were assumed to occur in grate discharge mills.

Grate Discharge o

90

θS

rm

o

θ

180

o

0

ri

θT o

270

Figure A9.2: Simplified AG/SAG Mill Charge Shape

By considering an element in the charge of cross sectional area r ds dθ and Len, the torque inertia of the element can be represented by the following equation. Torque Inertia of Element = gLenρr2 cosθ dθ dr

(A9.13)

Power can be defined in terms of torque (τ) and rotational rate (N) as follows: Power = 2π Nτ

Page A-90

Appendix 9

(A9.14)


Appendix A

Autogenous & SAG Mill Model (Model 430-431) For grate discharge mills, by integrating between the limits θs and θT and between ri and rm the net power (Pnet) is given by:

Pnet = 2π gLenρ

rm θ S

∫ ∫N

r

r 2 cosθ dθ .dr

(A9.15)

ri θ T

No-Load Power

The no-load power draw (i.e. that drawn by the mill when completely empty), is associated with various electrical and mechanical energy losses. The main ones are motor, gearing and bearing losses. None of these are fixed over the full mill operating range. Some, however, may have a fixed component. For example, bearing losses due to friction will be dictated by the mill's dead weight (though even this will vary as liners and lifters wear), and the mill charge weight which will clearly vary with grinding condition. To determine the relationship between no-load power and mill design parameters, data from pilot and industrial mills ranging from 1.7 to 7.2 m in diameter were analysed. However, these no-load powers are difficult to measure precisely. The problems are power factor effects at low loads and achieving a completely empty mill. The parameter Diam3Len N was regressed against no load power and found to provide a good fit (Figure A9.3). The relationship developed was as follows with N converted to the fraction of control speed: No Load Power (kW) = 2.62 (Diam2.5 Len φ)0.804 Hence, this equation estimates the likely indicated no-load power for an installed mill. 1000

Predicted (kW)

800 600 400 200 0 0

200

400

600

800

1000

Indicated (kW)

Figure A9.3: Indicated vs Fitted No-Load Power


Appendix A9

Page A-91


Appendix A

Power Calculation The most recent JKMRC database currently includes power data from 63 different mills. Details are shown in Table A9.1. Accuracy

Table A9.1: Data Base Details

Diameter (m) Belly Length Inside Liners (m) Length/Diameter Ratio Percent of Critical Speed (%) Ball Filling (Vol %) Total Filling (Vol %) Specific Gravity of Ore Number of Mills Number of Data Sets Power Draw (kW)

Ball Mills 0.85-5.34 1.52-8.84 1.00-1.83 60-83 20-48 20-48 2.6-4.6 38 41 6.8-4100

SAG Mills 1.80-9.59 0.59-7.95 0.33-1.50 48-89 3-25 7-38 2.6-4.1 20 28 14.8-7900

AG Mills 1.8-9.50 0.59-5.18 0.33-1.0 72-75 0 10-31 2.7-4.6 5 7 12.5-5500

The power model has been applied to this database and was found to give excellent results. The standard deviation of the relative error of the model was calculated to be 6.5% for gross power.. The model therefore requires a knowledge only of mill dimensions and speed, ball charge, volume occupied by balls and pulp, and the ore specific gravity. Full details of the model are given in Morrell (1991). Because of the industrial database, the prediction of gross power is the most reliable. Restrictions

Page A-92

This power model assumes the SAG mill grate and pulp lifters do not limit pulp throughput. For a large diameter mill (say > 7m) in closed circuit with hydrocyclones or fine screens, this assumption may not be justified. A build up of fine slurry in the mill will remove some of the charge imbalance and reduce the actual power draw.

Appendix 9


Appendix A



SAG Mill Printout

Appendix A9

Page A-93


Page A-94

Appendix A

A9.6

Symbols

Symbol

Meaning

aij

fraction of size j which breaks into size i

A

Ecs model parameter

b

Ecs model parameter

dmax

discharge rate at xm

di

discharge rate of size i

fi

feed rate of size i

Ecs

Energy absorbed per unit mass during breakage in each size fraction

E1,

particle potential energy at full height of mill

F

volumetric feed rate/mill volume

HE

High Energy

LE

Low Energy

L

mill volume fraction of minus grate size

m1, m2

mass transfer parameters

si

mill contents of size i

rj

rate of breakage out of size j

S20

average size of top 20% of mill load

t10

percentage which passes through aperture of 10% of the original size.

tp

percentage which will pass through a screen of aperture original size /p

ta

abrasion parameter

xi

particle size

xg

grate size (mm)

xm

size below which all will pass through the grate (mm)

g

gravitational constant

ρ

charge density

r

radial position of element

Appendix 9

a

screen


Appendix A

Autogenous & SAG Mill Model (Model 430-431) θ

angular position of the element

Nr

rotational rate at a radial distance r

rm

mill radius

ri

charge surface radius (see Figure A9.2)

θs

angular position of the shoulder

θr

angular position of the toe

Diam

mill diameter (m)

Len

mill length (m)

φ

fraction of critical speed.

A9.7

Known Restrictions

The model is not valid outside a range of 55% to 75% solids by weight in the feed. Mill speed is assumed to be 70% of critical or close to it. However for small changes in speed (~ ± 5%) a good approximation can be made by multiplying the rate at each knot by the relative change. That is, for +5% (ie. 70% increased to 73.5% critical) multiply by 1.05 or add ln (1.05) to the logarithm of the knot value. This assumes the number of impacts per mill revolution will not change. In reality more speed will give more lift and a slightly higher breakage energy. The classification model is very simple and only dependent on grate size. The xm parameter is driven by slurry viscosity. For viscous ores, xm may be up to 1mm. For clean ores (hard rock, clay free) 0.1-0.2mm is typical. This model has been tested against a large number of full-scale operations and a very wide range of pilot plant test data. The model has provided good predictions for design (Morrison, Kojovic and Morrell 1989) over a wide range of ore types. Detailed comparison with pilot plant data has highlighted areas where the model assumptions are not a sufficiently good approximation. Known areas to treat with caution are as follows. The assumption that grinding rates are constant at a given ball load is not true when •

there are large variations in mill feed sizing

•

the mill is taken from open circuit to closed circuit.


Appendix A9

Page A-95

Autogenous & SAG Mill (Model 430-431) Operating Limits

Appendix A

The model is numerically stable at any mill load (equation (A9.9)). Real world mills typically operate with maximum loads of 30 to 35% by volume of charge. However, they may be limited by motor power at much lower loads. There is usually a limit on ball load of 5 to 10% because of mechanical or power constraints. It is the engineer's responsibility to check these parameters against the limits for a particular mill.

Feed Sizing

The auto/SAG model 'forms its load' from the mill feed. If the mill feed size distribution is smooth (ie. a reasonably straight line on a Rosin-Rammler plot), simulated variations in feed sizing give sensible results. If the coarse end of the feed distribution is artificially adjusted for the feed is preclassified in some way, then the S20 assumption that the load can be treated as a single number becomes unjustified. Hence artificially adjusted top sizes will cause the model to predict wide variations in performance. (While these variations are excessive, it should be noted that real auto mills are also sensitive to feed top size). Similarly, if those fractions that limit throughput (notional critical size) are prescreened from mill feed, the model will be optimistic about increased throughput. (Once again, real SAG mills will also achieve much higher throughputs). However, predictions for recycle crusher are quite realistic. If mill operation is closed with a fine classifier (DSM screen or hydrocyclones) there is usually an increase in the observed grinding rates at 4mm. This means a typical SAG mill may have some 'free' grinding capacity for particles a few millimetres in diameter. Where the simulated mill is operating in closed circuit with a screen, the circulating load will tend to vary more (and the mill load less) with changes in hardness and feed sizing than the real mill. However trends will be correct and overall product sizing should be close.

Mill Power

Page A-96

Accurate measurements or estimates of mill dimensions, speed and ball and pulp load are required for the power calculation. Ensure that all data used are accurate.

Appendix 9


Appendix A Ball Size Effects

Autogenous & SAG Mill Model (Model 430-431) Ball effect is estimated by generating an equivalent load of ore particles. As the top 20% of this load is used to find S20, only the top one or two ball sizes can have any 'impact' on this calculation. Manipulating the finer ball sizes (ie. < half top size) have very little effect. In practice, it does change the fine grinding rates.

Ball Load Effects These have been investigated in some detail at pilot scale. In general, the harder the ore (low b and low ta) the less the grinding rates are affected. A soft ore however follows the accepted wisdom that increasing ball load will produce a coarser product. This may well be because the increased number of balls are now breaking the ore particles in the load which were doing the fine grinding. Discharge Rates

Considerable work has been carried out by Morrell (1990) on factors affecting discharge rates. These effects are also summarised in Morrell and Morrison (1989). See A11 for details. Overall, discharge rates will only become a limiting effect in very high viscosity ores. In this case, operation at a lower pulp density is recommended. The SAG mill is an effective pump and the charge will remain relatively 'dry'.

Mill Liner Effects The SAG mill model is valid for correctly designed traditional 'high/low' lifter type action. Wave liners or short lifters do not provide enough lift to achieve the default rates. If poor lift is combined with poor discharge, the mill only produces abrasion with a very fine product at a correspondingly low throughput. Further Developments

The JKMRC now has a substantial database of SAG/auto mill surveys and breakage characteristics. This data base has been used to develop the wider range variable rates AG/SAG model described in Appendix 11

Mill Load Limits

The autogenous and SAG mill model does not include an explicit maximum for the mill load. However, a warning will be flagged if the total load (ie. balls and pulp) exceeds 35% by volume. An error will be flagged if the total load exceeds 40%.


Appendix A9

Page A-97

Autogenous & SAG Mill (Model 430-431) A9.8

Appendix A

Fitting the Autogenous and SAG Mill Models

PARAMETER MENU XG XM Rate Rate Rate Rate Rate

1 2 3 4 5

These models are complex and calculation intensive. However, any computer which is suitable for MS Windows 95/98/NT should be adequate for AG/SAG model fitting. In the unlikely event that the fit is slow, the Select list may be used to restrict the scope of calculation or to fix recycle streams as “feed” streams. .

Initial Values

Use the grate width and 100 µm as initial estimates for xg and xm. The default breakage rates for auto and SAG will provide a good guess for each knot value.

Ore Type Parameters

For accurate results, these are best derived from tests carried out on representative samples at JKTech. For an existing operation, the values provided in the volume of supplementary information provide some guide to possible values.

Mill Load

Page A-98

If a reasonable estimate of load mass and sizing is available, then fitting with a range of A and b values may provide a way of estimating these values - that is - use the values which give the best fit for ratio work.

Appendix 9


Appendix A

Autogenous & SAG Mill Model (Model 430-431) Mill Load is fitted by inputting it as raw data into the dummy product stream. If you only have a total mill load estimate (eg. from bearing pressure), set the size fraction SDs to zero and the load SDs appropriately. Subtract the weight of balls from this load for a SAG mill and input it on the model screen.

Closed Circuit Operation

If the mill is being operated in closed circuit with hydrocyclones, it is better to reduce m1 from 0.37 to 0.25. This seems to provide a better approximation of the mass transfer response for a large recirculation of material finer than grate size.

Knot Positions

The spline knot positions are better left where they are for the 'normal' range of SAG mill feed sizings, 80mm < F80 < 250mm. However for very fine auto mill feeds, the limiting size fraction will also be finer and it may help to scale down all the knots. That is, reduce them by the same ratio. An alternative is to simply fix the larger knots at their default values. Hint: If the closed circuit simulation gives a very different circulating load, check carefully for size biases in the fit or in the data itself.


The Master/Slave fitting can be used with multiple sets of SAG/auto data. Ensure that you are using the same knots positions for each mill in the test. Similarly, each survey data set to be fitted simultaneously should have been collected with the same grate and pebble port size, and ball load.

A9.9

References

AUSTIN, L.G., LUCKIE, P.T. and KLIMPEL, R.R., 1984. The process engineering of size reduction: Ball Milling, S.M.E/A.I.M.E., NEW YORK: 561pp. AUSTIN, L.G., WEYMONT, N.P., PRISBREY, K.A. & HOOVER, M., 1976. Preliminary results on the modelling of autogenous grinding. 14th Int. A.P.C.O.M. Conf. The Penn. State Uni.: 207-226pp. LEUNG, K., 1987. An energy based ore specific model for autogenous and semi-autogenous grinding. Ph.D. Thesis, unpublished, University of Queensland. LEUNG, K., MORRISON, R.D. and WHITEN, W.J., 1987. An energy based ore specific model for autogenous and semi-


Appendix A9

Page A-99


Appendix A

autogenous grinding. Copper 87. Mining Engineers, Santiago, Chile.

Chilean Institute of

MORRELL, S. 1990. Simulation of bauxite grinding in a semiautogenous mill and DSM screen circuit. MEng Thesis, University of Queensland (unpublished). MORRELL, S. and MORRISON R.D. 1989. Ore charge, ball load and material flow effects on an energy based SAG mill model. SAG Conference, University of British Columbia, Vancouver. MORRELL, S., NAPIER-MUNN, T.J. and ANDERSEN, J. 1992. The prediction of power draw in comminution machines. Comminution-Theory and Practice, K. Kawatra (ed), SME, Chapter 17, pp. 235-247, 1992.

Page A-100

Appendix 9


Appendix A

Size Converter Model (490) A10

Size Converter Model (Model 490)

A10.1

Introduction

The model provides a product size distribution with a user specified P80. This is achieved by adjusting the feed size distribution finer or coarser as required. The model is useful when there is no process knowledge of upstream comminution devices, or when a size distribution of a particular size is required for sensitivity analysis.

A10.2

Model Details

The feed to the model is adjusted by moving it sideways on a Cum % Passing v size plot until the product P80 matches the specified P80 as closely as possible.

A10.3

Fitting the Size Converter

There are no fittable parameters in this model.

A10.4

Known Restrictions

The model is limited in its ability to generate a product which is coarser than the feed by the coarsest screen available in the feed combiner and product ports. It is always wise to plot and inspect the graph of the feed and product to ensure that the shape of the distribution is reasonable.


Appendix 10

Page A-101

Appendix A

Size Converter Model (Blank Page)

Page A-102

Appendix 10


Appendix A

Variable Rates SAG Model (435)

A11

VARIABLE RATES SAG MODEL

A11.1

Introduction

The Leung AG/SAG model (A9) typically requires a full scale plant or pilot mill survey combined with ore breakage testing to generate a set of grinding rates. However research in the mid 1990’s using a large database of pilot and full scale milling tests has lead to the development of a correlation between model grinding rates and mill operating conditions. A further correlation between mill feed sizing and ore breakage characteristics has also been developed. These two correlations now allow mill performance to be predicted for a wide range of mill sizes and operating conditions. Hence the model can be used to evaluate optimisation strategies in existing plants and to investigate (and compare) grinding circuit configurations at the pre-feasibility stage thus reducing the cost of pilot testing. The underlying model is still identical with that developed by Leung et al (1987) except that

• grinding rates have been related to mill diameter and operating conditions, and • A model which includes grate geometry (but does not incorporate pulp lifter capacity) now describes slurry holdup. This approach was reported by Morrell and Morrison, 1996. If you are new to SAG mill modelling, it is strongly recommended that you work through Appendix 9 (the Leung model) before attempting to use the Variable Rates model. The VR model interface has been slightly revised for Version 5 mostly to make recycle effects easier to specify.

A11.2

Scaling Approach

A large proportion of AG/SAG model users either carry out pilot scale tests and wish to predict full scale operation or carry out fullscale tests and wish to predict performance at different operating conditions. The variable rates model has been implemented to facilitate this scaling process as in the rod and ball mill models. The variations in rates also depend on recycle and feed sizing. Hence, this model allows the user to select appropriate streams for recycle data. For model fitting, the original and simulated cases will usually be identical. This is considered in detail in section A11.6.

A 11.3

Slurry Holdup Model

The transport of slurry through the mill is described by a function which relates the hold-up of slurry, grate design, grate open area and mill speed Version 5.1 November 2001

Appendix A11

Page A-103


Appendix A

to the volumetric discharge rate through the grate (Morrell and Stephenson, 1996):

Jp

= k Q0.5 γ-1.25 A-0.5 φ0.67 D-0.25

(A11.1)

where Jp = fractional slurry hold-up D = mill diameter (m) 2 A = total area of the grate apertures (m ) φ = fraction of critical speed 3 Q = volumetric flowrate out of the mill (m /hr) γ = mean relative radial position of the grate apertures γ =

∑ ri ai rm ∑ ai

ai = open area of all holes at a radial position ri rm = radius of mill inside the liners. Classification by the grate is related to the effective grate aperture by a simplified classification function. For illustrative purposes a conceptual view of the weighted radius model is shown in Figure A11.1.

0.75 - 0.8

0.85 - 0.95

Figure A11.1: Weighted Radius For Two Grate Designs

Page A-104

Appendix A11


Appendix A


A11.4

Variable Rates Model

Relationships between the operating conditions and changes in the breakage rate distributions within the JKMRC’s pilot mill database (Mutambo, 1993) were developed. These results were augmented with results from full-scale mill data in cases where the pilot mill database contained little or no variation in the parameter of interest e.g. mill speed. To indicate the extent of the pilot mill database, Table A11.1 summarises its details. Table A11.1: Pilot Mill Database Details

New Feed F80 (mm) Ball load (%) Recycle load (%) No. different ores No. tests

Range 35-140 0-12 0-500 16 52

The breakage rate distribution is described within the model using cubic splines (Ahlberg, 1967). This gives rise to five breakage rate values each of which relate to a particular particle size and which together characterise the entire breakage rate distribution. The five standard particle sizes chosen are 0.25, 4, 16, 44 and 128mm which have associated with them breakage rates which are labelled R1, R2, R3, R4 and R5 respectively.

Breakage rate (hr^-1)

1000 R5

100 R4

R2

R1

R3

10

1 0

0

1

10

100

1000

Size (mm)

Figure A11.2: Characterisation of the Breakage Rate Distribution These rate curves exhibit a characteristic shape. The coarser (R5 and R4) rates relate to abrasive breakage while the finer rates R1 and R2 exhibit similar characteristics to those of coarse ball milling, ie. predominantly impact breakage. The pronounced dip in the rates at R3 is associated with the critical size which may limit mill throughput by building up to excessive levels. Typically it is in the 25-75mm range and Version 5.1 November 2001

Appendix A11

Page A-105


Appendix A

varies with particular combinations of feed sizing, breakage characteristics and the magnitude of the breakage energy developed in the mill. To determine the relationship between operating conditions and the breakage rate distribution, the breakage rates R1-R5 were regressed against operating conditions. The resultant equations were of the following form: Ln (R1) = (k11 + k12Ln(R2) - k13Ln(R3) + JB (k14 - k15F80) - DB)/Sb ……(A11.2) Ln (R2) = k21 + k22Ln(R3) - k23Ln(R4) - k24F80

(A11.3)

Ln (R3) = Sa + (k31 + k32 Ln(R4) -k33 Rr) /Sb

(A11.4)

Ln (R4) = Sb(k41 + k42 Ln(R5) + JB(k43 - k44F80

(A11.5)

Ln (R5) = Sa +Sb(k51 +k52F80 + JB (k53 -k54F80) - 3DB)

(A11.6)

where Sa

= = Sb = = DB = = JB = associated Rr = = F80 kij

= =

rpm scaling factor Ln (simulated mill rpm/23.6) fraction of critical speed scaling factor simulated mill fraction of critical speed/0.75 ball diameter scaling factor Ln (simulated ball diameter/90) % of total mill volume occupied by balls and voids recycle ratio (tph recycled material_-20+4mm) (tph new feed) + (tph recycled material -20+4mm) 80% passing size of new feed (mm) regression coefficients

The regression coefficients for equations (A11.2)-(A11.6) are given below and are based on the JKMRC current database at mid 1996. As more data are collected and our understanding of the various factors increases, these coefficients are likely to be modified. Table A11.2: Regression Coefficients j 1 2 3 4 5 Page A-106

k1j 2.504 0.397 0.597 0.192 0.002 Appendix A11

k2j 4.682 0.468 0.327 0.0085 --

k3j 3.141 0.402 4.632 ---

k4j 1.057 0.333 0.171 0.0014 --

k5j 1.894 0.014 0.473 0.002 --


Appendix A

Variable Rates SAG Model (435) It can be seen from the equations that the finer size rates are functions of the rates of the coarser sizes. Hence R1 is a function of R2 and R3 etc. The rates can be considered as falling into 2 groups which represent the grinding media and product size fractions. Hence the grinding media group contains the rates R4 and R5 (related to particles >30mm) the magnitude of which affect the throughput. The product group incorporates rates R1, R2 and R3 (related to particles < 30mm) and the magnitude of these affects the final product size. It is of particular note that the rates are interrelated in a complex manner and are best understood by graphing the entire breakage rate distribution.

A11.5

Effect of Key Parameters

The variable rate model allows the effects of a number of key parameters to be considered independently.

It is worth mentioning that ‘original’ does not provide a basis for scaling in this model as it does in rod and ball mill models. It provides a marker to allow the user to see how much the rates have varied from the original case. Ball Load

The effect of changing ball load on the breakage rate distribution is illustrated in Figure A11.3.

10000

0% balls Breakage rate (1/hr)

1000

4% balls 8% balls

100

10

1 0

1

10

100

1000

Size (mm)

Figure A11.3: Effect of Ball Load on Breakage Rate Distribution The resulting relationship is as expected in that by increasing the ball load the breakage rates increase at coarser sizes but reduce at finer sizes. This has the effect of predicting higher throughputs at coarser grinds as the ball load is increased. However, it is commonplace to operate at too high a ball charge often because of historical experience with softer, Version 5.1 November 2001

Appendix A11

Page A-107


Appendix A

oxidised, surface ore. As the ore becomes harder it may well be possible to replace balls with ore as grinding media for more power effective operation.

Makeup Ball Size

No significant dependence of the breakage rates on ball size was found in the pilot mill database. The SAG model does account for ball size changes in terms of the energy provided during impact. It does this by changing the mean grinding media-size, which in turn changes the ‘energy level‘ of the mill. This ‘energy-level‘ term is used to determine the specific energy of impact. As the ball size is increased, therefore, the specific energy increases and hence for a given impact event a finer product size distribution occurs. However, as the ball size is increased the number of grinding media per tonne of charge will decrease. As the breakage rate is related to the number of impacts provided by the grinding media then a reduction in the breakage rate may be expected to occur. To account for this a ball scaling factor is used. Figure A11.4 illustrates the effect of the ball size correction factor on the breakage rate distribution. It should be emphasised that it is usually argued that a coarser ball size will give a higher throughput but with a coarser grind. In practice, experiments with full-scale mills are sometimes inconclusive and mill operators see little or no effect when experimenting with ball size. This may be due to the counter-effect of reduced numbers of balls providing higher breakage energies when increasing ball size. The model predicts such a response by increasing the breakage energy and reducing the breakage rate. In some instances the one effect may outweigh the other, in which case a response will be noted. Over some ranges of ball sizes, however, little or no effect will be seen.

Breakage rate (1/hr)

1000

100

10 94mm balls 125mm balls 1000

100

10

1

0.1

0.01

1

Size (mm)

Figure A11.4: Predicted Effect of Changing Ball Size

Page A-108

Appendix A11


Appendix A

Feed Size F80 Effects for SAG Milling


The effect of F80 was found to be the most difficult one to evaluate as it interacted with the ball charge level. At relatively high ball charges (10% or more) high F80 values were detrimental as evidenced by the reduction in the breakage rates illustrated in Figure A11.5.

10000

f80=75;Jb=10%

Breakage Rate (1/hr)

1000

f80=125;Jb=10%

100

10

1 0

1

10

100

1000

Size (mm)

Figure A11.5: Effect of F80 on Breakage Rate Distribution - (SAG mill)

Feed Size F80 Effects for Autogenous Milling

However in the case of autogenous grinding the pattern is different. In this case a higher F80 promotes breakage in the coarser size fractions (Figure A11.6). This is to be expected when it is considered that in autogenous milling large rocks are required to break ore in the R5 size range (128mm). As the F80 increases, this will typically result in more coarse rocks in the charge able to break R5-size ore and hence R5 will increase. In SAG mills running with higher ball charges, the rock component of the grinding media plays a lesser role in dictating the breakage rate and contributes more to the rock ‘burden’ which has to be ground down. Feeds with F80 values and hence more coarse feed rocks, can thus be expected to reduce the breakage rate. Caution needs to be exercised, however, as it has been found that the F80 is not always a good indication of the feed size distribution. This is particularly noticeable with autogenous mills whose performance may fluctuate considerably yet maintain a reasonably constant F80. In such cases the distribution changes systematically with performance and that typically higher proportions of 25-50mm material in the feed result in lower feedrates, ie. less sub-grate size material is present in the feed and more near size material has to be broken.


Appendix A11

Page A-109


Appendix A

1000 f80=75;Jb=0%

Breakage Rate (1/hr)

f80=125;Jb=0%

100

10

1 0

1

10

100

1000

Size (mm)

Figure A11.6: Effect of F80 on Breakage Rate Distribution - (AG mill)

Effect of Recycle Recycle loads broadly fall into 2 categories viz.: Load 1.

Coarse recycles from trommels, vibrating screens and recycle crushers which typically comprise only -20 + 4 mm material and have P80 values of the order of 8 - 12mm,

2.

Fine recycles from hydrocyclones and DSM screens which are predominantly –4 mm material and have P80 values of the order of 0.2 - 0.5 mm.

It has been found that the amount of recycled material in the -20 + 4 mm size range is inversely related to the amount of breakage that this material is subjected to. This can be explained if one considers that these rocks are broken by coarser rocks and balls whose frequency does not appreciably change with changes in recycle load. However as the amount of recycled -20 + 4 mm rock increases, the amount of this size material in the load will increase. As the breakage rate in a given size class is related to the ratio of the number of coarser rocks and balls to the number of rocks in the given size class, then increasing the -20 + 4 mm recycle will result in a drop in the breakage rate in this size range (R3 size = 16 mm). The changes in the breakage rate distribution as the coarser recycle increases is illustrated in Figure A11.7. Interestingly, recycle of fine material ie. –4 mm did not correlate with any of the breakage rates. This may be related to the breakage mode of this material which is believed to be dominated by attrition. Where the material has been recycle crushed, it is considered to have similar properties to new feed and is not included as -20 +4 mm recycle.

Page A-110

Appendix A11


Appendix A


Breakage rate (1/hr)

1000

100

10

Rec=0 Rec=.05 Rec=.1

1000

100

10

1

0.1

1

Size (mm)

Figure A11.7: Effect of Recycle Load on Breakage Rate Distribution


Appendix A11

Page A-111


Appendix A

Recycle Control in For the most part, the Version 5 model is identical with the V5 Variable Rates SAG model in Version 4. There are, however, a couple of important differences which relate to control of recycle of –20 +4mm material on the grinding rates. As for V4, the User inputs new feed rate tonnes per hour and 80% passing size for Simulated and “Original” mills. Recycle Options – In Version 4, there are two implied switches. The first is “Fixed Recycle”. If the User inputs a Fixed Recycle tonnage, all simulations will use this value to calculate the recycle ratio. Version 5 uses this implied switch as well i.e. the fixed recycle tonnage value is set to zero to allow for simulated recycle. The second implied switch in Version 4 is to select one (or more) recycle streams from the flowsheet. In version 5, this switch is now explicit as “Use Recycle in Calculations”. If this switch is set to one, the actual recycle is now calculated by the model as the difference between –20 +4mm in new feed (specified by the user) and in the total feed to the SAG mill. Hence the User uses the Ore Feeder size marker to estimate % 20mm and % -4mm and enters the difference into the appropriate field on the SAG model. Comment. The effect of recycle has always been difficult to model and it also the subject of current research. It provides some compensation for recycle material ‘survivors’ being likely to be somewhat ‘harder’ than new feed particles in the same size fraction. However, if the recycle stream is crushed, new flaws will be generated and the original feed properties retained. Therefore it is recommended that ‘Use Recycle …. ‘ be turned off when a recycle crusher is used, with the following note of caution. If K1 is larger than 4mm, a proportion of recycle crusher feed will not be crushed. The bypassed –20 +4mm can be compensated for by iteratively adding the ‘new’ –20 +4mm in the crusher product to the new feed % of –20 +4mm. Excessive fine recycle may make this model unstable. However, excessive fine recycle will often make real AG/SAG mills unstable and it a consequence of a realistic model.

Page A-112

Appendix A11


Appendix A Mill Speed/Mill Diameter

Variable Rates SAG Model (435) The breakage rate is related to the number of size reduction events per particle, per unit time and is hence a frequency. This in turn must be related to the frequency with which the mill rotates (rpm). A scaling factor is therefore applied to account for changes in the rotational rate. For a given fraction of critical speed the rpm decreases with mill diameter0.5 and hence this scaling factor will also change with mill diameter. All else being equal, therefore, a larger diameter mill will have a lower breakage rate than a smaller unit. However it is pointed out that the JKMRC model inherently scales on the basis of breakage energy which it relates to mill diameter. Therefore, whereas a larger diameter mill will have a lower breakage rate it will have a higher breakage energy. In a given mill as the rpm changes, apart from the rotational rate, the shape of the grinding charge will also change in line with the fraction of critical speed (Morrell, 1996). Typically as the fraction of critical speed increases the charge is subjected to increased lift and hence impact breakage is enhanced. It is at the expense of attrition breakage which is normally associated with cascading motion and which is prevalent at lower speeds. To account for these effects a further scaling factor is applied which is based on the fraction of critical speed. Figure A11.8 illustrates the predicted changes in the breakage rate distribution as speed is changed. 10000 85% Cs 75% Cs 1000

65% Cs

100

10

1

Size (mm)

Figure A11.8: Predicted Effect of Changing Speed on the Breakage Rate Distribution

Mill Power

The variable rates model allows the user to specify the conical slope inside the liners of each mill end. The mill power estimate includes the conical ends (Morrell, 1996).


Appendix A11

Page A-113


A11.6

Fitting Single Data Sets

Appendix A

Parameter Fitting the Variable Rates Model

Model fitting the variable rates model is quite similar to fitting the Leung model (A9). The defaults for the original mill grinding rates are all set to zero, ie. the intercepts of the rate equations (Table A11.2) are included in the model. Hence the fitted rates indicate how far the measured mill is operating from “typical” conditions. The recommend strategy is to first fit xg and xm with the grinding rate intercepts set to zero. If the mill has pebble ports, set the initial pebble port size to the largest measured particle in the mill discharge. If the xg and xm fit is plausible, add the pebble port size (PPSize). Use the measured open areas for pebble ports and grates and the measured weighted radius/mean relative radial position for the grates. Note that the grate open area includes grates and pebble ports. The recycle streams are selected from the unit menu. The measured recycle rate (-20 +4 mm) should also be entered as data. (When this field is zero, the calculated recycle is used. This is appropriate for simulation). The new feed size (F80) should be noted and entered for both Sim(ulated) and Org(inal) mills as should all of the other measured mill data. If the xg, xm and PP (pebble port) size fit is plausible, adjust the scale factors on Breakage Rate “Constants” to 0.1 and include them in the next fit. The open area fractions (Grate OA) can be selected to fit. They are only suited to matching wear conditions and should not be fitted together with grate or pebble port sizes as the parameters are likely to interact quite severely. Given good data and ore characterisation this model will often predict the measured results quite well and model fitting is very simple.

Page A-114

Appendix A11


Appendix A


Remember – xg, xm and PP size are all square mesh equivalent sizes. Therefore, aperture shape and particle shape will interact. A slabby particle will appear much larger to a square mesh screen than to a slotted grate aperture! Fitting Multiple Data Sets

A comprehensive pilot test program will produce data over a range of operational conditions. For sophisticated users, the variable rates model allows several sets of pilot data to be analysed simultaneously. The first step is to analyse each set by using its own select list. This should identify any data problems. Then add each data set onto a combined select list for master slave fitting. One of the pilot data sets is selected as a base case. For this set, simulated and original inputs are the same. For the other sets, change the simulated mill conditions as required (eg. Ball load) and use the base case original mill conditions in all tests. Add all of the measured load and product streams to the model fit data list. Use the master/slave capability to simultaneously fit, xg, xm, PPort size and grinding rate intercepts to all data sets at once. Notes: • a fast computer (Pentium 166 or better) is required for three or more SAG data sets • Multi-fit capability is not available in Version 5. However, the number of fittable sets of port data will be expanded in later releases. This approach can also be used to simultaneously analyse several sets of operating plant data, even between different sizes of mills treating similar ores. In either case, a good overall fit indicates a model which can be used for prediction over a wide range of operating conditions. A poor overall fit, particularly if the grinding rates are lower than typical (negative intercepts) may indicate shortcomings in data collection. More seriously, it may also indicate more significant problems such as poor liner design or inadequate pulp transport capacity (i.e. pulp lifters). Larger rates may indicate particularly good practice or at the coarse knots, decreasing ore competence at coarser sizes.


Appendix A11

Page A-115


A11.7

Appendix A

Using the Variable Rates Model for Simulation and Design

This model is quite complex and a good appreciation of both the model and SAG mill operations are recommended before use for design. Comprehensive industrial research work over the last decade has built up the database for this model and exposed some conceptual weaknesses which are being addressed with two new models. However, the variable rates model is now a powerful tool for data analysis, circuit evaluation and AG/SAG mill design. The following points should be noted. Recycle Streams

Up to three recycle streams can be selected from the model menu. These should be recycles which actually go into the mill, eg. Recycle crusher product, not feed. The “Fixed Recycle” input should be set to zero for simulation to allow the calculated flow of -20 +4mm to be used. (Input the measured flow for model fitting). Where the material has been recycle crushed, it is considered to have similar properties to new feed and is not included as -20 +4 mm recycle. NB: V5 handles recycle loads differently from V4. See pages 108109 for details of the differences.

Load Limits

The feed trunnion diameter indicates the maximum volumetric load limit. If the simulated mill limits at a lower level than the actual mill, reduce this diameter. Beyond a certain load, the power model is unlikely to be reliable and the power estimates are set to zero.

Grate Flow Limits (Mass Transfer “Law”)

The flow correlation detailed in A11.3 provides a maximum flow estimate at the simulated mill load. The user may enter a design maximum load level for which a maximum flowrate estimate is also calculated. These estimates relate to flow through the grate. They assume that the pulp lifters can remove all of the grate discharge. This is not always true for mills operating in closed circuit with cyclone or fine screens. If the simulated flow exceeds the maximum, the mill will likely fill up with fines and go into overload as the slurry pool reduces impact breakage. This effect is not simulated by the model.

Feed Size Considerations

Page A-116

The F80 values for new feed for both simulated and original mills are entered by the user.

Appendix A11


Appendix A

Variable Rates SAG Model (435) For design, a reasonable estimate of F80 is often difficult. Power based equations typically divide by the feed size so the assumption becomes unimportant but real mills are sensitive to feed sizing as are accurate models. The JK database shows reasonably systematic dependence of AG/SAG F80 (crusher P80) with all hardness measures. The harder an ore, the coarser the resulting crusher product at the same crusher closed side setting. The best correlation is with the JK abrasion parameter ta. For a design case, the F80 of the feed can be estimated from the measured ta with a standard deviation of about 10% of the primary crusher closed side setting. F80 (mm) = {css - 78.7 - 28.4 ln (ta)} s.d. = 0.1 css.

(A11.7)

This is not a perfect answer, as the size distribution slope also varies as shown below.

100

10

Coarse/hard ore Fine/soft ore 1 .01

.1

1

10

100

1000

Size (mm)

Figure A11.9: Typical AG/SAG mill feed sizings

The size converter model (see Appendix A10) can be used to adjust from a similar ore to the target range for simulation. (Note that it is also possible to conduct a test in a pilot adit to estimate the likely run of mine size distribution. This distribution can be fed to the crusher model to predict the mill feed distribution. Contact JKTech for assistance with test blast design.)


Appendix A11

Page A-117


A11.8

Appendix A

Known Restrictions

This model does not take account of the variation in breakage energy at different mill loads. Therefore pilot and industrial operation should be measured at realistic operating loads (ie. >20%). As noted earlier, pulp lifter capacity may limit before maximum grate capacity is reached. The single number grate characterisation (Mean relative radial position) is a useful approximation. However, it should be used with actual grate designs, not hypothetical variations which may not be able to be manufactured. As the database of very large mills expands, it is becoming apparent that the charge in a large coarse feed mill restricts the maximum circulating load. Hence for mills 11m in diameter (or larger) treating coarse feed, the simulated circulating load should be restricted to 25% of new feed rate. This can be done by reducing the grate open area parameter. This is an area of continuing research at JKMRC. With the large database of SAG mill test work, it is clear that maximum throughput does not always correspond to maximum mill power draw or maximum mill load. For hard ores, maximum throughput requires sufficient impact energy at the toe of the charge. Hence the maximum throughput (at maximum discharge coarseness) will often occur between 20 and 30% volume mill load. Research at JKMRC is developing models which will account for this effect and others such as the difficulty of removing pebbles for crushing from very large mills. For mills of larger diameter than 10m, a maximum recycle crusher flow of less than 25% of new feed rate is recommended as a constraint on simulations. (Mills with very fine feed and large grates may exceed this estimate) Manipulating the SAG mill feed size distribution by pre-crushing is another way of shifting the throughput/product relationship for hard ores. A limitation has been found on the accuracy of the response of the rate equations to changes in F80, particularly if the new feed F80 is outside the range of the data base. The recommended F80 for use in the model is calculated from the equation: F80 = 71.3 – 28.4 * ln (ta) This F80 value should be used as the Reference F80 value on the Recycles tab in the Variable Rates SAG Model equipment window.

Page A-118

Appendix A11


Appendix A


A11.9


Variable Rates SAG Model Printout

Appendix A11

Page A-119


Page A-120

Appendix A11

Appendix A


Appendix A


A11.10

References

Ahlberg J H, Nilson, E N & Walsh, J L, 1967. The Theory of Splines and Their Applications. Mathematics in Science and Engineering, 38, Academic Press, New York and London Andersen J S, 1989. Development of a Cone Crusher Model. M.Eng.Sc Thesis, University of Queensland. Leung. K, Morrison R D & Whiten W J, 1987. 1987. An Energy Based Ore Specific Model for Autogenous and Semi-autogenous Grinding Mills. Copper 87, Santiago Chile. Morrell, S. 1996. Power Draw of Wet Tumbling Mills and its Relationship to Charge Dynamics. Part I: A Continuum Approach to Mathematical Modelling of Mill Power Draw. Trans. Instn. Min.Metall, 105, C43-53. Morrell S & Stephenson I, 1996. Slurry Discharge Capacity of Autogenous and Semi-autogenous Mills and the Effect of Grate Design. Int. J. Miner. Process. (In press). Morrell S & Morrison R D, 1989. Ore Charge, Ball Load and Material Flow Effects on an Energy Based SAG Mill Model. Presented SAG 1989, University of British Columbia. Editors. Mular & Agar. Morrell S & Morrison R D, 1996. AG and SAG Mill Circuit Selection and Design by Simulation. SAG 96, edited Mular, Barrett and Knight, Vancouver 769-790. Mutambo. J, 1993. Further Development of an Autogenous and Semiautogenous Mill Model. M. Eng Sci. Thesis. University of Queensland (unpublished).

Needham T M & Folland G.V. 1994. Grinding Circuit Expansion at Kidston Gold Mine. Presented at SME Annual Meeting, Albuquerque, New Mexico. February 14 -17.


Appendix A11

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Appendix A

(Blank Page)

Page A-122

Appendix A11


Appendix A

High Pressure Grinding Rolls (Model 402)

A12

High Pressure Grinding Rolls (402)

A12.1

Introduction

The high pressure grinding rolls crusher(HPGR) - also known as the roller press or roller mill - was invented by Klaus Schönert in Germany as an outcome of his fundamental research on rock fracture (Schönert 1988). The device has been most widely used in cement clinker grinding in Europe, but is beginning to find application also in mineral processing. One of the first such applications was in diamond ore processing in Southern Africa and latterly in Australia, where it was shown that the device offered some degree of selective liberation of the diamond from the host rock. However the claimed advantage for most mineral processing operations is the very high reduction ratio achieved, and the favourable specific energy consumption, compared to conventional technologies. Some evidence has also been reported for downstream benefits such as reduced grinding strength and improved leachability due to microcracking (Knecht 1994). Potential applications therefore include preparation of material for fine grinding, replacement of tertiary crushing, rod milling and primary ball milling in primary grinding, and the attainment of enhanced leaching performance. The general principle is illustrated in Figure A12.1.

Figure A12.1: The high pressure grinding rolls (roller mill)

Schönert’s research has shown that the most efficient way to fracture a rock mechanically is to load it between two opposing platens until it fails. One way to do this at a high throughput is to compress a bed of such particles between two contra-rotating driven rolls. In industrial practice these rolls can be very large, up to 2.8 m in diameter. One roll is mounted on fixed bearings, and the other can move linearly against a hydraulic ram or (in small machines) a spring.


Appendix A12

Page A-123

High Pressure Grinding Rolls (Model 402) Appendix A The hydraulics are set to deliver a particular pressure to the bed of particles passing through the machine, compressing it to a density greater than 70% by volume. This pressure, which usually exceeds 50 MPa, controls the size reduction in the machine. The material leaves as a compressed cake (flake), which may have to be disagglomerated prior to further processing. Particular care must be taken to do this correctly when determining a product size distribution. The preferred method is to break-up the cake using a 2 or 3mm screen, take representative samples and then to use an ultrasonic bath to deagglomerate the particles. Deagglomeration can be completed in either water or acetone but preferably the latter. The objective is to produce a repeatable size distribution without additional comminution.

A12.2

Model Structure

Underlying the structure of the size reduction model are three assumptions about the inherent breakage mechanisms that occur in HPGRs. As shown in Figure 12.2. Pre-crusher

If particles are bigger than a certain critical size they will be broken directly by the roll faces as would occur in a conventional rolls crusher. The breakage in this zone can be considered as analogous to a ‘pre-crusher’, the products from which may subsequently pass to a region where a bed under compression has formed. The boundary between the pre-crusher and bed compression regions is defined by a critical gap (xc).

Edge Effect Crusher

Breakage at the edge of the rolls is different to that at the centre and conforms more to that experienced in a conventional rolls crusher. This is the so-called ‘edge effect’ which defines the proportion of relatively coarse particles usually seen in HPGR products. Its existence has been explained by the pressure gradient across the width of the roll and the static confinement of the ore at the edges of the rolls which the cheek-plates provide.

Compressive Bed Crusher

At some point away from the edges of the rolls, and extending upwards from the area of minimum gap (xg) to an area bounded by the critical gap (xc), is a compression zone where breakage conditions are similar to those experienced in a compressed packed bed. From a modelling viewpoint these assumptions can be accommodated in the conceptual structure shown in Figure A12.2. Feed firstly passes to the ‘pre-crusher’. Particles greater in diameter than the critical gap (xc) are crushed below this size in a single particle breakage mode. The products from this breakage

Page A-124

Appendix A12


Appendix A

High Pressure Grinding Rolls (Model 402) then combine with feed particles which are smaller than xc. A proportion is then diverted to another single particle crusher stage where all particles greater than the minimum gap (xg) are crushed to below this size. The remainder are diverted to a compression stage where all particles greater than xg are crushed below this size but in a compressed bed mode. All products then combine to produce the final HPGR product. Feed to the HPGR Precrusher: conventional rolls crusher; gap = x c Splitter: determines the fraction affected by the "edge" phenomenon

Compressive bed breakage crusher; gap = x g

Edge effect crusher: conventional rolls crusher; gap = xg

Combiner

Product from the HPGR

Figure A12.2: Schematic Structure of the HPGR Model

A12.3

Breakage Processes

HPGR Model

The model contains three breakage processes and one splitting process between the edge and compressed bed zones. For the breakage processes the JKSimMet crusher model is used to describe the size reduction. Four model parameters are required for each breakage process: K1, K2 and K3 and t10. The first three are used to describe the probability that a particle will be broken whilst the t10 is used to describe the product size distribution that results. For a detailed model description, refer to Appendix 6.3.

t10 Definition

The t10 is defined as the percentage passing one tenth of the original particle size in the product after breakage. Other tn parameters can be similarly obtained from a product size distribution, eg. t2 is the percentage passing one half of the original particle size. From breakage tests the t10 and a number of other tn values are determined from the breakage products. These values are stored in tabular form in the model which, given a value of t10, uses spline interpolation to determine the associated tn values and hence reconstructs the entire product size distribution.


Appendix A12

Page A-125

High Pressure Grinding Rolls (Model 402) Appendix A For the pre-crushing process, breakage of particles is assumed to be Pre-crushing in single particle mode in which rocks are nipped directly by the faces of the rolls, similar to a conventional rolls crusher. The parameters used to describe crushing in this zone are determined from tests conducted in a conventional (non-HPGR) laboratory rolls crusher and single particle breakage tests, and remain constant in the model fitting and scale-up. The parameter K2 is set as the critical gap, xc, which is expressed by Morrell et al (1997)

4 ρ g Dx g   x c = 0.5 {(D + x g ) (D + x g ) 2  ρc  

0.5

}

(A12.1)

where xg is the working gap, D is roll diameter, ρc is bulk density of feed and ρg is flake density.

xc

αc

xg

D

Figure A12.3: HPGR Schematic Showing Compression or Nip Angle

In the edge zones rock breakage is also assumed to take place in single particle mode. The parameters used to describe crushing in this zone are the same as that in the pre-crushing, except K2 which now takes the value of the working gap (xg). Compressed Bed In the compressed bed crushing zone, on the other hand, size reduction is assumed to be similar to that experienced by a bed of Breakage particles in a piston press. The parameters used to describe size reduction are determined from tests in a laboratory or pilot scale HPGR machine combined with breakage tests in a piston press. The piston press tests provide information on the relationship between size reduction and energy input in a compressed bed. They also provide a description of the characteristic shape of the product size distribution. If the piston press tests are not available, then the results from the single particle Drop Weight test may be used to determine the Compressed Bed Breakage Function (Section A12.4)

The parameter K2 for the compressed bed crushing is the working gap xg, whilst K1 is set as zero. Page A-126

Appendix A12


Appendix A


The parameters K3 and t10 are fitted to the laboratory scale HPGR test data. These are the only two breakage parameters required to be fitted to laboratory data. Edge Crushing Bypass

The last sub-process in the model is the split to the edge and compressed bed zones. The edge zones are associated with the drop in pressure that is experienced towards the edge of the rolls. Their extent is assumed to be a function of the working gap. The fraction of feed which is crushed in the edge zones (f) can therefore be expressed as: f

xg g L

=

(A12.2)

where g is split factor and L is the roll width. Using pilot scale HPGR test results where sizing data of both pure flake and total product were available, the split factor g was found to be approximately constant with a value of 3.4. In physical terms this means that the edge effect zone extended from the edge of the roll a distance equivalent to 1.7 times that of the working gap. By sizing the pure flake and total products from lab/pilot test results f can be determined experimentally. Recent work suggests that the fraction of material being subjected to edge crushing is usually about 10%. Thus, the model may be simplified by manipulating g (split factor) to ensure that 10% of the feed reports to the edge crushing zone.

A12.4

Compressed Bed Breakage Function

The product size distributions produced at different energy inputs (or reduction ratios) can be characterised by a family of “t” curves. Measurement and analysis for impact breakage are detailed in Appendices 6.3 and 6.4. This approach can be extended to predict required breakage power and scaled to net crushing power using an efficiency factor., typically - 1.25 (Appendices 6.5 and 6.6). Single particle impact breakage data.

t10 10.0 20.0 30.0

t75 6.05 8.33 10.0

t50 7.94 10.90 13.10

t25 12.60 17.30 20.70

t4 46.70 62.60 74.50

t2 74.60 90.30 99.20

This approach can be extended to compressive breakage by using a piston press to compress closely size fractions (

( 2 ) in a controlled manner. 4

The resulting products are sized and fitted to a spline surface. This surface can be regenerated by the model from a matrix of spline function values. These values are input to the model as Version 5.1 February 2003

Appendix A12

Page A-127

High Pressure Grinding Rolls (Model 402) Compressed Bed Breakage Test.

t10 10.0 30.0 50.0

t75 4.04 13.53 23.02

t50 6.48 19.71 31.91

Appendix A t25 7.51 22.24 38.00

t4 17.65 41.35 52.37

t2 35.44 58.36 69.01

It can be clearly seen that these breakage models are different. The power requirements can also be characterised with particle size dependence if required and also related to motor power (Section A12.6).

A12.5 Throughput Throughput is controlled principally by roll dimensions, speed and profile, and material characteristics such as size hardness and particle-roll friction (and thus nip-angle). The profile and material of the roll surface is important in controlling both wear and machine performance, and various options are offered by the different manufacturers. The rolls throughput can be theoretically expressed as Q

= 3600 U L xgf ρg

(A12.3)

where

Q U L xgf ρg

= = = =

mass throughput (tph) circumferential velocity of the rolls (m/s) length of rolls (m) working gap (m) – from the flake thickness measurements = flake density (t/m3)

It is realised that A12.3 does not take into account the slip between feed material and the rolls surface, nor does the feed characteristics (particle size and size distribution, moisture, etc). Figure A12.3 shows the deviation between the measured throughput and the calculated one using Equation A12.1 for Primary diamondiferous ore treated through a 100 mm Polysius laboratory scale HPGR. It is obvious that Equation A12.3 over-predicts the HPGR throughput at high rolls speed, which may indicate that slip exists in the HPGR operation at these speeds.

Page A-128

Appendix A12


Appendix A


12 0.38 m/s 1.50 m/s 2.50 m/s 3.10 m/s

10

tph (measured)

8 6 4 2 0

0

2

4

6

8

10

12

tph (calculated)

Figure A12.4: Deviation of the Throughput Calculated from Equation A12.4 for Diamondiferous Ore Treated through a Laboratory HPGR at Various Speeds

To correct for the slip effect it is considered that for a specific feed the slip is a function of the rolls speed and the dimensionless working gap which is defined as xg /D, where D is the rolls diameter. Qm Figure A12.4 plots the correction factor c (c = Q , where Qm is c the measured throughput and Qc is the calculated by Equation A12.3) versus the product of the speed and the dimensionless gap xg (U* D ) for the Diamondiferous ore using the laboratory HPGR data. A linear regression on the plot was obtained and Equation A12.3 was accordingly modified as: Q

=

3600 U L xg ρg c

(A12.4)

where c is the correction factor determined from Figure A12.2. Recent work by Schonert (2000) suggests that under normal operating conditions, slip does not occur in the compression zone. If normal operating conditions are assured, then the correction factor should be set to 1.0.


Appendix A12

Page A-129


Appendix A

c = Qm / Qc

2.0

1.5

1.0

0.5

0

0.01

0.02

0.03

0.04

0.05

0.06

U * (Xg / D)

Figure A12.5: Throughput Correction Factor for Diamondiferous Ore Treated through a Laboratory Scale HPGR

15

Q (predicted tph)

LAB (D = 0.25 m) KHD (D = 0.80 m) POLYSIUS (D = 0.71 m)

10

5

0

0

5 10 Q (measured tph)

15

Figure A12.6: Prediction of Throughput for Two Pilot Scale HPGRs from Equation A12.4 with Model Parameter c Calibrated Using Laboratory Scale HPGR data

Using Equation A12.4 with c determined from Figure A12.5 the throughput of a laboratory scale HPGR (D = 0.25 m) and two pilot scale HPGRs (KHD, D = 0.8 m; Krupp Polysius, D = 0.71 m) was predicted. A comparison between the calculated and the measured throughputs is given in Figure A12.6. The rolls speeds varied from 0.29 m/s to 3.1 m/s, rolls length from 0.1 m to 0.21 m, rolls diameters from 0.25 m to 0.80 m, and working gaps from 3 mm to 23 mm. The throughput model prediction is seen to be good.

Page A-130

Appendix A12


Appendix A


A12.6 Conventional Crusher Power

Power Draw

The impact size reduction model contains an energy balance equation (Andersen and Napier-Munn, 1988) which ensures that the energy for size reduction is compatible with that provided by the motor. The t10 parameter is related to the specific energy used by the machine and will follow a curve described by the equation: =

t10

A (1 - e-bEcs)

(A12.5)

where A and b are parameters and Ecs is the specific energy. HPGR Crusher In the size reduction model the two parameters K3 and t10 were Power fitted to the laboratory scale HPGR power data. It was found that the fitted t10s for 24 sets of Diamondiferous ore tests under various rolls speeds and feed size conditions fell on a t10 - Ecs master curve, as shown in Figure A12.7

Equation A12.5 was hence fitted to these data to generate the A, b parameters, which are used for the scale-up as will be demonstrated in the next section. In JKSimMet, the points for t10 = 10, 30 and 50 are placed in the Compressive Breakage Specific Community Energy Matrix.

100 A = 100, b = 0.2084

Fitted T10 (%)

80

60

40 9.5 mm feed, 0.38 m/s speed 9.5 mm feed, 1.50 m/s speed 9.5 mm feed, 2.50 m/s speed 9.5 mm feed, 3.10 m/s speed 6.7 mm feed, 0.38 m/s speed 6.7 mm feed, 3.10 m/s speed A,b fitted to Lab

20

0

0

2

4

6

8

10

Ecs of motors (kWh/t)

Figure A12.7: The Fitted t10 vs Specific Energy Ecs for Diamondiferous Ore Treated through a Laboratory HPGR

A power coefficient kp is required which relates the measured power to that predicted by the model for size reduction. This model uses the specific energy (kWh/t) and associated t10 values from the piston press breakage experiments. From these it calculates the overall specific energy in a piston press. The Version 5.1 February 2003

Appendix A12

Page A-131

High Pressure Grinding Rolls (Model 402) Appendix A difference between this value and that observed from the motor is accommodated by kp, ie. kp is the ratio of the observed to the theoretical piston press specific energy. This coefficient has been found to be reasonably constant over a range of specific energies but increases rapidly beyond a certain limiting value. This is shown in Figure A12.8 for the 24 sets of data.

4.0

Power coefficient of HPGR

3.5

3.0

2.5

2.0

0

2

4

6

8

10

Ecs of motors (kWh/t)

Figure A12.8: Relationship between Power Coefficient (kp) and Specific Energy for Diamondiferous Ore Treated Through a Laboratory Machine . Where kp = Observed power/Piston Power

Power Draw vs Working Gap

The prediction of the working gap xg is also required for simulation. The working gap depends on pressure and power draw.

Working Gap/Specific Energy Relationship

This relationship is developed from the laboratory/pilot scale test. The specific motor energy is plotted against the working gap.

Page A-132

The parameters ρc and ρg in Equation A12.2 are functions of feed type, operating conditions (eg working pressure) and the roll surface (eg smooth, chevroned, studded). Therefore, provided the pilot scale or the full scale machines are operating under similar conditions to the laboratory unit, then xg will be proportional to the diameter of the rolls. The principal dependence of the working gap will be on the working pressure, with the gap reducing as the pressure increases. As working pressure is directly related to specific energy, then it will be found that as the specific energy increases the gap will decrease. An example of this is shown in Figure A12.9 for Diamondiferous ore treated through a laboratory machine.

Appendix A12


Appendix A


7

Working gap (mm)

6

5

4

3

2

0

2

4

6

8

10

Specific energy of motors (kWh/t)

Figure A12.9: Relationship between Working Gap and Specific Energy for Diamondiferous Ore Treated Through a Laboratory Machine


Appendix A12

Page A-133


A12.7

Page A-134

Appendix A

HPGR Model Printout

Appendix A12


Appendix A


A12.8

Split Factor (g) (SpFact)

Fitting the HPGR Model

SpFact K1H T10H Power Coeff. H This factor determines the proportion of material which is crushed in bypass mode. This is usually 1.7 times the effective gap width on each side for a default value of 3.4. (Section A12.3) Setting the split factor to zero and running a simulation generates the size distribution expected from pure compression crushing, ie. “pure flake” and may be compared with (or fitted to) an actual sample taken from the centre of the roll discharge.

Pre and Edge Crusher Model Parameters (K1H & T10H)

Using the same feed material as for the pilot/lab HPGR test, laboratory roll crusher is operated at close to the nipping gap and the working gap of the HPGR. The Whiten/Awachie/Anderson crusher model (Appendix 6) is used to derive K1 and t10 where K2 is the crusher gap and K3 is set at 2.3. The ratio K1/K2 is the input to the pre crush and edge effect model along with the fitted t10 values. It is unlikely that power can be measured with sufficient accuracy in this test to justify using other than the default power factor of 1.25.

Throughput Relationship

As noted in Section 12.5, throughput is strongly controlled by geometry at low throughputs and by slippage at high throughputs. Pilot or laboratory scale tests can be used to derive the slope and intercept for the slip correction factor Cp. The model defaults are for smooth rolls. It is highly likely that different roll surfaces will generate different correction factors.

Compressed Bed Breakage within the compressed bed is assumed to be uniform and able to be described by a single parameter t10 . The t10 parameter Breakage (t10 will increase as the reduction ratio increases. In compression, all HPGR) particles are assumed to be able to be selected for breakage ie. K1 = 0 and every particle larger than the working gap will always be broken, ie. K2=cacluated Working Gap. Power Model Fitting

The HPGR model takes a somewhat circuitous approach to power modelling. As noted in Section 12.6, the combination of piston press tests and laboratory/pilot scale HPGR produces a relationship between the compressive bed t10 and net motor power (Figure A12.7).


Appendix A12

Page A-135

High Pressure Grinding Rolls (Model 402) Appendix A Developing this relationship requires some modelling using the Andersen/Whiten model (A6). The objective is to find a t10 for each data set with K2 set to the working gap and K3 a constant value over all sets. To do this, enter all sets of data into one test, master slave K3, set K2 to working gap and fit each of the t10 values. This provides a set of t10 values which can be plotted against the motor power per tonne (Ecs) corrected for no load and the power drawn by pre-crush and edge crushing (as in Figure A12.7). Equation A12.5 is fitted to this data with A=100 and Ecs values calculated at t10 =10, 30 and 50 for input into the Compressed Bed Breakage Matrix.

This relationship allows compressive power draw to be calculated (as in Section 6.6) for any set of K1, K2, K3 and t10 values. Figure A12.7 shows the power coefficient (observed motor power divided by calculated “piston” power) for a range of energy inputs expressed as power per tonne. If this model was ideal, the coefficient would be constant. Between zero and 5 kWh/t it is approximately constant at, say, 2.5 and increases rapidly at high powers (ie. the crusher becomes less energy efficient). More energy is converted into heat and does not result in further comminution.

A12.9

Scaling the HPGR Model

To predict the performance of pilot scale and full scale HPGRs the model is firstly calibrated using the results from the laboratory, conventional rolls, single particle breakage and piston bed breakage test. Figure A12.10 illustrates the scale-up procedures. Also shown in Figure A12.10 are the values of the parameters obtained from the calibration, which have been used to predict the two pilot scale units and one full size machines treating a Diamondiferous ore (Morrell, Shi and Tondo, 1997).

Page A-136

Appendix A12


Appendix A


Input data Rolls dimension: diameter, length Select rolls speed, required specific energy Ecs Feed size distribution Bulk density of feed, flake density Working gap: chose the lab working gap by Ecs from Figure 12.9, multiplying the gap by the ratio of full scale to lab rolls diameters Nipping gap calculated from Equation 12.1 Throughput calculated from Equation 12.4 Power draw = Ecs required x throughput

Single particle breakage test (using a drop weight device)

Pre-crusher (parameters from the conventional rolls test) K1p=0.64 K2p K2p = nipping gap K3p = 1.0 K3p = 1.0 t10p = 12.04

Mass Splitter Fraction split to the edge effect crusher is calculated by Equation 12.2 in which γ = 3.4 as determined from the KHD tests

Edge Effect Crusher (parameters from the conventional rolls test) K1e = 0.64 K2e K2e = working gap K3e = 1.0 t10e = 12.04

Bed breakage test (using a piston press device)

Power coefficient determined from Figure 12.8

HPGR k1h = 0 K2h = working gap t10h calculated from Equation 12.5 in which A = 100, b = 0.2084 determined from lab tests

Calculated power = observed power

?

N

Adjust K3

Y Combined Product

Figure A12.10: Schematic of the Model Algorithm and Scale-up Procedure

The full scale-up procedure is implemented in JKSimMet. When running the simulations of pilot scale or of full scale machines, the parameter K3 for the compressed bed crushing zone is automatically adjusted until the model predicts the same power draw as was originally chosen for the simulation. As a result, the calculated power draw is identical to that observed, and the product size distribution is predicted based on this power consumption. In the simulation the maximum throughput of a scale-up HPGR is calculated using the throughput model (Equation A12.4) with the correction factor c determined in the laboratory unit with similar rolls surface on the same type of ore. The required power is then calculated from the maximum throughput and the specific energy Version 5.1 February 2003

Appendix A12

Page A-137

High Pressure Grinding Rolls (Model 402) Appendix A selected. The model is iterated until the breakage power, which is the sum of the power used in the three sub-processes of precrushing, compressed bed crushing and edge effect crushing, matches the required power. The overall product size is then predicted based on the breakage power.

A12.10 Roll Surface

Limited Base

Known Restrictions

Tests using a Krupp Polysius pilot roll (rolls diameter 0.71 m), with 4 mm profiles (on the rolls) resulted in a considerably larger working gap than was observed for the KHD pilot tests using smooth rolls. Therefore, laboratory tests must be conducted with a rolls surface similar to that proposed on the full scale machine. Data As only limited production scale data were available, the models

need to be further tested and validated against more real data in the future, and their capabilities explored in case studies.

Power Coefficient Ideally, this coefficient should be constant. A better understanding and (possibly) a better representation need to be developed. (kp)

A12.11

Page A-138

Nomenclature

αc γ ρc ρg c D Ecs f

-

g K1,K2,K3 kp L Qm Qc

-

t10 U xc xgf

-

nip angle (degree) split factor bulk density of feed (t/m3) flake density (t/m3) correction factor for rolls throughput rolls diameter (m) specific energy (kWh/t) fraction of feed which is crushed in the edge zones split factor size reduction model parameters power coefficient rolls length (m) measured mass throughput (tph) calculated mass throughput without correction tph) size distribution parameter rolls circumferential speed (m/s) critical gap (m) working gap (m).

Appendix A12


Appendix A


A12.12

Acknowledgments

This model was developed with the financial support of the sponsors of the AMIRA P428 project (Application of High Pressure Grinding Rolls in Mineral processing) including the Centre for Mining Technology and Equipment (CMTE). Considerable assistance was also provided by the staff at KHD and Krupp Polysius, as well as the staff and students at the JKMRC and CSIRO, Division of Mineral products.

A12.13

References

Andersen J S and. Napier-Munn T J, 1988. Power prediction for cone crushers. Proc. 3rd Mill Ops Conf, Cobar, Aus. Inst. Min. Met. Andersen J S, 1988. Development of a cone crusher model. M. Eng. Sc. Thesis, University of Queensland (JKMRC). Fuerstenau D W, Shukla A and. Kapur P C. 1991. Energy consumption and product size distributions in choke-fed, high compression roll mills. Int. J. Miner. Process., 32: 59-79. Kapur P C, 1972. Self - preserving size spectra of comminuted particles. Chem. Engng. Science, 27: 425-431. Knecht, J, 1994. High pressure grinding rolls, a tool to optimise treatment of refractory and oxide gold ores. Fifth Mill Operators Conf. Roxby Downs, Oct, 51-59 (AusIMM, Melbourne) Morrell, S, Shi F & Tondo, L. 1997. Modelling and scale-up of High Pressure grinding rolls. IMPC Aachen. Morrell S, Lim, W, Shi F and Tondo L. 1997. Modelling of the HPGR crusher. SME Annual Conference, Denver, Colorado. Comminution Practices Symposium, Ed Kawatra, 117-126. SchÖnert K. 1988. A first survey of grinding with high compression roller mills. Int J of Min Proc, 22, 401-412. SchÖnert K.and Sander, U., 2000. Pressure and shear on the roller surfaces of high pressure roller mills, Proc. XXI IMPC, Rome, Italy, Sect A4, 97 - 103. Tondo L, 1996. Modelling of HPGR crushers. M. Eng Science Thesis, University of Queensland (unpublished). Whiten W J, 1972. The simulation of crushing plants with models developed using multiple spline regression. J. South Afr. Inst. Min. Metall. 72: 257-264.


Appendix A12

Page A-139


Appendix A

(Blank Page)

Page A-140

Appendix A12


Appendix A

Simple Degradation (Model 480) A13

Simple Degradation (Model 480)

A13.1

Introduction

The concept of a degradation model has its origins in iron ore and coal operations where particles may undergo significant size reduction during mechanical handling such as dropping on to a stock pile from a conveyor or perhaps at a conveyor transfer point.

A13.2

Model Structure

The model structure is a simple representation of a single drop which results in the particles being broken to a specified t10 value. The breakage distribution parameter, t10, characterises the size distribution of the broken product. More details of this parameter and the concepts behind it are given in Appendix 6.4. The appearance function data which are discussed in Appendix 6.4 are required for the degradation model and are derived from the JKMRC Drop Weight test. This test is described in Appendix 15. Breakage Distribution Parameter (t10)

The breakage distribution parameter, t10, is entered as a model parameter. It must be calculated by the user and is generally based on the Energy – Size Reduction relationship for the particular ore derived from the JKMRC Drop Weight test.

Specific Comminution Energy

The Specific Comminution Energy in a drop is a function of the height of the drop and can be calculated using the following equation: Ecs = 0.00272 * h

(A13.1)

Where: Ecs = specific comminution energy (kWh/t) h = height of the drop (m)


Appendix A13

Page A-141

Simple Degradation (Model 480) Energy – Size Reduction Relationship

Appendix A

The relationship between Specific Comminution Energy and size reduction represented by t10 is also one of the results of the JKMRC Drop Weight test. The relationship is of the form: t10 = A * ( 1 – exp( - b * Ecs ))

(A13.2)

Where: t10 = Breakage Distribution Parameter Ecs = specific comminution energy (kWh/t) A & b are ore characteristic parameters Conditioning

In most cases, the damage inflicted by a second drop is less than that inflicted by the first drop. This effect is known as conditioning. Of course, the height of each drop is important as well as the number of drops. Effectively, the particles become a little more resistant to impact after each successive drop. The amount of this effective increase in resistance depends on the ore type and on the drop heights. This effect can be included in the simulation by an appropriate reduction in the b value used in equation A13.2. For an ore which is only a little affected by conditioning, a reduction of b to 75% of its starting value is typical. For an ore which is significantly affected by conditioning b is typically reduced to 40% of its starting value.

Page A-142

Appendix A13


Appendix A Example

Simple Degradation (Model 480) The A and b values from the JKMRC Drop Weight test for the example ore are 50 and 0.5 respectively. For a drop height of 20 m, from equation A13.1: Ecs = 0.00272 * h = 0.00272 * 20 = 0.054 kWh/t and from equation A13.2 t10 = A * ( 1 – exp( - b * Ecs )) = 50 * ( 1 – exp( - 0.5* 0.054)) = 1.33 this value of t10 is then entered into the model. For a second 20 m drop of an ore which is strongly affected by conditioning, b is reduced to 0.2 (40% of 0.5) and from equation A13.2 t10 = A * ( 1 – exp( - b * Ecs )) = 50 * ( 1 – exp( - 0.2* 0.054)) = 0.54 this value of t10 is then entered into the model for the second drop.

Use for the Vertical Shaft Impactor

The degradation model can be used to represent a lightly loaded Vertical Shaft Impactor. In this case, the energy of an impact is calculated from the velocity of the particle imparted by the rotor. This energy must be converted to units of kWh/t before equation A13.2 can be applied. For example, for a VSI with a rotor diameter of 0.6 m spinning at 2000 rpm, the energy imparted to a particle leaving the rotor at its peripheral speed is: Ecs = 0.5 * m * v2 / ( 3600 * m ) = 0.5 * v2/ 3600 = 0.5 * ( π * 0.6 * 2000 / 60 )2/ 3600 = 0.55 kWh/t Where: m = Particle mass (which cancels out) Ecs = specific comminution energy (kWh/t) v = peripheral velocity of rotor (m/s) 3600 is the conversion factor for kWh/t The Ecs value is substituted into equation A13.2 to calculate t10 for use in the model.


Appendix A13

Page A-143

Simple Degradation (Model 480)

Appendix A

A13.3

Degradation Model Printout

A13.4

Fitting the Degradation Model

This is a very simple model to fit, the only fittable parameter being t10. A typical range of starting estimates for degradation by drop is 0.2 to 0.8 depending on amenability to degradation and drop height. A typical range of starting estimates for the VSI is 5 to 20 depending on rotor diameter and speed and ore type.

A13.5

Known Restrictions

It is recommended that the ore specific appearance function is measured by a Drop Weight test rather than using the default values. Although the variation of the crusher appearance function data in the JKTech data base (of ores subjected to Drop Weight testing) is not particularly large, ore specific values will provide better results. If several drops actually occur, it may be better to simulate these as separate drops than as a single drop of the total accumulated drop height, particularly if conditioning is likely. It should also be noted that ores which are particularly susceptible to degradation are also likely to be degraded during the process of screening to determine the size distrbution, thus making the size distributions somewhat doubtful.

Page A-144

Appendix A13


Appendix A

Splitters (Models 810, 811, 812, 870) A14

Splitters (Models 810, 811, 812, 870)

A14.1

Introduction

These models provide splitters of varying complexity, from a simple mass split to two (810) or three products (870), independent mass splits of solids and water (811) and a split generating a specific volume flow rate to one product (812).

A14.2

Model Details

A14.2.1 Simple Mass Split – Two Products (810) The feed to this model is split into two streams with size distributions and pulp densities identical to the feed. The controlling parameter is the Fraction Split to Top Product. The top product is the upper product on the equipment icon and is marked with a T. The parameter range is 0.0 – 1.0.

A14.2.2 Simple Mass Split – Three Products (870) The feed to this model is split into three streams with size distributions and pulp densities identical to the feed. The controlling parameters are the Fraction Split to Top Product and the Fraction Split to Bottom Product. The top product is the upper product on the equipment icon and is marked with a T. The parameter range is 0.0 – 1.0.


Appendix A14

Page A-145

Splitters (Models 810, 811, 812, 870)

Appendix A

A14.2.3 Simple Mass Split – Two Products – Water and Solids (811) The feed to this model is split into two streams with size distributions identical to the feed. The controlling parameters are the Fraction Split to Top Product (Water) and Fraction Split to Top Product (Solids). The top product is the upper product on the equipment icon and is marked with a T. The parameter range is 0.0 – 1.0.

A14.2.4 Fixed Volume Split – Two Products (812) The feed to this model is split into two streams with size distributions and pulp densities identical to the feed. The controlling parameter is the Volumetric Flow Rate to Top Product (m3/h). The top product is the upper product on the equipment icon and is marked with a T. Should the volumetric flow rate of the feed stream be less than the required flow to the top product, the entire feed stream is directed to the top product.

Page A-146

Appendix A14


Appendix B

Error Messages

APPENDIX B

Error Messages


Appendix B

Page B-1

JKSimMet Error Messages B.

Error Messages

ERROR MESSAGES

These messages occur during operation of JKSimMet. The display warns that an error has occurred and provides the error number. The descriptions provided here give more information about the possible cause of the error message. ERROR 58

Not enough size distribution data in the feed to an equipment item for spline interpolation to work. Check combiner ports with Exp TPH Solids values > 0.0 with limited or no Exp Size Distribution data. One of the combiner ports of one of the equipment items on the select list has Exp TPH Solids greater than zero but limited or no size distribution data. Thus JKSimMet is not able to perform the required Spline Interpolation. Either add some size distribution information or zero the Exp TPH Solids.

ERROR 110

Hydrocyclone - SPOC predicts roping. The results of the simulation violate the SPOC roping constraint indicating that under the simulated conditions, the hydrocyclone is likely to be roping. See Section A2.5 for more details. The simulation results may be unreliable.

ERROR 111

Plitt et al constraint predicts roping. The results of the simulation violate the Plitt et al roping constraint indicating that under the simulated conditions, the hydrocyclone is likely to be roping. See Section A2.5 for more details. The simulation results may be unreliable.

ERROR 120

No data in a stream or streams. Please correct. One of the streams you have selected in the Balance List contains no data.

ERROR 121

Two or more streams have different sieve series. Please correct. For Mass Balancing with GSIM format data, all selected streams must have the same screen series.

ERROR 122

Sum of % component does not equal control value. correct.

Please

If you have specified a component sum (on the active COMPONENT LIST) your assays must total this sum or less. A component sum of zero turns off this constraint. Normally a REMAINDER TERM is added to achieve the sum in the experimental data. To force a constraint, omit one of your categories and it will be the remainder term.

Page B-2

Appendix B.1


Error Messages ERROR 123

JKSimMet Error Messages

No COMPONENT LIST is currently selected. Please select or enter one. You must have a current Component List before attempting to mass balance data. Either select one you have already created or create one.

ERROR 124

No BALANCE LIST is currently selected. one.

Please select or enter

You must have a current Balance List before attempting to mass balance data. Either select one you have already created or create one. ERROR 125

Modifications to flowsheet detected. Please check your current data. Modifications have been made to the flowsheet since the last mass balance. You should check that your selected streams are still correct.

ERROR 126

No stream input to unit. Please check current SELECT list. One of the units selected for inclusion in the balance has no input stream. You should check that input streams are selected for all of the selected units.

ERROR 127

No stream output from unit. Please check current SELECT list. One of the units selected for inclusion in the balance has no output stream. You should check that output streams are selected for all of the selected units.

ERROR 128

Stream is not connected to unit. Please check current SELECT list. One of the selected streams is not connected to any selected unit. You should check that all selected streams are connected to selected units.

ERROR 129

No unit/node is currently selected. Please check current SELECT list. There are no units selected on the SELECT list. At least one unit and its associated streams must be selected to run a mass balance.

ERROR 130

Morrison solution error. See Morrison solution error Section 6.10. The simple solution has not worked correctly. Check your data carefully and then read section 6.10. If you can find no data problems, try increasing the number of steps. Note that only one flow rate should be tightly constrained - not all of them.

ERROR 131

Morrison solution convergence error. Please increase step number


Appendix B.2

Page B-3


Error Messages

See also Error 130. ERROR 132

Consistent assays convergence error. Please increase step number. Check the SELECT screen to see that the step count has reached its nominated maximum. If so you may increase that count by a few steps. Caution: such long searches indicate poorly defined flows or some variation of the middlings problem. Refer to section 6.10.

ERROR 133

Adjusting sum convergence error. Please increase step number. See also Error 132.

ERROR 134

Main loop convergence error. Please increase step number. See also Error 132.

ERROR 135

Negative balance flow rates. See also Error 132.

ERROR 136

Balance size distributions cal. err. Increase adj. sum step number. See also Error 132.

ERRORS 137-139 are reserved for later versions. ERROR 140

No Model-Fit data are selected. Fitting requires data. No data have been selected on which to do the Model-Fit. Select some and try again.

ERROR 141

No Model-Fit parameters are selected. Fitting requires parameters. No parameters have been selected on which to do the Model-Fit. Select some and try again.

WARNING 142

Model-Fit data include a stream with no experimental data. One or more of the streams selected for the Model-Fit has no experimental data entered for it. It is ignored. Enter the necessary data before attempting the Model-Fit again or remove the stream from the data list.

WARNING 143

Model-Fit data do not include this stream. Normal editing only. The Stream selected is not included for Model-Fit. Therefore, the extra information cannot be edited.

ERROR 144

Model-Fit data do not contain any streams. Fitting requires data. No streams are selected for Model-Fit. The list of streams, whose data must be fitted, is empty.

WARNING 145 Page B-4

Poor convergence of fit. Check SDs / data. Appendix B.1


Error Messages


The Model-Fit has not been able to make effective use of the data given. Try different SDs or reject some of your data. Check your circuit and unit details also. Rerun the survey. ERROR 146

No streams in the circuit have data. Please add some. None of the Streams selected for the Model-Fit have data entered for them. At least one stream must have data. See ERROR 51.

ERROR 147

No parameters are selected for fitting. Please select some. Model fitting works by adjusting parameters of models until simulated results match experimental data. You must specify at least one parameter to adjust.

ERROR 148

There are too many streams on the circuit. Please simplify! Please simplify the circuit or break it into two circuits, The ModelFit function has strict limits on the number of units and streams allowed. Please reduce the number you have selected, then try again. Refer to the manual for the current limits (there is a limit of 10 units, 20 streams).

ERROR 149

There are too many units on the circuit for fitting. Please simplify. The Model-Fit function has strict limits on the number of units and streams allowed. Please reduce the number you have selected, then try again. Refer to the manual for the current limits (there is a limit of 10 units, 20 streams).

FAULT 150

An illegal parameter is selected. It won't be fitted. This error should never occur. Please make a note of the error number and what you were doing, and contact JKTech.

ERROR 151

Constant residual SDs/parameters/scales.

error

during

fitting.

Check

See ERROR 154. The model fit gauges its success by a diminishing error between experimental and simulated data. The error was not changing with different parameter values. SDs, scales or the initial parameter estimates may be responsible. ERROR 152

Fitting is not getting anywhere. Try again with better guesses. The Model-Fit has not been able to make effective use of the data given. Please enter new parameter guesses and try again.

FAULT 153

Model fit array sizes were in error. This error should never occur. Make a note of the error number and what you were doing, and contact JKTech.

ERROR 154

No errors were calculated.


Only non zero SDs contribute an error. Appendix B.2

Page B-5


Error Messages

The errors between experimental and simulated data are combined with each values SD. A zero SD implies the value should be ignored. If all SDs are zero, fitting has no data. WARNING 155

No SDs have been entered on a stream. Unit SDs are assumed. See ERROR 154.

ERROR 156

You have duplicate data entries.

Please remove duplicate.

If you want one stream to have a greater significance reduce its SDs. ERROR 157

You have duplicate parameter entries. Please remove duplicate. Each parameter entry is independently adjusted. This becomes nonsense if one parameter is repeated.

ERROR 158

Only two parameters may be fitted per stream. Please correct. There are only two independent parameters for a stream. ERROR 157.

ERROR 159

See

Only one water parameter may be fitted per stream. Please correct. Once stream's water parameters are independent. See ERROR 157. All water parameters control the water content of a stream. There is only one way this may be selected. See Error 157.

WARNING 160

A new stream was selected. Model-fitting is complex. It thus tries to select streams automatically when it starts. Occasionally this changes the selections you have made. The warning is then issued.

WARNING 161

A new unit feed stream was selected. Refer to WARNING 160 above.

WARNING 162

New Model Fit data were selected. Refer to WARNING 160 above.

WARNING 163

New Model Fit parameters were selected. Refer to WARNING 160 above.

ERROR 164

That unit doesn't have experimental data suitable for model-fitting. The unit selected has no parameters and can not be fitted.

ERROR 165

No units in the circuit have data. Please add some. None of the units in the circuit have data. You must supply some.

WARNING 166 Page B-6

A new unit was selected. Appendix B.1


Error Messages


The currently selected unit does not appear in the Parameter List WARNING 167

The coarsest particles in the feed to the AG/SAG mill are in a size range either finer than 200 mm or coarser than 300 mm. This affects the calculation of energy values and the results of simulations using this feed are likely to be unreliable. Please modify your feed size distribution. The energy calculations in the Variable Rates SAG model were based on data from mills with the top size of the feed in the region 200 – 300 mm. Simulating with feeds outside this region using the default rates will be unreliable.


Appendix B.2

Page B-7


Error Messages

(blank page)

Page B-8

Appendix B.1


Appendix C

JK Breakage Testing

APPENDIX C

JK BREAKAGE TESTING


Appendix B

Page C-1

JK Breakage Testing

Appendix C

C

JK Breakage Testing

C.1

Drop Weight Test Procedure

This section provides a brief description of the drop weight test procedure. To characterise ore breakage at different energy levels, the JKTech method uses two complementary techniques: 1. To characterise breakage at moderate to high energy levels (i.e. impact breakage), a drop weight device is used. 2. To characterise breakage at low energy inputs (i.e. the abrasion component of breakage), a tumbling test is used.

C.2

Impact Breakage Testing

The JK drop weight device comprises a steel drop-weight which is raised by a winch to a known height. A pneumatic switch releases the drop weight which falls under gravity and impacts the rock particle which is placed on a steel anvil. The device is enclosed in perspex and incorporates a variety of features to ensure operator safety. By varying the height from which the drop weight is released and the mass of the drop weight, a very wide range of energy power inputs can be generated. A schematic drawing of the device is given in Figure C.1.

Perspex enclosure

5kg lead weights Guide rail

Adjustable height (energy)

Rock Steel anvil

Large concrete base

Figure C.1: Schematic of the Drop Weight Device Page C-2

Appendix C


Appendix C

JK Breakage Testing After release of the drop weight, it descends under the influence of gravity and impacts the target particle. The particle is broken by the impact. The drop-weight is brought to rest at a distance above the anvil approximately equal to the largest product particle. The difference in distance between the initial starting point and the final resting place of the drop-weight is used to calculate the energy that is expended in breaking the particle. The following equation is used: Ei = Mg(h - xM)

(C.1)

Where: Ei = energy used for breakage M = drop-weight mass g = gravitational constant h = initial height of the drop-weight above the anvil xM = final height of the drop-weight above the anvil. Providing the drop-weight does not rebound after impact, the application of equation (C.1) is valid. Where rebound occurs an additional term is required to account for the energy retransmitted to the drop-weight. Rebound has been seen to occur only at elevated input energies. This energy will be measured during the testwork programme. It is likely, however, that its magnitude will be relatively small and can be ignored with only a minimal loss in accuracy. The assumption is made that all the energy provided is utilised in the breakage of the particle. Thus Ecs = Eis = Ei / m

(C.2)

where: Eis = specific input energy Ecs = specific comminution energy m = mean particle mass To test an ore type, the original 100 kg sample is sized into selected fourth-root-of-two size fractions. Ten to thirty particles are required in each size fraction for each energy level, depending on particle mass. Typically fifteen size/energy combinations are selected. The input energy levels for a particular test are designed to suit ore hardness.


Appendix C

Page C-3

JK Breakage Testing

Appendix C

The breakage products of all particles for each size/energy combination are collected and sized. The size distribution produced is normalised with respect to original particle size. For a wide range of energy input, particle sizes and ore types, the relative size distributions remain similar in shape and can be described by a single point on the distribution. The JKTech convention is to use the percentage passing one-tenth of the original particle size. This is referred to as the “t10”. In the manner described above, a set of t10 and Ecs values are produced for the 15 energy/size combinations.

C.3

Abrasion Breakage Testing

It is possible to characterise low energy (abrasion) breakage with a miniature drop weight and repeated impacts. However, Leung (1987) demonstrated that a tumbling test of selected single size fractions could produce a similar result with less experimental effort. The standard abrasion test tumbles 3 kg of -55 +38 mm particles for 10 minutes at 70% critical speed in a 305 mm by 305 mm lab mill fitted with four 6 mm lifter bars. The resulting product is then sized and the t10 value for the product is determined. The mean particle size of the original size fraction 55 x 38 mm is 45.7 mm. The t10 size is: 1/10 x 45.7 = 4.57 mm.

Page C-4

Appendix C


Manual JKSimMet V5.1

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