Techlog Interactive Suite 2008.Full

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Techlog Interactive Suite 2008

What’s the big idea? Bring all of your petrophysical and geological data together within a single graphical environment. Techlog Interactive Suite© 2008 is designed for the petrophysical interpretation of wellbore data and offers a complete processing and modelling toolbox. You can display what you want, how you want and perform high level analyses of core, log, image and related data types together in one program. Data integration...right here, right now.

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F l e x i b i l i t y

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Our bright ideas (we have many)

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© 2008 Techsia. All rights reserved. Techlog is a registered trademark of Techsia - Texts and images are not contractual.

C o o n nn e n c e c t ti i v v i it t y y

I n nt e eg r a t i i o a on o f d a t a a

What’s What’ s the big idea?

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One big happy family. ©

Introducing the Techlog Interactive Suite 2008. Application modules (in purple) are available to suit your specific needs and objectives. You You can add application modules one at a time or you can add an entire focus area (see page 11) depending on your requirements. ©

The Techlog platform (in orange) is the foundation for everything that you want to do with any of the modules. It comprises a package of tools for loading, manipulating and viewing the enormous range of data handled by Techlog. Turn the pages to read the individual strengths and capabilities of each module.

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Techlog Interactive Suite 2008 Application modules

CoreDB

Techcore

Saturation-height modelling

Quanti

Quanti.min

Thin bed analysis

FPress

Fluid contact

Wellbore imaging

Ipsom

K.mod

Geophy

Techplot

3D Vue

PythonTM

Techstat

Nuclear magnetic resonance

Platform modules

Techdata


One big happy family family..

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Welcome to our world. Our world encompasses 6 main focus areas (shown in the graphic to the right). Collectively, the subjects cover the gamut of reservoir characterisation. Techlog Interactive Interacti ve Suite© 2008 is organised as a series of application modules, founded upon a robust platform comprising all the data management and viewing utilities. The program enables you to bring together, within a simple data structure and single, powerful GUI, every type of data that falls within the “world of reservoir characterisation”.


Welcome to our world

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Make the connection. Find your focus area on the next page (bottom), then see the module that’s right for you. Our world encompasses 6 main focus areas (shown in the graphic to the right). Collectively, the subjects cover the gamut of reservoir characterisation. Techlog Interactive Suite© 2008 is organised as a series of application modules, founded upon a robust platform comprising all the data management and viewing utilities. The program enables you to bring together, within a simple data structure and single, powerful GUI, every type of data that falls within the “world of reservoir characterisation”.

Application modules

CoreDB

Techcore

FPress


Fluid contact

Quanti

Wellbore imaging

Quanti.min

Ipsom

Thin bed analysis

K.mod


Geophy

Focus areas Core

Log

Fluids

Geology

Earth Model

Geophysics

Core data storage/ manipulation

Conventional interpretation

Formation pressure QC

Cross-sections/ correlation

Wellbore trajectories

SEG-Y import

Mapping

Checkshots editor

Reservoir rock typing

Mineralogicalinversion

Surfaces

Depth-time conversion

Capillary pressure

NMR

Cross-sections

Fluid substitution


Thin bed analysis

Dip analysis Textural map analysis*

Relative permeability


Upscaling/1D kriging

Cased hole analysis

Fluid typing Fluid contact management

Facies prediction Image processing

Synthetic seismograms Interactive frequency filtering

Resistivity modelling* Production logging*

*Coming soon


Make the connection.

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Focus areas. Core. Petrophysics depends on access to many types of data, particularly log and core together. A wide choice of tools are available for bringing the core data into the interpretation including plotting, editing, upscaling, classifying and fitting function definition. All of these can be found in the application modules Techcore (Tco),, Saturation-height modelling (SHM), (Tco) (SHM), and CoreDB (CDB) (CDB).. Core data storage and manipulation are vital tasks. Once they are properly managed, the effective integration of core data with other sources requires reconciliation for reasons of differences in measurement scale and measurement environments. Integration and reconciliation are facilitated by visualisation, quantification and upscaling.

Log. Log data are the fundamental data resources available to petrophysicists. Now, the term includes a wide variety of data types and modes of acquisition: Wireline, LWD, continuous recording, irregularly sampled, single value at a sample, multiple values at a sample (array data), image data, real-time data streaming. streaming. Day after day petrophysicists and log specialists are loading, manipulating and analysing large quantities of log data. Experts go further with specialised interpretations addressing advanced petrophysical questions. Find these activities in the following modules: Quanti (Q), Quanti.min (Q.m), NMR, Thin bed analysis (TBA) and Saturation-height modelling (SHM)



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Focus areas. Fluids. Reservoir layering, continuity and compartmentalisation are key elements of detailed reservoir characterisation. Their effective analysis is enhanced by bringing many different strands of data to bear on the problem. You can do this within Techlog© where the FPress (FP°) and Fluid Contact (Fc) modules evaluate multiple contacts within compartmentalised reservoirs to derive minimum, maximum and most likely depths for fluid contacts in complex reservoirs. The resultant contact surfaces and fluid typing, by compartment, can be visualised in 3D and instantly updated, should analyses change.

Geology. In addition to the well-by-well view, you can post data onto maps, see the well spatial relationships in 2D/3D and assess correlations and trends qualitatively and quantitatively through the subsurface. Primary tools in the geological workflows include log data for correlation and geological characterisation, core data for facies descriptions and image data for structural and fracture analysis. Core and log data are used very effectively together within Ipsom (Ips) for example to characterise facies; borehole image interpretation in all its forms is the main activity covered by the Wellbore imaging (Wbi) module.



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Focus areas. Earth Model. Show petrophysical and geological data and results as a 3D view of the sub-surface within the same environment where detailed interpretation of those data are performed. Access the 3D graphical library of 3D Vue (3DV) to build a visualisation of an “Earth Model” which you can then use to explore the interwell space. The 3D graphics toolkit is also used within Wellbore imaging (Wbi) to represent image data and dip planes. Now petrophysicists work within the context of the ©

full reservoir view in Techlog .

Geophysics. The need to tie seismic survey data into well information is paramount in successful seismic analysis. Well data are often considered the “ground-truth” for seismic data. Preparation of the log data is best done within the log domain using the neural network in K.mod (K.m); (K.m); thus, in Techlog Techlog© you can use Geophy (GeΦ ) a comprehensive, single-offset, synthetic seismogram package that includes time-depth functioning from checkshot and/or sonic log data, fluid substitution and synthetics filtering. Then compare these and other petrophysical results directly against seismic data (loaded from SEG-Y).



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What you get out of the box. Techlog Interactive Suite© 2008 is a comprehensive range of highlevel capability for managing all your petrophysical data. This section will take you through the 5 main utilities including data connectivity, data handling, viewers, user programming and statistical analysis. analysis. Techlog is especially designed for interpretation of all types of wellbore data. It is a complete processing and modelling toolbox dedicated to reservoir characterisation. Techlog offers a tightly integrated environment with everything you need to process data for tomorrow as well as today.

Data connectivity Input/Output Data API OpenSpirit® compliant PetrisWINDS RecallTM link WITSML Data handling Data management Data editing Data processing Viewers Single/multi-well viewers Plots: 1D, 2D, 3D, array and matrix Interactivity


User programming Python™ Stand-alone scripts Multi-well/zone scripts Statistical analysis Exploratory analysis - Factor analysis - Decision Tree - Correspondence analysis Regressions - Line fitting linear/ non-linear - Multilinear regression

What you get out of the box.

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Data connectivity. There is a full range of data loaders and there is a developing family of data connectors, so that you can easily source your data from corporate data stores, other applications or external suppliers: DLIS, LIS, LAS 2, 2 , LAS 3, WITSML, CSV, CSV, ASCII, OpenSpirit®, RecallTM, CGM, SVG, EMF, JPG, GIF, TIFF, BMP, PNG, SEG-Y, etc.

We have accommodated every type of data that you could want to use during an analysis. TechlogDataAPI is available to enable clients’ programmers to build connectors for other programs to directly access Techlog© data objects.

Log data

Core data

Wellbore image data

Formation pressure and seismic data

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Types of data handled by Techlog Core Routine core data Special core data Core reports Core photos Thin sections Core logs Log Wireline LWD Images Arrays Fluids Pressure Cased hole logs Production logs Contacts

Geology Mud log Geological layering Geological facies Structural data Dips Geophysics Seismic Checkshots Earth Model Trajectories Horizons Maps/Surfaces



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Data handling. Rapid and effective organisation of data is paramount. Understand the data that are present, understand their limitations, plan the steps required to repair data and then carry out those repairs on large amounts of data at once, either through detailed query commands or through graphical tools.

Data Management Within a Techlog project there can exist one or more wells, each with one or more datasets, each with one or more variables. There are no software limitations to the storage. Make sense of what can amount to very large quantities and variety of data through data tools such as inventories for each data type in the project. Search for and repair erroneous naming or unit assignment; ensure the correct family and/or alias attribution is made. By this means, performing multiple well data processing becomes very efficient in the system. Datasets hold data at a single reference, which can be regular, irregular, depth (MD, TVD, TVDSS, etc.) or time-based, or just a simple index count (e.g. sample ID for core data).

Data inventory and query

Images and complex array data curves are stored within the same robust data model.

Data Editing Inspection and review of the values or content of simple curves, arrays, zonations and well properties are facilitated by dedicated spreadsheettype editors. These can often be linked or copied directly into ExcelTM

Data Processing for reporting or sharing data with colleagues. Combine, re-size datasets within wells or merge data from several wells into a composite well as the process may require.

When simple editing is not sufficient, turn on the power of the many graphical and calculation-based tools for more complex data processing. Data can be re-sampled, shifted, despiked, clipped or upscaled. Perform mathematical operations such as find derivatives, integrate, filter, spline or linearly interpolate or standardise. Frequency domain filtering is a powerful option in this category of tool. Multiple wells may require inter-well normalisation, for instance before computing formation properties. Ensure full and close user control of this operation with a graphical interface to view progress and results at all times.

Data editor



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Viewers. There is an enormous range of customisable and interactive viewers that you can use to look at your data. All plots can be conditioned by depth or zone ranges to focus your views to the matter in hand. Once a plot is made for one well, apply it to many other wells directly, or after storage. Run previous templates again by the double-click. Rapidly build matrix plots of histograms, cross-plots, box-plots to see cross-relationships between many data simultaneously. Data selected in plots are instantly identified in all other plots that share a common reference.

Customisable All aspects of the plots are customisable; freely mix regular and irregular sampled data; drag & drop arrays and images onto the plot and easily add log or core data on top; vary the scale factors of tracks to amplify sections, or look in detail at core photos; create cross-plots and histograms on the plot that can be live with the data in the display and updated by dragging up and down the plot; add colours and shadings to custom designs or choose the built-in templates.

Plot template default property table

Broad and interactive

Innovative

Box-plots, histograms and cross-plots allow you to take data out of the depth domain; in one dimension look at CDFs and PDFs across one or more wells; in two dimensions explore relationships with fit lines, fixed or free; see the actual data plotting or the frequency density distribution, that is such an aid to picking end points in analyses; choose subsets of data and calculate instantly the fit lines through the restricted data; see your data choice highlighted in all other viewers using the same reference system.

In Techlog©, graphical tools are more than cosmetic “add-ons” to the system. Intelligent use of plot structure and colours make the pictures a truly integrated part of

the solution process, facilitating complete incorporation of all data types within the many plot options available.

Multi-well cross-plot defining two groups of interaction

Multi-well spectrum display of multivariate log patterns within the two selections only


Multi-well layout displaying the selected points in depth


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User programming. PythonTM is an opensource scripting language that has been harnessed to work inside Techlog©. You can use u se the full power of the Python language; for example you can customise integrated workflows or generate data access routines that link directly into Oracle® databases. It is powerful, yet can be incredibly simple.

Comprehensive Within the platform, there is an editor/parser environment for TM the Python language together with libraries of access-functions to the data, plot objects and the calculations under the hood in Techlog©.

There is no need to maintain a dedicated compiler for the language, which keeps installation very simple and managed entirely within the Techlog program.

Reservoir fluid units identification based on the Lorenz plot analysis:

Python script editor TM

Phi vs K with Lucia, Winland, FZI charts

Short learning curve

Workflow automation

Tap into the brainpower of thousands of developers and practitioners in PythonTM, from all over the world, to make your special application that accesses the Techlog© data and plot objects that much more efficient.

Python scripts permit the automation of many tasks; for example, establish a batch process that periodically reads a real-time data stream and automatically processes a set analysis workflow to produce a preformatted output product.

Be effective with a few lines of program that yet can be run on multiple wells and multiple zones without the user having to program a lot of housekeeping code to make it happen.

Depth plot showing reservoir flow units


Lorenz plot: reservoir fluid units identification


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Statistical analysis. There are many statistical analysis techniques available for obtaining a different insight into your data. Looking at data “shape”, data “structure”, looking for data patterns, every analyst knows that these are extremely important tasks. In the Techlog© platform these are aided by the GUI and the inter-process in ter-process interactivity.

The basics Create tables of simple exploratory statistics that cut through the data in many different ways. Easily produce reports and synthesise large volumes of data. For final output archiving or compilation,

Calculation of statistics on histograms and in the Data editor further facilitate this

important means of data characterisation. Access multiple linear regression for a quick look at multivariate trends in your data.

Multi-well histogram with univariate statistics for each well or all wells

Data editor: one click data summary

Factors Increasing in sophistication, use different techniques of Factor analysis to make choices amongst input data when preparing specialised neural network models for classification and function building.

directly transfer the reports into ExcelTM or into the plot header/footer region of the output product.

Mode: 54.9727

Mean: 54.5878

Median: 54.582

Average deviation: 16.8918

PossibleStatistics: values: 172284 Number of missing values: 1128

Standard deviation: 22.987 Variance: 582.402

Minimum value: -381.75 Maximum value: 447.25

Skewness: -0.630273 Kurtosis: 81.7896

Correspondences Another more frequent task is to perform data reduction and correlation analysis to assess importance amongst input data.

Correspondence analysis allows you to compare descriptive data class assignments in an objective manner.

Make use of the new Decision Tree analysis tool for building classification rule sets.

For instance, measure the performance of your facies prediction results.

Principal component projection cross-plot

Contingency table: line frequency between core facies description and facies predicted with Ipsom (Ips) .

Vector correlation (contribution) in Principal Component Analysis



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Which modules are you? Techlog© is designed in a modular fashion and companies or users can choose the ones to which they want to have access. Users have the ability to condition the menu system used in Techlog to suit their own working style. Unused functions can be hidden; used functions can be grouped just the way you like. Customised systems can be saved at Company, Project or User level. There is a licensing strategy that is easy and flexible. Pick and choose modules to suit your needs.

Application modules

CoreDB

Techcore

FPress


Fluid contact


Quanti

Wellbore imaging

Quanti.min

Ipsom

Thin bed analysis

K.mod


Geophy

Which modules are you?

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CoreDB.

CDB

Import, view and manage core data from anywhere

Tco SHM

Locate user data

Generate inventories

Within countries, fields and wells, search for data with complex search filters. Filters can use data values as limiting criteria, e.g. porosity > 0.2.

Filters execute complex queries to organise the data; queries can be saved for re-use.

Q

Tables are easily compiled with core results data and experimental conditions data. Click on a report document to see its associated

plug data highlighted. Create mono-well or multi-well inventories by grouping core information through the query tools.

Q.m TBA Nmr FP° Fc

Wbi Ips K.m GeФ

Build complex queries to find data

Inventories of data and experimental conditions

Country, field, well listing

View data

Browse images

Keep audit trail

There is full user access to pre-defined standard plot templates, with full customisation of plots, histograms and logs. Plots, with their associated data, TM may be exported to Excel spreadsheets.

A click on a sample in a table brings the core images into view; click on the image to see photos of core plugs listed; click on the core plug picture brings the plug information table. View core images at low and high resolution.

CoreDB (CDB) keeps (CDB) keeps user activity history that can be accessed from the administrator console. See when data were uploaded, by whom, and whether any edits have been performed.

Low and high resolution core images in the viewer panel

Maintain audit trail records permanently in the database

Fully customisable, standard plot templates



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Techcore.

CDB

Your solution for core data interpretation Tco SHM Integration

Processing

• Rapidly and effectively synthesise and combine both log and core domains

• Incorporate robust and validated methods of data manipulation with new, state-of-the-art statistical techniques

• A unique tool to reconcile core and log data

Q and access this powerful combination within a fully interactive graphical user interface

• Perform specific processing tasks within one user environment, e.g. calculation of capillary functions (Thomeer,

Buckley-Leverett, Lambda, Wright-Wooddy-Johnson and Hyperbolic Tangent methods), grain size, pore throat distributions, etc.

Q.m TBA Nmr FP° Fc

Wbi Ips K.m GeФ

Routine and special core data on the left, displayed at log scale; expanded scale photographs reveal full details on right

PHI vs vs K K cross-plot with Winland callibration lines and power function regressions

Other applications include:

Outputs

Upscaling

• Upscaling with kriging or representativity

Partition the core data into “Reservoir Rock Types” or (“petrophysical groups”) that reflect zones in which storage and transmissivity of fluids are likely to be similar.

• Combine the maximum amount of data available to generate “petrophysical logs” (representative of the variation in core data upscaled by rigorous methods to be comparable to the scale of the wireline or LWD log data)

• Relative permeability • XRD transformation

• Upscaling performed by reference to either continuous core description data or to the most finely resolved quantitative measurements on the core (e.g. mini-K or core-gamma) by 1D kriging interpolation (several external drifts are possible)

Pore throat distribution from MICP data

Saturation vs vs Pressure Pressure from MICP data


Output from 1D kriging to upscale core plug data in presence of mini-log data (e.g. mini-perm)


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Saturation-height Saturation-he ight modelling.

CDB

SCAL-based calibration of log data Tco SHM Workflow

Solutions

Model design

• Each functional solution has 3 coefficients

• Template loading of special core data

• Model capillary pressure data shapes

• Brooks-Corey function

• Graphical review and edit for QC

• Apply models within log domain

• Thomeer function

• Lambda function

Q

• Automatically correlate the coefficient values against formation properties such as φ, K, sqrt(K/ φ ) using 5 different fit criteria (linear, logarithmic, exponential, power and average)

• Transform or normalise pressure data

• Set the coefficients to be functions of the formation parameters or to be constants, as desired

Q.m TBA

• Instant comparison against “standard” models for rock-typing

Nmr FP° Fc

Wbi Ips K.m GeФ

First step: equation fits to samples to derive parameters

Model application

Third step: combined single function applied across all data in a single rock type group

Outputs

• Easily apply saved capillary pressure models • Direct graphical and quantitative comparison against log derived results

• Optimise models to reconcile log and core data fully using an integrated solver

Saturation-height model results; comparison of core model and optimised model using solver


• Characterising parameters sample by sample

• Saturation-height function in the log domain

• Fully defined functions

• FWL estimation

• Parametric variation with formation properties and/or rock types

• Export of the equations to reservoir modelling software

Cross-plot comparison of core model vs vs log log results (red points) and solver model vs vs log log results (black points)


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Quanti.

CDB

The smart alternative to conventional log interpretation

Tco SHM

Workflow design

Log quality control

Graphical & interactive parameter selection

• Design your own petrophysical workflow

• Detection of pure minerals (coal, halite etc.)

• Save and quickly re-apply workflows to new data

• Detection of borehole geometry effects (bad hole, oval hole, rugosity, etc.)

• Multi-well control of • Plots are dynamically linked petrophysical parameters to parameter tables for can be achieved by setting graphical and interactive defaults for well/dataset/zone selection of equation combinations parameter values

• Easily transfer workflows to other Projects

• Flag and/or treat environmental effects (tension pulls, baryte, KCl, washouts) • Several pre-computations of fluid properties

Q Q.m TBA Nmr

• Multi-well and multi-zone • Edit parameter values graphical and tabular and monitor effects on parameter management gives consequent results through the users control at all times cascade function

FP° Fc

Wbi Ips K.m GeФ

Multi-well parameter control table interactively linked to plots Pickett plot

ND cross-plot

Petrophysical computations

Zone Summary Tables

• Comprehensive list of petrophysical computations: lithology, porosity, saturation, productivity

• User may insert scripts into Quanti (Q) workflow (Q) workflow for instant multi-well, multi-zone application

• Define parameter defaults at Project/Well/Zone levels; hierarchical parameter management facilitates scenario comparison

• Monte Carlo relative and absolute uncertainty modelling

Multi-well Quanti (Q) output (Q) output layout interactively linked to Quanti Quanti ttable


• User-defined cut-offs and output table content

• One-click save of multi-well output table and direct link TM to Excel

• Multi-well and multi-zone summary calculation to • Produce graphical output different references (MD, from cut-off sensitivity TVDSS, etc.), possibility to analysis as a one-click manage weighting, fluid operation code separation and roll up, • Monte Carlo uncertainty reporting bed-by-bed. analysis

Sensitivity to cut-offs


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Quanti.min

CDB

The multi-component inversion model Tco SHM Workflow design

• Build multi-component model with linear and nonlinear tool response functions • Save and easily re-apply models to new data

Solutions

• Optionally use curves instead of constants for end-point, curve uncertainties and other control parameters

Q

• Sequential Quadratic Programming: a very powerful family of robust, non-linear optimisation methods • Resistivity models: Archie, Dual Water, Juhasz, Simandoux and Waxman-Smits

• Easily transfer models to other projects

• Sonic models: Wyllie, Raymer-Hunt-Gardner, RaigaClemenceau, Field equation

Q.m TBA

• Neutron equations: equation s: NPHI, TNPH, APLS, SNP, SWN_BA, BA2435, BA2420

Nmr FP°

Parameter control cross-plots interactively linked to Quanti. min (Q.m) table (Q.m) table

Fc

Wbi Ips K.m GeФ

ND cross-plot to pick endpoints interactively Parameter control table and default results layout, clastics model example m* plot

Model design

• Models may be defined as single mineral sets per zone • Multiple mineral sets per zone can also be established with sets switching automatically according to a partitioning curve that changes as the log facies change • Interactive parameter management e.g. for wet clay

Outputs

• Solutions constrainable against a priori information priori information e.g. XRD or CEC data; both single component and multiple component volume constraints are possible • Incorporate “Special fluids” to account for the effect of baryte in the drilling mud • User control of tool uncertainties

Parameter control table and default results layout, carbonate model example


• Detailed automatic layout, can be fully customised by the user • Unique array-histograms clarify data relationships by plotting all the components against input log data or log data residuals • Juhasz and m* plots

• Characterise the output result curves (e.g. mineral volumes, Sw,Φ ) with calculated uncertainties due to choice of model components and parameters • Sensitivity analysis with a Tornado plot to investigate the contribution of different parameters in the model

Calculated uncertainty bands on output volumes (kaolinite and quartz) and petrophysical parameters (Sw, ΦT)


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Thin bed analysis.

CDB

Resolve your highly laminated formations Tco SHM Workflow

Solutions

Model design

• Drag & drop curves into the dedicated layout associated with the application

• Deterministic Thomas-Stieber

• Drag & drop selection of input curves

• Probabilistic Thomas-Stieber, with sensitivity analysis for equivalent hydrocarbon column uncertainty

• Application control table automatically populates • User makes choices for work streams and sets fluid parameters

• VLSA method with interactive controls

• Interactive cross-plots appear automatically to allow optimisation of the Thomas-Stieber control points

• Tabular control screens for clarity • User options cause table to react and update – infeasible combinations of inputs are prevented

Q • Interactive picking of Thomas-Stieber end-points facilitates correct choice of parameter values

Q.m TBA

• Laminated or isotropic resistivity models may be chosen

Nmr FP° Fc

• The evaluation completes using the selected end-points

Wbi

• Depth ranges chosen for analysis are controlled either by input zones, by input flag curve, by typing depth ranges or by graphical selection of intervals on the plot

Ips K.m GeФ

Thomas-Stieber default results layout

Model application

Outputs

• Completely flexible application depth range specification

• Sand fraction porosity and saturation accounting for nonreservoir shale laminations

• Zones

• Net sand volume (used to weight volumetric analysis of the sand fraction analysis)

• Input flag curve • Graphical selection • Typing

• Full sensitivity analysis available within the probabilistic model • Tornado plot highlights main effects on Equivalent Hydrocarbon Column (EHC)

• Detailed automatic depth plots and cross-plots

Interactive parameter control cross-plots for Thomas-Stieber analysis


“Low Resistivity Pay” sensivity tornado plot and EHC uncertainty


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Nmr.

CDB

Pore network and fluid distribution Tco SHM T2 Conversion: data “regularisation”

Toolbox

• Adjust the T2 data into a single data range and a single number of bins across that range, irrespective of tool source. The application is designed to accept all industry T2 distribution data and to convert them into a regularised T2 distribution

• Compute porosities, permeabilities, water and hydrocarbon volumes through an intuitive user interface; the results can be displayed immediately and controlling parameters/functions adjusted graphically if necessary

Q Q.m TBA Nmr FP°

• Using the clay-bound water (CBW) cut-off (from constant or curve), the NMR NMR clay-corrected clay-corrected porosity and the CBW volume are computed. The Free-Fluid-Index (FFI) cut-off is used to compute the hydrocarbon volume. The total porosity is an integration of the regularised T2 distribution • Two estimates of permeabili ty, the Coates and SDR permeability, are automatically computed from standard equations whose parameters can be again curves or constants and can be adjusted graphically if necessary

Fc

Wbi Ips K.m GeФ

NMR toolbox NMR toolbox and capillary pressure module output

Capillary Pressure from T2 distribution

Coming soon

• Compute a capillary pressure curve from the T2 data.

• Wettability estimation

• In the intervals with hydrocarbon, a hydrocarbon correction can be applied to the T2 • The computed capillary distribution pressure depends on the oil volume and the height above free water level.

Echo chain visualisation


• Pre-processing analysis

Pc inverted from T2 displayed in an array-array plot

GR vs vs TT2 bins displayed in histogram-array plot


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FPress.

CDB

Control the pressure Tco SHM Quality control

Analysis

Within an interactive and graphical tool, analysts can:

• Multi-well and pre-test data analysis for contacts and fluid typing by determination of densities

• Integration of the fluid connectivity concept: groups defining potential reservoir regions

• Graphical interface for faster and intuitive analysis

• FPress (FP°) Quality (FP°) Quality Control output used as weighting factor for gradient/ density calculation

• start from raw data • concatenate all the pressure readings into a pressure-time array by depth format

Q Q.m TBA Nmr FP°

• Define free fluid levels and hydraulic barriers

• display and review the quality of the pressure picks, adjusting graphically if required:

Fc

- final build up pressure

Wbi

- pressure drawdown

Ips

- pressure, before and after

K.m GeФ

Quality control table interactively linked to plots

Investigate the uncertainties

Coming soon

• Input uncertainty ranges for depth and pressure measurements

• Work by group (e.g. “hydraulically connected units”)

• Estimate ranges of gradients consistent with the uncertainty model

• Known gradient comparison

Pressure-Time plot interactively linked with QC table

• Residuals analysis

• Quantify the impact on fluid levels or connectivity of data uncertainty

Pressure-Depth plot for gradient analysis interactively linked to control table


Formatted multi-well template summarising FPress (FP°) analysis (FP°) analysis results


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Fluid contact.

CDB

Management of complex reservoir compartmentalisation

Tco SHM

Raw material

Input multiple zonation schemes in which you can incorporate information from geology (layering, structure, faults from a 3D Earth Model), reservoir engineering

Process

(initialisation regions from a simulator) and petrophysics (fluid codes, net reservoir intervals, fluid levels and gradients from FPress (FP°) )

Q

Resolves the depth data of within the reservoir as seen all these multiple inputs in through well data measured depth and/or TVD within a single wellbore or across multiple wellbores to identify compartments

Q.m TBA Nmr FP° Fc

Wbi Ips K.m GeФ

Scheme of compartmentalised reservoirs: common contact and hydraulically connected reservoirs

Views

Output

• Results are presented • Able to visualise the contacts graphically for ease of within the 3D environment comparison; depth plots can directly within Techlog©, using easily be supplemented with the 3D Vue (3DV) dynamic (3DV) dynamic any other relevant log or core plotting engine data to build a useful multiwell summary template plot

• The main output is a table • Information for each of minimum, most likely and “initialisation region” or maximum depths of each fluid reservoir compartment is contact between pairs of fluids separately reported for ease of transfer into external models

Fluid contact (Fc) table: (Fc) table: multi-well/multi-zone summary view of fluid contacts Fluid contact (Fc) multi-well (Fc) multi-well default output plot showing contacts, compartments and fluid codes



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Wellbore imaging.

CDB

Sophisticated image analysis Tco SHM Workflows

Pre-processing functionality

Image processing ability

• Designed from the ground up to be a generic imaging module, from handling raw data to processed images

• Graphical and intuitive interface to maximise clarity for users

• Perform a host of image • Batch process by well or zone normalisations with preview ability and full control on outliers

• Ability to bulk process on a multi-well basis, process by zone, save and apply imaging workflows

• Full support for all commonly run imaging services from raw data stage or for already processed images

• Full support of a variety of image filters to further enhance image feature clarity

• Utilisation of clear graphical interfaces, and a comprehensive video-based help system

• Efficiently perform speed correction and image concatenation with multiwell ability

Q Q.m TBA Nmr FP° Fc

Wbi Ips K.m GeФ

Graphical interface offering guidance to users; list of imaging tools handled by Wbi module

Multiple image output plot to illustrate stages of image processing/enhancement

Dip Processing

• Innovative methods of manual dip picking, classification and display to enhance efficiency

• Full range of dip display plots, dip conversion, import/ export, dip picking from multiple images

• Auto-dip picking ability through graphical workflows, maximising ease of use

Parameter Extraction

Coming soon

• Dip removal processing

• Schmidt and Wulff plots

• Image parameter extraction workflows

• Eigenvalue and Eigenvector analysis

• Precision variable extraction for downscaling process, through utilisation of the versatile PythonTM script module

Caliper associated with images Dip picking, classification and pictorial representation as “Rose” diagrams


• Net to gross and sand count • Textural map • Fracture property quantification

3D cylindrical view of image data, diameter of cylinder modulated by variable - in this case the caliper


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Ipsom.

CDB

The intelligent classifier Tco SHM Advanced classification technique

Comprehensive statistical tools

Automatic facies identification is playing a key role within the Oil & Gas industry. Ipsom (Ips) is (Ips) is a unique classification module that brings added value to interpretation workflows.

During the final control and validation phase, results are quantified and refined through an iterative process. High quality statistical and graphic tools with total interactivity and great ease of use, lead to a better

The 2D indexed and probabilised self-organizing map ( Ipsom Ipsom ) is designed for use in: • geological interpretation of well log data and facies prediction • optimal derivation of petrophysical properties ( Ф, K, K, hydraulic units etc.).

Q

understanding of coherence between core description, log responses and consistency on the map.

Q.m TBA Nmr FP° Fc

Wbi Ips K.m GeФ

Self-Organising Map at initialisation phase

Sorting and organisation phase of the grid of nodes

Accurate model calibration

The key to the classification process is calibration. The aim of calibration is to give each neural unit an actual geological meaning: this is known as the indexation phase. Each neural unit is assigned a code that

Indexation phase with facies core description

Outputs

corresponds to a geological interpretation (detailed core description). This stage is essential for a direct interpretation of electrofacies in sedimentological terms.

• Optimised partition of log data calibrated to facies described in core • Facies output curve associated with a probability of occurrence of predicted facies at each depth

Spectrum plot illustrating log patterns for different geological facies ND cross-plot colour coded by Ipsom (Ips) predicted (Ips) predicted facies


Default output layout from Ipsom (Ips) ; probability of facies’ presence is indicated at extreme right


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K.mod

CDB

Objective reconstruction of missing data

Tco SHM

Quantitative parameter modelling

Supervised Neural Networks

K.mod (K.m) is (K.m) is designed to extract essential information from log data in order to:

• bring solutions for scale shift management from core to reservoir scale

• predict non-recorded parameters ( Ф,K)

• potentially reduce the need for coring and plug analysis for the subsequent appraisal wells by comparing well log and core data

• reconstruct missing or poor quality measurements and therefore compensate for bad hole conditions, environmental effects, acquisition problems, etc.

• Parameters can be reconstructed or modelled directly from log data, via an interactive learning process

Q

• Multi-Layer Perceptron: a powerful non-linear modelling tool that retains all the original variability in the data

Q.m TBA Nmr FP° Fc

Wbi Ips K.m GeФ

Network design diagram

Progression of error minimisation

Fully quantified uncertainties

Interactive, easy-to-use and very fast

K.mod (K.m) is (K.m) is not a “black box” tool: the users keep full control of the input parameters and receive clear feedback on the log quality and model quality, at all times.

• K.mod (K.m) is (K.m) is based on a complex technology but remains easy-to-use

Uncertainties can be managed: • on inputs: back propagation method to check the contribution of each input

Default output layout showing fit quality assessment in right-hand track: permeability example

• It is a straightforward but efficient tool that offers a simple interpretation and a more accurate reservoir characterisation

• on output: self-organised map is categorising data samples in the training and validation data for their effectiveness in modelling the target data Possibility to weight inputs to force the model to reach extreme values. Optionally standardise output and learning data distributions to match dynamic ranges.

Reconstruction of poor data sonic affected by cycle skip or wash-out



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Geophy.

CDB

Comprehensive solution for combining petrophysical and geophysical data

Tco SHM

Specialised tools available

Time-Depth computation methods

• Create a Time-Depth function using one of several techniques based on checkshot and/or sonic log data

• Apply filters in frequency domain to the seismic wavelet and interactively observe impact on calculated synthetic seismogram

• Automatically convert selected log data to time basis

• Apply Gassmann fluid substitution to prepare log data for comparison to seismic data

• Compute reflection coefficients (RFC) and impedance curves and convolve with chosen seismic wavelet

• Checkshot only • Sonic only • Least-squares fit of sonic data onto checkshot data

Q

• Drag & drop log data to convert into time-based data using an antialiasing filter

Q.m TBA

• User control of sampling frequency

Nmr

• Forced-fit of sonic data onto checkshot data with automatic view of the adjusted sonic curve

FP° Fc

Wbi

Frequency band pass filter and wavelet signature plot

Ips K.m GeФ

Checkshot editing by graphical comparison with sonic transit time

Adjusted sonic output from one method of Time-Depth function definition

Synthetic seismogram generation

Gassmann fluid substitution

• Simply drag & drop timebased log data sampled at the desired frequency into the control window

• Drag & drop log data into the control window

• One click to create the RFC, impedance and synthetic trace

• Parameter input by constant or curve; controllable over zones or intervals

• View pre-formatted output layouts for clear results

• Edit settings manually or use the graphical wheel controls

• Use the graphical wheel control of the frequency domain band filters and immediately view the results of using different filter settings • Filters available: Chebyshev, Bessel, Sync, user-defined wavelet and Butterworth

1D synthetic with repeat plot


Gassmann fluid substitution default layout


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Your essential platform. The platform includes all the fundamental activities to which everyone who uses petrophysical data needs access. The modules included (next page) within the platform are bundled together and offered as a complete package. Every time Techlog is run on a computer, a platform seat is used irrespective of the application module or modules that will eventually be applied in that session. ©

Platform modules


Your essential platform.

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Techdata.

Td

Data management Tp 3DV

Data management is all about data harmonisation for efficiency of access. Multi-well capability is built-in from the ground up. Powerful tools are available in Techlog Techlog© with which to identify the data that are present, to understand any naming or unit problems, to correct those issues rapidly in order to arrive at a state where access to 1000 wells’ data is as straightforward as access to two wells’ data.

Clarity

Py

The simple principles of a “Data Family” or a “Data Alias” allow you to rapidly harmonise names, units, scales, colours etc. across your entire project,

and allow you automatically to control preferential data selection

Ts

Techlog easily handles regular or irregular depth or time reference systems simultaneously.

Attribute data families available for editing by users

Access

Efficiency

From potentially many errors of naming, units and hundreds of wells in a project, families assignment, etc. use powerful data mining tools to rapidly understand the data that are present and any

Using the combination of data Arrive at fully harmonised inventories and detailed data datasets ready for efficient queries, search, find and repair multi-well work in a fraction of spurious names, units and the time. family/alias assignment.

Variable inventory

Detailed query tools find and repair errors in data names, units, step increment, etc.



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Techdata.

Td

Data editing Tp 3DV

Techlog’ echlog’s s powerful data editing tools form an integrated interactive toolkit that allows users to enhance their data and dataset quality effectively and efficiently efficiently..

Operations on Data

Py

Several editors have been developed to facilitate access to data of different types for numerical editing. Variable and zone editing are also fully supported within the graphical display tools.

Ts

Spreadsheet link to ExcelTM ensures simple, direct reporting.

Spreadsheet type Data editor with direct link to Excel

Statistical view of the data in Data editor

TM

Operations on Datasets Datasets are logical groups of curves held to a common reference. Many operations can be performed on one or more datasets at a time; for example: • trim raw data to interval of interest • combine many datasets for further focussed processing

Clear tabular control eases complex processing on entire datasets (combine and resize datasets)



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Techdata.

Td

Data processing Tp 3DV

The final key step in the data preparation workflow is the processing of curves to enhance their accuracy and usability. Techlog© provides a broad range of graphically based tools to make the most of your data and ensure full user control at all times.

Graphical It is very important in data manipulation to be able to visualise the process quickly. The platform includes the means of graphically editing, trimming, clipping, depth shifting, deleting, joining, merging

Py (splicing), despiking, smoothing, interpolating and standardising your data right off the plot.

Ts

Graphical methods allow the analyst to keep control of the process.

Depth shifting Despiking

Powerful Handle large amounts of data at the same time, for example: • merge/splice or resample whole datasets

The powerful data management tools enable rapid access to relevant curves even in the most complex projects.

• data normalisation graphically across multiple wells

Multi-well Gamma Ray histogram Raw data

Multi-well Gamma Ray histogram after normalisation


Default layout display of the normalisation processing


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Techplot.

Td

Single well Tp 3DV

Flexible • Entirely customisable layouts provide enormous flexibility in designing depth or time-based plots. Every aspect of these plots is at user control, and the final design can be saved as a template for instant recall for the next case

Adaptable • Add other plots within the tracks on the plot with full control over the depth range selection • Combine images and log curves by a simple drag & drop operation

Py

• Tracks may each have their own plot • Many curve editing and processing scale, called “zoom factor”. Use this operations are accessible through powerful feature to create montages these plot combining overview scale with • All plots can be constrained by depth detailed scale plots, for example when range or zone range. Print out to incorporating core photographs (see system plotters (page, continuous or illustration below) large format) or export your work to soft copy .CGM, .PDF, or .EMF file formats

Ts

MICP pore throat distribution General layout integrating different types of data (core, log, images) and incorporating histograms and cross-plots into dedicated tracks

Saturation vs vs Pressure Pressure data grouped by rock types

Adaptable (cont.) • 2D and 3D cross-plots are rapidly created by drag & drop of data from the Project Browser

• Crop data, add simple and complex filters and constrain plots by depth(s) or zone(s)

• Fit lines and regressions, linear or • Plot array data in specialised non-linear, fixed point or floating can displays for visual review and be easily created for all data on a graphical editing plot or for subsets of data selected

PHI vs vs K K cross-plot with Winland calibration lines and power function regressions

Polar plot of dip data classified by dip types Matrix plot of multivariate data



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Techplot.

Td

Multi-well Tp 3DV

Interactive

Accessible

• Full interactivity interacti vity make Techlog’s • Design a layout for a single well, then viewers an easy to use and powerful right-mouse click to apply the design to analysis tool. Choose data in one view one or more other wells in the project. and all instances of those references There are no software limits to the are highlighted within any type of number of wells included in a plot, so co-existent plot. The selection is live in these tools can accommodate many tens the memory of the computer so plots of thousands of data points, as required can be linked if they have no curves in common but only the same references

• Specialised plots: customisable plots for the management of parameter selection interact with the parameter tables and the result plots; users modify parameter values graphically and see the results update automatically. Plots include the Pickett plot, Thomas-Stieber plots, m* plot and Juhasz plot

Py

Data selected in multi-well plots appear highlighted in all plots that share a “reference” in common

Ts

Pickett plot

m* plot

Accessible (cont.)

Reproducible

• Bring large amounts of data together in multi-well displays

• Complex plot templates involving many wells may be adapted by duplication and altering the input data control, or by applying the same template to other groups of wells

• Equations can be saved and used directly from the plot within spreadsheets and other editors • Multi-well cross-plots have all the functionality of single well tools; generate any kind of regression through all the data present or through sub selections across multiple wells in the plot or automatically by zone or by well Multi-well cross-plot with frequency display and histograms

Depth plot cross-section linked by zonation

Multi-well box-plot



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Techplot.

Td

Composite output Tp 3DV

Custom design

Py

• A key function for the • In an operational • Build well composites • Annotate the details of user is to produce copy to environment, re-usable piece-by-piece, save the the plots for ease of illustrate reports or share templates that combine template design and apply reference long after the data and interpretations headers, footers, tables, directly to the next well in operation is completed with colleagues cross-plots, histograms the operational sequence and layout tracks within a single display often describe a “product” that defines the operation

• Other methods of output of plot copy include screen shots, .CGM, .WMF or .PDF files, and hard copy to page, continuous sheet or large format plotters located anywhere on your network

Ts

e . S s e E h C T I V R .

E S A I S H C

COMPANY W EL L FIELD COUNTY STATE COUNTRY API WELL No .

H C A C G E B O & D T E 4 N L E O U C O N U A G N R R N A T l e A T E A R T W C H L F : : : : : :

:TTTO &G : W el l 4 :CARNON BEACH :HERAULT :LANGUEDOC- ROUSSILLON LLON :FRANCE :

WELLLOCATION Montpellier SouthOfFrance

: . Y N Y Y A L T E R P L D N T o T N M E L N A U E U T O W I I C F O O P C S C A

OTHERSERVICES

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RANGE :

: K KB B : 260 Ft( KellyBushing 230 Ft ( GroundLevel

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s E r e o e T s y s o o l r g r p m f o e o r e o s d e s r a r c u t n e c e n g h i t s a n e i s t n p e , e p c x e x e r , o s e g a m a t d o n , l a h s s t s e o o W c d e . , w d n a s t e l n u e d e m h e r c u S s e a c e i r m P t r e n h e t r r o u r s c o s r l o l u a c r r s o i r o e n t f i i c c t e f e i l l u b f e i o s o t r e n u m o o o s r p f f s s s e o a r e s e n c r n n o o o i e t s l r n e y i e o d b b f n i i a e o n t i l a C n t e d e b a d o r n d r p m a e e , s s n s a t n i o b i m t r s y a T e n n t e l o a i r a n f p r i r o e p s e n t o s n e e i e r t G n y r a c n u s e a o n r r f o o o t o i t c t t l a r t u c e o s e t r j e b r r p c y a r u e r a p a s t r s n u u a o i c o s l c e l a A a n n e o r e o y h e n a - t c s e n a n e g e y i t o b t n i E r a a l g d t e e n r C a n e I u l i p a r T g u t f e l s O t i t o w u n N n

4 l l e W : l e W

Magnified views of header and footer

5 2 . 0

. S e s e E C h I T V R .

e n i l e s a

E S A I S H C E T

COMPANY W EL L FIELD COUNTY STATE COUNTRY API WEL LN LNo .

H C A C G E O B & D T E 4 N L O U U E C O l N A G N R E R N T l A e A T A R T W C H L : : : : : F : : . Y N Y Y A L R T E T P D N o L L T M E A N N E O I U I O T U C W F O P C S C A

DEPTH REF E LE VA TIO N

:TTTO &G : W el l 4 :CARNONBEACH :HERAULT :LANGUEDOC-ROUSSILLON :FRANCE :

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OTHERSERVICES

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.

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: KB : 2 60 F t ( K e ell yl Bu Bu sh ni g 2 30 F t ( G ro ro un dL dL ev el

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r s e o e s y s o o l r p g m f e o r o r e o s d e s r a r c u t n e c e h i n g t s a n e i s , t n p e e c x p x e e r , o s e g a m a t d o n , l l a h s s s e t o o W c d e . , w d n a s t e l n u e d e m e h r c u S s e a c e i r m P r t e n h e t r r o u r s c o s r l o u l a c r r s o i r o n t f e i i c c t e e l f i u l b f e i o o t s r n m e o o u s r p o f s s f a s e o s e r c e n r n n o o i e o s l t r n e y i e d b b f o i n i n t a e o i a l d C n t e e b a d o r d r p m n e e , s a s t n s a n o i i b m t r s y a T e t n n e l o a i r a n f p r i o r e p s e n o s t n e e i e r t n y G a r n c u s e a o n r r f o o t o i o t t t c l a r t c e o t u s j e r e b r r y a p c r u p a s e r a r t s n u i c u a s o l l c o e l a A a n n e o r e o y h e - t n a c a s e n n e e y o t g b t i i n l E a a d g r e e t C u e a n I n p r i l t T g a r u s f e l O t i t o u n N n w s i

4 l e W : l l e W

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t u O y a h R M I s 2 _ P I a L N a M A I A G W A m G o C m t a S G B

6

0 0 7 7

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t u O h M I s 2 _ a I N M P L I A A W A G G o C t S B

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0 5 6 7

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Composite headers and footers combined with multiple track sections to provide report quality output for publication



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3D Vue.

Td

Visualise multiple wells in a 3D environment Tp 3DV Multiple well 3D dynamic engine

Use wellpath trajectories to locate wellbores within their spatial positions to create a 3D model of the reservoir or geological structure under study.

• Possibility to view several wells from unlimited angles

• Display continuous parameters as modulations of well cylinders

• TVDSS, X and Y coordinates display

• Unlimited colour palettes

• Zones displayed on each individual wellbore

Cross-sections

Py

• Link wells together in regular or random line cross-sections to explore spatial relationships in your data

Ts

• Continuously update your view with data from real-time data acquisition

3D representation of wellbore trajectories

Random line cross-section showing zonation scheme between wells

Maps and surfaces

3D borehole visualisation

• Propagate across the model by 2D kriging between wells any © parameter carried within Techlog ; these can be formation results data, zone average log data, core data, parameters extracted from images, facies, etc.

• Well display using Wellbore imaging (Wbi) module (Wbi) module • Direct interactive link between the depth plot and 3D Vue (3DV)

• Post surfaces in the 3D cube: layers, parameter values, seismic and geological horizons, fluid contacts, etc.

Post surfaces and contour maps in 3D Vue (3DV)



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PythonTM

Td

Go further with user programming Tp 3DV Introduction TM

Python is an open-source scripting language that Techsia has incorporated within the Techlog© platform. In the world at large, it is in use today across many industries; it is being developed by many individuals to perform all manner of programming activities from simple calculations to complex interface and database implementations. When you use Python in Techlog, you have available an enormous resource of technology that is derived from a user-base numbered in the many thousands.

What Techlog© provides ©

Py

TM

Techlog Python editor combined with “libraries” that permit access to:

Ts

• All Techlog data objects (e.g. wells, datasets, curves, properties etc.) • Maths/Statistics routines • Petrophysical calculations (e.g. shale, porosity and saturation equations) • Plot objects (e.g. access a pre-defined template or create a new template within a Python script)

Python script editor: example of data manipulation with interactive help TM

More resources

How to use it

• Additional tools and library functions through Internet TM access from the Python community

• Techsia has provided a large • Scripts can be run “standnumber of ready-made alone” directly from the scripts that accomplish many Python editor; any script tasks; these can be used can access other scripts as as completed, functioning “sub-routines” scripts or as starting points for adaptation to a specific task of interest

• Scripts can be used to access previously compiled code written in C++ or Fortran, for example

• Scripts can be incorporated into Quanti (Q) workflows (Q) workflows and thus be applicable over many wells and/or data interval ranges without the analyst having to write a lot of data access/housekeeping code

TM

Qvn calculation: Python script within a Quanti (Q) workflow table and output display in the layout



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Techstat.

Td

Comprehensive exploratory data analysis Tp 3DV Classification and normalisation

Hierarchical clustering:

Decision Tree:

• find similarities between wells

• powerful classifiers where inputs are mixed and incomplete variables (qualitative and quantitative)

• group wells together • if necessary, align data responses using sophisticated Gaussian analysis, group-bygroup amongst wells

• rank inputs by their information gain • deduced rules can help to understand the input data

Regressions

Py

• Linear (RMA, Major Axis, x/y, y/x), non-linear, polynomial algorithms are available

Ts

• Fit lines may be calculated for user-defined subsets of data using the data selection tools and interactivity between viewers • Regression and other fit lines and functions may be created and • Regressions can be freely conditioned on filters, zonation, calculated or forced through a well-by-well or multi-well fixed point on a plot • Input user defined-equations graphically and by keyboard entry

• results are displayed in a dendrogram

Regressions by selections and table of resulting equations for reporting

Hierarchical cluster analysis (HCA) dendrogram

Decision Tree rules

Factor analysis

Coming soon

• Principal Component • Linear Discriminant Analysis (PCA) is a Analysis (LDA) is used useful tool to summarise to determine the best data, since it separates projection space to the dominating features discriminate between in the dataset two or more naturally occurring groups. It clarifies subsequent cluster analyses on users’ data

• Multiple Correspondence Analysis compares qualitative variables that may either be of similar type (observed vs predicted vs predicted curves) or be of dissimilar type (geology vs vs petrophysics) petrophysics)

• Extend the reporting of exploratory statistics with a new and comprehensive reporting module. Partition your wells by zones or facies or fluid types, for example, and select from many summary statistics

• Build P10, P50, P90 output reports for sharing with colleagues • Analyse uncertainties in zone summary information with Monte Carlo analysis of results tables Correspondence analysis formatted report

Principal Component Analysis: comparison of vectors Principal Component Analysis: comparison of projections



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