Static Analysis of Slug Flow

Static Analysis of Slug flow: A Presentation for Beginners The purpose of this article is to explain the static analysis of slug flow using Caesar II. This article will cover the following points in brief:  

Introduction Calculation of Slug Force

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Static Analysis

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Inputs Required

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Assumptions

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Case Study showing an example

INTRODUCTION 

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Slug Flow is typical two phase flow where a wave is picked up periodically by the rapidly moving gas to form a frothy slug, which passes along the pipe at a greater velocity than the average liquid velocity. In this type of flow, slugs can cause severe and, in some cases, dangerous vibrations in piping systems because of the impact of the high-velocity slugs against fittings such as bend, Tee etc. Slug flows generate dynamic fluid forces, which may induce structural vibration.

Slug Flow  

Excessive vibration may lead to component failures due to fatigue or resonance. Such vibration problem may be avoided by thorough analysis, preferably at design stage.

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Two types of Analysis Methods are prevalent o Static Analysis and o Dynamic Analysis

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Examples of Slug flow: o Vacuum Transfer Lines o Condenser Outlet Lines o Re-boiler Return Lines o Fired Heater outlets 1

o Boiler Blow down lines.

SLUG FORCE 

Slug force is equal to the change in momentum with respect to time. Refer the below attached figure:

Diagram Showing Slug Force Application  

Use the following equations to calculate Slug Force. Multiply the calculated value with a suitable DLF. Normally a DLF of 2.0 is common to use.

Diagram Showing Slug Force Equation

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STATIC ANALYSIS INPUTS REQUIRED FOR ANALYSIS:  

Stress isometrics of complete system. Line parameters such as line temperatures, pressures, fluid density, pipe material, corrosion allowance, insulation thickness, density etc.

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Parameters required for Slug force calculation like slug density or liquid density, two phase velocity etc.

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Nozzle allowable if connected to equipment.

ASSUMPTIONS FOR ANALYSIS: 

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It is assumed that the slug is formed across the full cross section of the pipe for the maximum impact. This configuration is least probable for vertically down word flow as no hold – up is possible for accumulation of liquid and eventual formation of slug. Hence slug force at elbows for vertically downward flow lines are not considered. It is assumed that the reader knows normal static analysis of piping system using Caesar II.

CASE STUDY FOR ANALYSIS: Lets assume the shown system is subjected to slug flow. The parameters for the pipe are as mentioned below:  

Pipe: A106B, 6”, Sch 40 CA=3 mm

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T1=100 degree C

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T2=75 degree C

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P1=15 bar

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Liquid Density=950 Kg/m^3

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Two phase Velocity=10.53 m/s

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Stress System under consideration After modeling the piping system following conventional method we have to calculate the slug force and apply the same into the system. Normally all organizations have their excel spreadsheet to calculate Slug Force. A typical excel spreadsheet for slug force calculation is shown in the below attached figure for your reference.

Excel Spreadsheet for Slug force calculation

So if we use a DLF of 2 then each of axial and orthogonal force will be 4240N. We have to incorporate this force in Caesar II input spreadsheet. Check the below mentioned figure for direction of forces.

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Slug force in Bends with Application direction

Now we will input the axial and orthogonal forces at all changes in direction as shown in attached figure.  

To enter forces click on the Forces button in Caesar II spreadsheet. Provide the node number and magnitude of forces with proper direction.

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Similarly input forces in all bends (other than vertically downward bends).

Caesar Spreadsheet Showing input methodology of Slug Force

Next step is to prepare the required load cases. Few additional load cases need to be prepared for static analysis of slug force. The same has been shown in the below mentioned figure.

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Caesar II Load cases for Slug Flow Analysis  

Prepare the load cases as mentioned in the figure. Make stress types as occasional

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Use combination methods as Scalar

OUTPUT REPORT

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Additionally We have to check code compliance for load cases L14 to L17 and ensure that the values are well within code allowable values. We have to check forces and displacements for load cases L1 to L9.

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Refer below mentioned figures for reference:

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Caesar II Code compliance check report

Caesar II Restraint Summary check report Keep all stresses, forces and displacements within allowable limit. If exceeds then try iteration with support location change, support type change or routing change.

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