Mechanistic flow modelling in pipes

September 11, 2012Pablo Adames

in pipesMechanistic flow modelling

Mechanistic flow modelling in pipes

Problem context

Steady

state

software

Hydro-dynamicmodels

empirical

corre-

lations

mechanis-

tic

models

inclination

range-10 to

+30◦

90◦

90 to

0◦

uni�ed

Network

wells

tie ins

trunk

lines

gathering

systems


The problem

What difference does it make

to select one type of hydrodynamic model

over the other?


Basic concepts

To understand how gas-liquid flow models were developed:

Flow patterns

Slip and holdup

Angle of inclination

Model types: Analytical ⇔ mechanistic ⇔ empirical

Fluid properties


Horizontal gas-liquid flow patterns


Flow pattern observation

In the following slides

we will look at early

flow pattern observations


Horizontal dispersed bubbleUofC, circa 1970


Horizontal stratified wavyUofC, circa 1970


Horizontal slug flowUofC, circa 1970


Horizontal slug flow IIHigher liquid loading, more frequent slugs


Horizontal annular mistUofC, circa 1970


Slip and holdup in multiphase pipe flow

Fundamental to understanding multiphase flowHoldup: phase fractionSlip: relative phase velocity

Holdup and slip change in a flowing system

Their changes are interrelated

There is no equivalent concept in single phase flow


Holdup as a fraction

Stratified flow

Concept applicable to all flow patterns

Gas phase flows on top

Liquid flows in the bottom

Area fraction of liquid, EL:EL = AL

AG +AL


The Hydrodynamic Slip

vslip = vG − vL

The lighter phase will generally use energy more effectively totravel along faster. . .

vslip > 0

But sometimes when descending. . .

vslip < 0


Input and in situ phase fractionsWhy does phase fraction change in a pipe?

A recipe for phase fraction change:Ingredients

1 Inmiscible phases (they don’t blend)2 A pipeline3 Inertial forces (phase motion)4 Gravitational forces5 Dissipative forces (friction)6 Residence time

Hydrodynamic phase separation

Input phase fraction changes downstream

Each phase uses energy differently


Input vs. in situ phase fractionsAn highway analogy


Input vs. in situ fractionAnalysis and conclusion

Top view of highway:

Road ≈ pipelineTrucks ≈ liquidCars ≈ gas

The in situ fraction of the slower moving vehicle/fluid isgreater than its input fraction

There is hydrodynamic retention in steady state of the heavierphase

This is known as the holdup or slip effect


The first flow pattern maps

Mandhane et al. horizontal Aziz et al. vertical upReturn

Source: Engineering Data Book, Gas Processors Suppliers Association, 2004. 12th Edition FPS,Tulsa, Oklahoma


Types of flow models

Analytical: built with first principles

Empirical: built from observations alone

Mechanistic: built from general laws and observations


Empirical versus mechanisticWhy bother?

Empirical flow correlations

Developed by correlatingdimensionless numbers

Extrapolation is uncertain

Interpolation can be verygood

Can be simple to solve byhand

Mechanistic flow models

Developed from physicallaws

Closed with empiricalcorrelations

Reduced dependence onrange of data

Usually computers needed tosolve


























History of the multiphase flow models

Source: Shippen, M., Steady-State Multiphase Flow -Past, Present, and Future, with a Perspectiveon Flow Assurance. Energy & Fuels, 2012. 26: p. 4145-4157.

Next Slide


Next Slide


Next Slide


Next Slide


Mechanistic flow pattern mapsAngle of inclination dependency

Remember the Mandhane and Aziz et al flow pattern maps?

First Flow Maps

What happens between horizontal and vertical?Only the mechanistic flow pattern maps answer that question

Let’s see an example using the Xiao et al Mechanistic modelBetween -10 and +10 degrees of inclination with the horizontal


The angle sensitivity of flow patterns


The operating line and the flow pattern map(s)?


Concluding on angle dependency

Would you use a single empirical flow patternmap for the whole pipeline again?


Flow model challenge

What is the nature of the modelling challenge?Too many variables for a simple cause effect analysis

There are good models but the search for understanding is stillon. . .

Three-phase flow patterns

Heavy oils

Sand transport

Non Newtonian rheologies

Transient real time simulation

Complex fluids






Heavy oils

Sand transport



Complex fluids






Heavy oils

Sand transport



Complex fluids






Heavy oils

Sand transport



Complex fluids






Heavy oils

Sand transport



Complex fluids






Heavy oils

Sand transport



Complex fluids


Effect of increasing water cutInclination +0.25◦, VSL = 0.05m/s, VsG = 1.3m/s, WC=1%






Effect of increasing inclination to +1◦

Inclination +1.0◦, VSL = 0.1m/s, VsG = 1.4m/s, WC=10%


Effect of increasing the gas superficial velocityInclination +1.0◦, VSL = 0.1m/s, VsG = 1.7m/s, WC=10%


Effect of increasing the gas superficial velocityInclination +1.0◦, VSL = 0.1m/s, VsG = 2.5m/s, WC=10%


Main idea of unit cell modelFixed frame of reference


Main idea of unit cell modelMoving frame of reference


A case Study

Now let us consider a real life case. . .

Comparing published field measurementsversus different model predictions.

Frigg to St. FergusUK

Return

http://www.uk.total.com/pdf/Library/PUBLICATIONS/Library-StFergusBrochure.pdf

Frigg to St. FergusSlug catcher

http://www.uk.total.com/pdf/Library/PUBLICATIONS/Library-StFergusBrochure.pdf


Frigg to St. FergusDescription

d i =774 mm (30.5 inch)

Frigg to MCP01: 188.4km, 15 point elevation profile

MCP01 to St. Fergus: 175km, 15 point elevation profile

Detailed gas composition

Specified variables: Pdowstream, Tupstream

Calculated variable: Pupstream



d i =774 mm (30.5 inch)








d i =774 mm (30.5 inch)








d i =774 mm (30.5 inch)








d i =774 mm (30.5 inch)






Frigg to ST. FergusMeasured values Measured values

Eq-gas ΔP Pup Pdown Tup

MMsm3d bar bara bara C

Group 1

15.679 25.0 114.0 88.9 47.0

20.001 42.0 108.0 66.0 47.0

21.308 55.0 105.0 50.0 47.0

22.614 43.0 131.0 88.0 47.0

27.438 60.5 145.0 84.5 47.0

28.846 82.0 132.0 50.0 47.0

31.760 93.0 143.0 50.0 47.0

33.569 100.4 149.1 48.7 28.0

Group 2

33.400 39.7 149.1 109.4 28.0

38.900 59.4 148.4 88.9 29.3

40.900 118.4 148.4 30.0 32.6

43.800 131.0 147.9 16.9 27.9

Group 3

32.400 58.1 109.2 51.1 5.6

33.400 60.6 109.3 48.7 2.0

36.100 69.8 117.5 47.7 5.1

38.400 74.5 122.9 48.5 5.1

38.900 77.1 125.1 48.0 23.3

40.900 82.9 131.4 48.5 33.3

43.800 91.2 140.3 49.1 45.6

Group 1: Frigg to St. Fergus; Group 2: Frigg to MCP01; Group 3: MCP01 to St. Fergus Field view

Results for pressure dropRelative error

EatOli B&B rev B&B OliMec Xiao XiaoMod OLGAS2P

-11.86 0.93 -19.85 -10.26 1.73 5.72 -9.46

-1.59 -10.41 -19.15 2.46 6.74 9.84 -0.16

-2.56 -12.80 -19.28 1.62 3.80 6.71 -1.11

-5.59 -9.77 -19.53 -2.33 2.32 5.11 -4.42

-5.95 -18.85 -24.80 -3.30 -0.66 1.49 -5.45

-1.55 -14.48 -8.50 1.50 2.36 4.19 -0.82

-1.72 -14.94 -19.35 1.07 1.50 3.23 -1.40

-1.40 -14.84 -33.96 1.19 0.30 1.79 -1.20

-4.95 -22.83 -28.36 -2.43 -2.93 -1.17 -4.44

-5.17 -22.67 -26.88 -2.48 0.21 1.56 -5.51

-17.98 -28.28 -27.27 -15.53 -16.88 -15.95 -18.23

-11.60 -21.37 -20.69 -9.24 1.30 2.06 -11.76

-3.82 -16.56 -18.45 -0.21 -1.59 0.30 -3.65

-1.82 -14.53 -16.01 1.81 0.49 2.14 -1.66

-4.26 -16.59 -17.74 -0.97 -2.40 -0.97 -4.26

-3.44 -15.93 -17.01 -0.35 -1.83 -0.49 -3.71

-3.22 -15.42 -16.45 -0.11 -1.66 -0.37 -3.61

-4.51 -16.45 -17.53 -0.78 -2.34 -1.14 -4.27

-3.97 -15.70 -16.90 -1.33 -2.76 -1.77 -4.73

-5.10 -15.87 -20.41 -2.09 -0.65 1.17 -4.73

Group 1

Group 2

Group 3

ei, %


Results for pressure dropSummary

EatOli B&B rev B&B OliMec Xiao XiaoMod OLGAS2P

% % % % % % %

ei -5.10 -15.87 -20.41 -2.09 -0.65 1.17 -4.73

|ei| 5.10 15.96 20.41 3.10 2.83 3.47 4.73


Results for holdupSummary (only two measurements)

Measured EatOli B&B rev B&B OliMec Xiao XiaoMod OLGAS2P

Holdup

630 1624.0 21271.0 4953.0 308.0 321.0 432.0 540.0

418 1504.0 18945.0 4323.0 294.0 317.0 424.0 520.0

Measured EatOli B&B rev B&B OliMec Xiao XiaoMod OLGAS2P

Holdup

630 157.78 3276.35 686.19 -51.11 -49.05 -31.43 -14.29

418 288.98 4994.85 1086.35 -26.23 -23.11 3.47 29.34

m3

ei, %


Conclusions

1 The angle of inclination is very important for gas-liquid flow

2 Flow pattern maps provide insight into pipeline gas-liquidsimulations

3 Mechanistic flow models are safer general purpose options

4 Mechanistic flow models are better holdup predictors

Thank you

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Mechanistic flow modelling in pipes

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