Mechanistic flow modelling
in pipes
Pablo Adames
September 11, 2012
Mechanistic flow modelling in pipes
Problem context
gathering
systems
trunk
lines
Network
tie ins
empirical
correlations
Steady
state
software
mechanistic
models
Hydrodynamic
models
inclination
range
wells
unied
90 to
0◦
-10 to
+30◦
90◦
Mechanistic flow modelling in pipes
The problem
What difference does it make
to select one type of hydrodynamic model
over the other?
Mechanistic flow modelling in pipes
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
Mechanistic flow modelling in pipes
Horizontal gas-liquid flow patterns
Mechanistic flow modelling in pipes
Flow pattern observation
In the following slides
we will look at early
flow pattern observations
Mechanistic flow modelling in pipes
Horizontal dispersed bubble
UofC, circa 1970
Mechanistic flow modelling in pipes
Horizontal stratified wavy
UofC, circa 1970
Mechanistic flow modelling in pipes
Horizontal slug flow
UofC, circa 1970
Mechanistic flow modelling in pipes
Horizontal slug flow II
Higher liquid loading, more frequent slugs
Mechanistic flow modelling in pipes
Horizontal annular mist
UofC, circa 1970
Mechanistic flow modelling in pipes
Slip and holdup in multiphase pipe flow
Fundamental to understanding multiphase flow
Holdup: phase fraction
Slip: relative phase velocity
Holdup and slip change in a flowing system
Their changes are interrelated
There is no equivalent concept in single phase flow
Mechanistic flow modelling in pipes
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 :
L
EL = AGA+A
L
Mechanistic flow modelling in pipes
The Hydrodynamic Slip
vslip = vG − vL
The lighter phase will generally use energy more effectively to
travel along faster. . .
vslip > 0
But sometimes when descending. . .
vslip < 0
Mechanistic flow modelling in pipes
Input and in situ phase fractions
Why does phase fraction change in a pipe?
A recipe for phase fraction change:
Ingredients
1
2
3
4
5
6
Inmiscible phases (they don’t blend)
A pipeline
Inertial forces (phase motion)
Gravitational forces
Dissipative forces (friction)
Residence time
Hydrodynamic phase separation
Input phase fraction changes downstream
Each phase uses energy differently
Mechanistic flow modelling in pipes
Input vs. in situ phase fractions
An highway analogy
INPUT SECTION:
Input ratio of trucks to cars:
3
3
= 1.0
Input fraction of trucks to trafic:
3
3+3
= 0.5
in situ SECTION:
in situ ratio of trucks to cars:
6
3.5
in situ fraction of trucks to trafic:
= 1.71
6
6+3.5
= 0.63
Mechanistic flow modelling in pipes
Input vs. in situ fraction
Analysis and conclusion
Top view of highway:
Road ≈ pipeline
Trucks ≈ liquid
Cars ≈ gas
The in situ fraction of the slower moving vehicle/fluid is
greater than its input fraction
There is hydrodynamic retention in steady state of the heavier
phase
This is known as the holdup or slip effect
Mechanistic flow modelling in pipes
The first flow pattern maps
Mandhane et al. horizontal
Aziz et al. vertical up
Return
Source: Engineering Data Book, Gas Processors Suppliers Association, 2004. 12th Edition FPS,
Tulsa, Oklahoma
Mechanistic flow modelling in pipes
Types of flow models
Analytical: built with first principles
Empirical: built from observations alone
Mechanistic: built from general laws and observations
Mechanistic flow modelling in pipes
Empirical versus mechanistic
Why bother?
Mechanistic flow models
Empirical flow correlations
Developed by correlating
dimensionless numbers
Developed from physical
laws
Extrapolation is uncertain
Closed with empirical
correlations
Interpolation can be very
good
Reduced dependence on
range of data
Can be simple to solve by
hand
Usually computers needed to
solve
Mechanistic flow modelling in pipes
Empirical versus mechanistic
Why bother?
Mechanistic flow models
Empirical flow correlations
Developed by correlating
dimensionless numbers
Developed from physical
laws
Extrapolation is uncertain
Closed with empirical
correlations
Interpolation can be very
good
Reduced dependence on
range of data
Can be simple to solve by
hand
Usually computers needed to
solve
Mechanistic flow modelling in pipes
Empirical versus mechanistic
Why bother?
Mechanistic flow models
Empirical flow correlations
Developed by correlating
dimensionless numbers
Developed from physical
laws
Extrapolation is uncertain
Closed with empirical
correlations
Interpolation can be very
good
Reduced dependence on
range of data
Can be simple to solve by
hand
Usually computers needed to
solve
Mechanistic flow modelling in pipes
History of the multiphase flow models
Source: Shippen, M., Steady-State Multiphase Flow -Past, Present, and Future, with a Perspective
on Flow Assurance. Energy & Fuels, 2012. 26: p. 4145-4157.
Mechanistic flow modelling in pipes
Mechanistic flow pattern maps
Angle 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 model
Between -10 and +10 degrees of inclination with the horizontal
Mechanistic flow modelling in pipes
The angle sensitivity of flow patterns
Mechanistic flow modelling in pipes
The operating line and the flow pattern map(s)?
Mechanistic flow modelling in pipes
Concluding on angle dependency
Would you use a single empirical flow pattern
map for the whole pipeline again?
Mechanistic flow modelling in pipes
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 still
on. . .
Three-phase flow patterns
Heavy oils
Sand transport
Non Newtonian rheologies
Transient real time simulation
Complex fluids
Mechanistic flow modelling in pipes
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 still
on. . .
Three-phase flow patterns
Heavy oils
Sand transport
Non Newtonian rheologies
Transient real time simulation
Complex fluids
Mechanistic flow modelling in pipes
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 still
on. . .
Three-phase flow patterns
Heavy oils
Sand transport
Non Newtonian rheologies
Transient real time simulation
Complex fluids
Mechanistic flow modelling in pipes
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 still
on. . .
Three-phase flow patterns
Heavy oils
Sand transport
Non Newtonian rheologies
Transient real time simulation
Complex fluids
Mechanistic flow modelling in pipes
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 still
on. . .
Three-phase flow patterns
Heavy oils
Sand transport
Non Newtonian rheologies
Transient real time simulation
Complex fluids
Mechanistic flow modelling in pipes
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 still
on. . .
Three-phase flow patterns
Heavy oils
Sand transport
Non Newtonian rheologies
Transient real time simulation
Complex fluids
Mechanistic flow modelling in pipes
Effect of increasing water cut
Inclination +0.25◦ , VSL = 0.05m/s, VsG = 1.3m/s, WC=1%
Mechanistic flow modelling in pipes
Effect of increasing water cut
Inclination +0.25◦ , VSL = 0.05m/s, VsG = 1.3m/s, WC=5%
Mechanistic flow modelling in pipes
Effect of increasing water cut
Inclination +0.25◦ , VSL = 0.05m/s, VsG = 1.3m/s, WC=10%
Mechanistic flow modelling in pipes
Effect of increasing inclination to +1◦
Inclination +1.0◦ , VSL = 0.1m/s, VsG = 1.4m/s, WC=10%
Mechanistic flow modelling in pipes
Effect of increasing the gas superficial velocity
Inclination +1.0◦ , VSL = 0.1m/s, VsG = 1.7m/s, WC=10%
Mechanistic flow modelling in pipes
Effect of increasing the gas superficial velocity
Inclination +1.0◦ , VSL = 0.1m/s, VsG = 2.5m/s, WC=10%
Mechanistic flow modelling in pipes
Main idea of unit cell model
Fixed frame of reference
Mechanistic flow modelling in pipes
Main idea of unit cell model
Moving frame of reference
Mechanistic flow modelling in pipes
A case Study
Now let us consider a real life case. . .
Comparing published field measurements
versus different model predictions.
Frigg to St. Fergus
UK
Return
http://www.uk.total.com/pdf/Library/PUBLICATIONS/Library-StFergusBrochure.pdf
Frigg to St. Fergus
Slug catcher
http://www.uk.total.com/pdf/Library/PUBLICATIONS/Library-StFergusBrochure.pdf
Mechanistic flow modelling in pipes
Frigg to St. Fergus
Description
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
Mechanistic flow modelling in pipes
Frigg to St. Fergus
Description
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
Mechanistic flow modelling in pipes
Frigg to St. Fergus
Description
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
Mechanistic flow modelling in pipes
Frigg to St. Fergus
Description
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
Mechanistic flow modelling in pipes
Frigg to St. Fergus
Description
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
Frigg to ST. Fergus
Measured values
Group 1
Group 2
Group 3
Eq-gas
MMsm3d
15.679
20.001
21.308
22.614
27.438
28.846
31.760
33.569
33.400
38.900
40.900
43.800
32.400
33.400
36.100
38.400
38.900
40.900
43.800
Measured values
Pup
Pdown
bara
bara
25.0
114.0
88.9
42.0
108.0
66.0
55.0
105.0
50.0
43.0
131.0
88.0
60.5
145.0
84.5
82.0
132.0
50.0
93.0
143.0
50.0
100.4
149.1
48.7
39.7
149.1
109.4
59.4
148.4
88.9
118.4
148.4
30.0
131.0
147.9
16.9
58.1
109.2
51.1
60.6
109.3
48.7
69.8
117.5
47.7
74.5
122.9
48.5
77.1
125.1
48.0
82.9
131.4
48.5
91.2
140.3
49.1
ΔP
bar
Group 1: Frigg to St. Fergus; Group 2: Frigg to MCP01; Group 3: MCP01 to St. Fergus
Tup
C
47.0
47.0
47.0
47.0
47.0
47.0
47.0
28.0
28.0
29.3
32.6
27.9
5.6
2.0
5.1
5.1
23.3
33.3
45.6
Field view
Results for pressure drop
Relative error
Group 1
Group 2
Group 3
EatOli
B&B rev
B&B
-11.86
-1.59
-2.56
-5.59
-5.95
-1.55
-1.72
-1.40
-4.95
-5.17
-17.98
-11.60
-3.82
-1.82
-4.26
-3.44
-3.22
-4.51
-3.97
-5.10
0.93
-10.41
-12.80
-9.77
-18.85
-14.48
-14.94
-14.84
-22.83
-22.67
-28.28
-21.37
-16.56
-14.53
-16.59
-15.93
-15.42
-16.45
-15.70
-15.87
-19.85
-19.15
-19.28
-19.53
-24.80
-8.50
-19.35
-33.96
-28.36
-26.88
-27.27
-20.69
-18.45
-16.01
-17.74
-17.01
-16.45
-17.53
-16.90
-20.41
OliMec
ei, %
-10.26
2.46
1.62
-2.33
-3.30
1.50
1.07
1.19
-2.43
-2.48
-15.53
-9.24
-0.21
1.81
-0.97
-0.35
-0.11
-0.78
-1.33
-2.09
Xiao XiaoMod OLGAS2P
1.73
6.74
3.80
2.32
-0.66
2.36
1.50
0.30
-2.93
0.21
-16.88
1.30
-1.59
0.49
-2.40
-1.83
-1.66
-2.34
-2.76
-0.65
5.72
9.84
6.71
5.11
1.49
4.19
3.23
1.79
-1.17
1.56
-15.95
2.06
0.30
2.14
-0.97
-0.49
-0.37
-1.14
-1.77
1.17
-9.46
-0.16
-1.11
-4.42
-5.45
-0.82
-1.40
-1.20
-4.44
-5.51
-18.23
-11.76
-3.65
-1.66
-4.26
-3.71
-3.61
-4.27
-4.73
-4.73
Mechanistic flow modelling in pipes
Results for pressure drop
Summary
ei
|ei|
EatOli
%
-5.10
5.10
B&B rev
%
-15.87
15.96
B&B
%
-20.41
20.41
OliMec
%
-2.09
3.10
Xiao
%
-0.65
2.83
XiaoMod OLGAS2P
%
%
1.17
-4.73
3.47
4.73
Mechanistic flow modelling in pipes
Results for holdup
Summary (only two measurements)
Measured
Holdup
630
418
EatOli
Measured
Holdup
630
418
EatOli
1624.0
1504.0
157.78
288.98
B&B rev
21271.0
18945.0
B&B rev
3276.35
4994.85
B&B
4953.0
4323.0
B&B
OliMec
m3
308.0
294.0
OliMec
ei, %
686.19
-51.11
1086.35
-26.23
Xiao
321.0
317.0
Xiao
-49.05
-23.11
XiaoMod OLGAS2P
432.0
424.0
540.0
520.0
XiaoMod OLGAS2P
-31.43
3.47
-14.29
29.34
Mechanistic flow modelling in pipes
Conclusions
1
The angle of inclination is very important for gas-liquid flow
2
Flow pattern maps provide insight into pipeline gas-liquid
simulations
3
Mechanistic flow models are safer general purpose options
4
Mechanistic flow models are better holdup predictors
Thank you