Presented are reduced-order models of one-dimensional transient two-phase gas–liquid flow in pipelines. The proposed model is comprised of a steady-state multiphase flow mechanistic model in series with a transient single-phase flow model in transmission lines. The steady-state model used in our formulation is a multiphase flow mechanistic model. This model captures the steady-state pressure drop and liquid holdup estimation for all pipe inclinations. Our implementation of this model will be validated against the Stanford University multiphase flow database. The transient portion of our model is based on a transmission line modal model. The model parameters are realized by developing equivalent fluid properties that are a function of the steady-state pressure gradient and liquid holdup identified through the mechanistic model. The model ability to reproduce the dynamics of multiphase flow in pipes is evaluated upon comparison to olga, a commercial multiphase flow dynamic code, using different gas volume fractions (GVF). The two models show a good agreement of the steady-state response and the frequency of oscillation indicating a similar estimation of the transmission line natural frequency. However, they present a discrepancy in the overshoot values and the settling time due to a difference in the calculated damping ratio. The utility of the developed low-dimensional model is the reduced computational burden of estimating transient multiphase flow in transmission lines, thereby enabling real-time estimation of pressure and flow rate.

References

References
1.
Owen
,
R. G.
,
Hunt
,
J. C. R.
, and
Collier
,
J. G.
,
1976
, “
Magnetohydrodynamic Pressure Drop in Ducted Two-Phase Flows
,”
Int. J. Multiphase Flow
,
3
(
1
), pp.
23
33
.
2.
Ginoux
,
J. J.
,
1978
,
Two-Phase Flows and Heat Transfer With Application to Nuclear Reactor Design Problems
,
Hemisphere Publishing
,
Washington, DC
.
3.
Bansal
,
P. K.
, and
Rupasinghe
,
A. S.
,
1998
, “
A Homogeneous Model for Adiabatic Capillary Tubes
,”
Appl. Therm. Eng.
,
18
(
3–4
), pp.
207
219
.
4.
Faghri
,
A.
, and
Zhang
,
Y.
,
2006
,
Transport Phenomena in Multiphase Systems
,
Elsevier
,
Burlington, MA
.
5.
Awad
,
M. M.
, and
Muzychka
,
Y. S.
,
2008
, “
Effective Property Models for Homogeneous Two-Phase Flows
,”
Exp. Therm. Fluid Sci.
,
33
(
1
), pp.
106
113
.
6.
Martinelli
,
R. C.
, and
Nelson
,
D. B.
,
1948
, “
Prediction of Pressure Drop During Forced Circulation Boiling of Water
,”
Trans. ASME
,
7
(
7
), pp.
695
702
.
7.
Lockhart
,
R. W.
, and
Martinelli
,
R. C.
,
1949
, “
Proposed Correlation Data for Isothermal Two-Phase Two-Component Flow in Pipes
,”
Chem. Eng. Prog.
,
45
(
1
), pp.
39
48
.
8.
Gopalakrishman
,
A.
, and
Schrock
,
V. E.
,
1964
,
Void Fraction From the Energy Equation
,
Heat Transfer and Fluid Mechanics Institute, Stanford University Press
,
Palo Alto, CA
.
9.
Premoli
,
A.
,
Francesco
,
D.
, and
Prima
,
A.
,
1970
, “
An Empirical Correlation for Evaluating Two-Phase Mixture Density Under Adiabatic Conditions
,”
European Two-Phase Flow Group Meeting, Paper B9, Milan, Italy.
.
10.
Friedel
,
L.
,
1979
, “
Improved Friction Pressure Drop Correlations for Horizontal and Vertical Two-Phase Flow
,”
3R Int.
,
18
(
7
), pp.
485
491
.
11.
Levy
,
S.
,
1980
, “
Steam Slip-Theoretical Prediction From Momentum Model
,”
ASME J. Heat Transfer
,
82
(
2
), pp.
113
124
.
12.
Richter
,
H. J.
,
1983
, “
Separated Two-Phase Flow Model: Application to Critical Two-Phase Flow
,”
Int. J. Multiphase Flow
,
9
(
5
), pp.
511
530
.
13.
Richter
,
H. J.
, and
Minas
,
S. E.
,
1979
, “
Separated Flow Model for Critical Two-Phase Flow
,”
Nonequilibrium Interfacial Transport Processes
,
ASME
,
New York
.
14.
Wongwises
,
S.
,
Chan
,
P.
,
Luesuwanatat
,
N.
, and
Purattanarak
,
T.
,
2000
, “
Two-Phase Separated Flow Model of Refrigerants Flowing Through Capillary Tubes
,”
Int. Commun. Heat Mass Transfer
,
27
(
3
), pp.
343
356
.
15.
Ishii
,
M.
,
1975
, “
Thermo-Fluid Dynamic Theory of Two-Phase Flow
,” NASA STI/Recon Technical Report A, 75, pp. 29657.
16.
Saito
,
T.
,
Hughes
,
E. D.
, and
Carbon
,
M. W.
,
1978
, “
Multi-Fluid Modeling of Annular Two-Phase Flow
,”
Nucl. Eng. Des.
,
50
(
2
), pp.
225
271
.
17.
Bouré
,
J. A.
, and
Delhaye
,
J. M.
,
1986
,
General Equations and Two-Phase Flow Modeling
,
Hemisphere-McGraw-Hill
,
New York
.
18.
Bouré
,
J. A.
,
1986
, “
Two-Phase Flow Models: The Closure Issue
,”
European Two-Phase Flow Group Meeting
, Munich.
19.
Stevanovic
,
V.
,
Prica
,
S.
, and
Maslovaric
,
B.
,
2007
, “
Multi-Fluid Model Predictions of Gas-Liquid Two-Phase Flows in Vertical Tubes
,”
FME Trans.
,
35
(
4
), pp.
173
181
.
20.
Zuber
,
N.
, and
Findlay
,
J. A.
,
1965
, “
Average Volumetric Concentration in Two-Phase Flow Systems
,”
ASME J. Heat Transfer
,
87
(
4
), pp.
453
468
.
21.
Ishii
,
M.
,
1977
, “
One-Dimensional Drift-Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes
,” Report No. ANL-77-47.
22.
Wallis
,
G. B.
,
1979
,
One-Dimensional Two-Phase Flow
,
2nd ed.
,
McGraw-Hill
,
New York
.
23.
Chexal
,
B.
, and
Lellouche
,
G.
,
1992
, “
Void Fraction Correlation for Generalized Applications
,”
Prog. Nucl. Energy
,
27
(
4
), pp.
255
295
.
24.
Coddington
,
P.
, and
Macian
,
R.
,
2002
, “
A Study of the Performance of Void Fraction Correlations Used in the Context of Drift-Flux Two-Phase Flow Models
,”
Nucl. Eng. Des.
,
215
(
3
), pp.
199
216
.
25.
Choi
,
J.
,
Pereyra
,
E.
,
Sarica
,
C.
,
Park
,
C.
, and
Kang
,
J. M.
,
2012
, “
An Efficient Drift-Flux Closure Relationship to Estimate Liquid Holdups of Gas-Liquid Two-Phase Flow in Pipes
,”
Energies
,
5
(
12
), pp.
5294
5306
.
26.
Taitel
,
Y.
, and
Dukler
,
A. E.
,
1976
, “
A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow
,”
AIChe J.
,
22
(
1
), pp.
22
24
.
27.
Barnea
,
D.
,
1987
, “
A Unified Model for Predicting Flow Pattern Transitions for the Whole Range of Pipe Inclinations
,”
Int. J. Multiphase Flow
,
13
(
1
), pp.
1
12
.
28.
Xiao
,
J. J.
,
Shoham
,
O.
, and
Brill
,
J. P.
,
1990
, “
A Comprehensive Mechanistic Model for Two-Phase Flow in Pipelines
,”
65th SPE Annual Technical Conference and Exhibition
, SPE Paper No. 20631.
29.
Ansari
,
A. M.
,
Sylvester
,
A. D.
,
Sarica
,
C.
,
Shoham
,
O.
, and
Brill
,
J. P.
, “
A Comprehensive Mechanistic Model for Upward Two-Phase Flow in Wellbores
,”
SPE Prod. Facil.
,
9
(
2
), pp.
143
152
.
30.
Petalas
,
N.
, and
Aziz
,
K.
,
1996
, “
Development and Testing of a New Mechanistic Model for Multiphase Flow in Pipes
,”' Proceedings of the ASME Fluids Engineering Division Summer Meeting, Part 1(of 2), San Diego, CA, pp.
153
159
.
31.
Petalas
,
N.
, and
Aziz
,
K.
,
2000
, “
A Mechanistic Model for Multiphase Flow in Pipes
,”
J. Can. Pet. Technol.
,
39
(
6
), pp.
43
55
.
32.
Moore
,
K. V.
, and
Rettig
,
W. H.
,
1973
, “
RELAP4—A Computer Program for Transient Thermal-Hydraulic Analysis
,” Aerojet Nuclear Company, National Reactor Testing Station, Report No. ANCR–1127.
33.
Fischer
,
S. R.
,
1975
, “
Use of Vertical Slip Flow and Flooding Models in LOCA Analysis
,” Aerojet Nuclear Co., Idaho Falls, ID,
Report No. CONF-750607–30
.
34.
Lyczkowski
,
R. W.
,
Gidaspow
,
D.
,
Solbrig
,
C. W.
, and
Hughes
,
E. D.
,
1975
, “
Characteristics and Stability Analyses of Transient One-Dimensional Two-Phase Flow Equations and Their Finite Difference Equations
,” ASME Paper No. Paper No. CONF-751106–13.
35.
Solbrig
,
C. W.
, and
Hughes
,
E. D.
,
1975
, “
Governing Equations for a Seriated Continuum: An Unequal Velocity Model for Two-Phase Flow
,” Aerojet Nuclear Company, Report No. ANCR–1193.
36.
Cunliffe
,
R. S.
,
1978
, “
Prediction of Condensate Flow Rates in Large Diameter High Pressure Wet Gas Pipelines
,”
APEA J.
,
18
, pp.
171
177
.
37.
Modisette
,
L.
, and
Whaley
,
R. S.
,
1983
, “
Transient Two-Phase Flow
,”
PSIG Annual Meeting
, Detroit, MI, pp.
27
28
.
38.
Bendiksen
,
K.
,
Malnes
,
D.
,
Moe
,
R.
, and
Nuland
,
S.
,
1991
, “
The Dynamic Two-Fluid Model OLGA: Theory and Application
,”
SPE Prod. Eng.
,
6
(
2
), pp.
171
180
.
39.
Bendiksen
,
K.
,
Brandt
,
I.
,
Jacobsen
,
K. A.
, and
Pauchon
,
C.
,
1987
, “
Dynamic Simulation of Multiphase Transportation Systems
,” Multiphase Technology and Consequences for Field Development Forum, Stavanger, Norway.
40.
Bendiksen
,
K. H.
,
Brandt
,
I.
,
Fuchs
,
P.
,
Linga
,
H.
,
Malnes
,
D.
, and
Moe
,
R.
,
1986
, “
Two-Phase Flow Research at SINTEF and IFE: Some Experimental Results and a Demonstration of the Dynamic Two- Phase Flow Simulator OLGA
,”
Offshore Northern Seas Conference
, Stavanger.
41.
Black
,
P. S.
,
Daniels
,
L. C.
,
Hoyle
,
N. C.
, and
Jepson
,
W. P.
,
1990
, “
Studying Transient Multiphase Flow Using the Pipeline Analysis Code (PLAC)
,”
ASME J. Energy Resour. Technol.
,
112
(
1
), pp.
25
29
.
42.
Pauchon
,
C.
,
Dhulesia
,
H.
,
Binh-Cirlot
,
G.
, and
Fabre
,
J.
,
1994
, “
TACITE: A Transient Tool for Multiphase Pipeline and Well Simulation
,”
SPE Annual Technical Conference
, New Orleans, LA.
43.
Pauchon
,
C.
,
Dhulesia
,
H.
,
Lopez
,
D.
, and
Fabre
,
J.
,
1993
, “
TACITE: A Comprehensive Mechanistic Model for Two-Phase Flow
,”
The 6th International Conference on Multiphase Production
, Cannes, France.
44.
Taitel
,
Y.
,
Ovadia
,
S.
, and
Brill
,
J. P.
,
1989
, “
Simplified Transient Solution and Simulation of Two-Phase Flow in Pipelines
,”
Chem. Eng. Sci.
,
44
(
6
), pp.
353
359
.
45.
Brown
,
F. T.
,
1972
, “
The Transient Response of Fluid Lines
,”
ASME J. Basic Eng.
,
84
(
4
), pp.
547
553
.
46.
Huang
,
Y. W.
,
2012
, “
Lumped Parameter Modeling of Fluid Line Dynamics With Turbulent Flow Conditions
,” Ph.D. thesis, Mechanical Engineering, University of Texas, Arlington, TX.
47.
Bratland
,
O.
,
2010
,
Pipe Flow 2: Multi-Phase Flow Assurance
, Ove Bratland Flow Assurance Consulting, Chonburi, Thailand.
48.
Colebrook
,
C. F.
,
1939
, “
Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between Smooth and Rough Pipe Laws
,”
J. Inst. Civ. Eng.
,
11
(
4
), pp.
133
156
.
49.
Moody
,
L. F.
,
1944
, “
Friction Factors for Pipe Flow
,”
Trans. ASME
,
66
(
8
), pp.
671
684
.
50.
Goudar
,
C. T.
, and
Sonnad
,
J. R.
,
2008
, “
Comparison of the Iterative Approximations of the Colebrook-White Equation
,”
Hydrocarbon Processing
,
87
(
8
).
51.
Young
,
T.
,
1808
, “
Propagation of Impulse Through an Elastic Tube
,”
Philos. Trans. R. Soc. London
,
98
, pp.
164
186
.
52.
Wood
,
F. M.
,
1937
, “
The Application of Heaviside's Operational Calculus to the Solution of Problems in Water Hammer
,”
Trans. ASME
,
59
(
8
), pp.
707
713
.
53.
Iberall
,
A. S.
,
1950
, “
Attenuation of Oscillatory Pressures in Instrument Lines
,”
J. Res. Natl. Bur. Stand.
,
45
, pp.
85
108
.
54.
Rohmann
,
C. P.
, and
Grogan
,
E. C.
,
1957
, “
On the Dynamics of Pneumatic Transmission Lines
,”
Trans. ASME
,
79
(
4
), pp.
853
867
.
55.
Nichols
,
N. B.
,
1961
, “
The Linear Properties of Pneumatic Transmission Lines
,”
Joint Automatic Control Conference
, pp.
28
30
.
56.
Karam
,
J. T.
, and
Franke
,
M. E.
,
1967
, “
The Frequency Response of Pneumatic Lines
,”
J. Basic Eng.
,
89
(
2
), pp.
371
378
.
57.
Franke
,
M. E.
,
Malanowski
,
A. J.
, and
Martin
,
P. S.
,
1972
, “
Effects of Temperature, End Conditions, Flow and Branching on the Frequency Response of Pneumatic Lines
,”
ASME J. Dyn. Syst., Meas., Control
,
94
(
1
), pp.
15
20
.
58.
Ravindran
,
V. K.
, and
Manning
,
J. R.
,
1973
, “
The Frequency Response of Pneumatic Lines With Branching
,”
ASME J. Dyn. Syst., Meas., Control
,
95
(
2
), pp.
194
196
.
59.
Oldenburger
,
R.
, and
Goodson
,
R. E.
,
1964
, “
Simplification of Hydraulic Line Dynamics by Use of Infinite Products
,”
ASME J. Basic Eng.
,
86
(
1
), pp.
1
8
.
60.
Hsue
,
C. Y.
, and
Hullender
,
D. A.
,
1983
, “
Modal Approximations for the Fluid Dynamics of Hydraulic and Pneumatic Transmission Lines
,”
Fluid Transmission Line Dynamics
,
ASME
,
New York
, pp.
51
77
.
61.
Johnston
,
D. N.
,
2011
, “
Numerical Modelling of Unsteady Turbulent Flow in Tubes, Including the Effects of Roughness and Large Changes in Reynolds Number
,”
Proc. Inst. Mech. Eng., Part C
,
225
(
8
), pp.
1874
1885
.
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