We report a detailed investigation on the measurement and prediction of pressure gradient characteristics of moderately viscous lubricating oil-water flow through a horizontal pipe of 0.025 m internal diameter. Experiments are carried out over a wide range of phase velocities of both oil (USO = 0.015–1.25 m/s) and water (USW = 0.1–1.1 m/s). Experimental pressure gradients yield significant errors when fitted to the existing correlations, which are largely used for gas-liquid flow. To predict pressure gradient characteristics for liquid-liquid flow, the existing correlations need to be modified. We propose two correlations, based on the Lockhart–Martinelli's approach (by modifying the correlation between the Lockhart–Martinelli parameter and a two-phase multiplier suitable for the present system) and dimensionless analysis, following the Buckingham's Pi-theorem. We observe significant improvement in the prediction of pressure gradient. The correlation based on the dimensionless analysis predicts better with an average absolute error of 17.9%, in comparison with the modified Lockhart–Martinelli correlation, which yields an average error of 22%, covering all the flow patterns. The present analysis shows better prediction as compared to two-fluid model Zhang et al. (2012, “Modeling High-Viscosity Oil/Water Concurrent Flow in Horizontal and Vertical Pipes,” SPE J., 17(1), pp. 243–250) and Al-Wahaibi (2012, “Pressure Gradient Correlation for Oil-Water Separated Flow in Horizontal Pipes,” Exp. Therm. Fluid Sci., 42, pp. 196–203) work.
References
1.
Brauner
, N.
, 2001
, “The Prediction of Dispersed Flows Boundaries in Liquid-Liquid and Gas-Liquid Systems
,” Int. J. Multiphase Flow
, 27
(5
), pp. 885
–910
.10.1016/S0301-9322(00)00056-22.
Brauner
, N.
, and Maron
, M. D.
, 1992
, “Flow Pattern Transitions in Two-Phase Liquid-Liquid Flow in Horizontal Tubes
,” Int. J. Multiphase Flow
, 18
(1
), pp. 123
–140
.10.1016/0301-9322(92)90010-E3.
Russell
, T. W. F.
, Hodgson
, G. W.
, and Govier
G. W.
, 1959
, “Horizontal Pipeline Flow of Mixtures of Oil and Water
,” Can. J. Chem. Eng.
, 37
(1
), pp. 9
–17
.10.1002/cjce.54503701044.
Charles
, M.
, Govier
, G. W.
, and Hodgson
G. W.
, 1961
, “The Horizontal Flow of Equal Density Oil-Water Mixtures
,” Can. J. Chem. Eng.
, 39
(1
), pp. 27
–36
.10.1002/cjce.54503901065.
Trallero
, J. L.
, Cem
, S.
, and Brill
J. P.
, 1997
, “A Study of Oil/Water Flow Patterns in Pipes
,” SPE Production & Facilities
, 12
(3
), pp. 165–172
.10.2118/36609-PA6.
Beratta
, A.
, Ferrari
, P.
, Galbiati
, L.
, and Andreini
, P. A.
, 1997
, “Horizontal Oil-Water Flow in Small Diameter Tubes Pressure Drop
,” Int. Comm. Heat Mass Transf.
, 24
(2
), pp. 231
–239
.10.1016/S0735-1933(97)00009-27.
Angeli
, P.
, and Hewitt
, G. F.
, 1998
, “Pressure Gradient in Horizontal Liquid-Liquid Flows
,” Int. J. Multiphase Flow
, 24
(7
), pp. 1183
–1203
.10.1016/S0301-9322(98)00006-88.
Chakrabarti
, D. P.
, Das
, G.
, and Ray
, S.
, 2005
, “Pressure Drop in Liquid-Liquid Two Phase Horizontal Flow: Experiment and Prediction
,” Chem. Eng. Tech.
, 28
(9
), pp. 1003
–1009
.10.1002/ceat.2005001439.
Raj
, T. S.
, Chakrabarti
, D. P.
, and Das
, G.
, 2005
, “Liquid-Liquid Stratified Flow Through Horizontal Conduits
,” Chem. Eng. Tech.
, 28
(8
), pp. 899
–907
.10.1002/ceat.20050006710.
Sotgia
, G.
, Tartarini
, P.
, and Stalio
, E.
, 2008
, “Experimental Analysis of Flow Regimes and Pressure Drop Reduction in Oil–Water Mixtures
,” Int. J. Multiphase Flow
, 34
(12
), pp. 1161
–1174
.10.1016/j.ijmultiphaseflow.2008.06.00111.
Grassi
, B.
, Strazza
, D.
, and Poesio
, P.
, 2008
, “Experimental Validation of Theoretical Models in Two-Phase High-Viscosity Ratio Liquid–Liquid Flows in Horizontal and Slightly Inclined Pipes
,” Int. J. Multiphase Flow
, 34
(10
), pp. 950
–965
.10.1016/j.ijmultiphaseflow.2008.03.00612.
Poesio
, P.
, Strazza
, D.
, and Sotgia
, G.
, 2009
, “Very-Viscous-Oil/Water/Air Flow Through Horizontal Pipes: Pressure Drop Measurement and Prediction
,” Chem. Eng. Sci.
, 64
(6
), pp. 1136
–1142
.10.1016/j.ces.2008.10.06113.
Yusuf
, N.
, Al-wahaibi
, Y.
, Al-wahaibi
, T.
, Al-Ajmi
, A.
, Olawale
, A. S.
, and Mohammed
, I. A.
, 2012
, “Effect of Oil Viscosity on the Flow Structure and Pressure Gradient in Horizontal Oil–Water Flow
,” Chem. Eng. Res. Des.
, 90
(8
), pp. 1019
–1030
.10.1016/j.cherd.2011.11.01314.
Strazza
, D.
, Grassi
, B.
, Demori
, M.
, and Poesio
, P.
, 2011
, “Core-Annular Flow in Horizontal and Slightly Inclined Pipes: Existence, Pressure Drops, and Hold-Up
,” Chem. Eng. Sci.
, 66
(12
), pp. 2853
–2863
.10.1016/j.ces.2011.03.05315.
Angeli
, P.
, and Hewitt
, G. F.
, 2000
, “Flow Structure in Horizontal Oil-Water Flow
,” Int. J. Multiphase Flow
, 26
(7
), pp. 1117
–1140
.10.1016/S0301-9322(99)00081-616.
Ooms
, G.
, Segal
, A.
, and Van Der Wees
, A. J.
, 1984
, “A Theoretical Model for Core-Annular Flow of a Very Viscous Oil Core and a Water Annulus Through a Horizontal Pipe
,” Int. J. Multiphase Flow
, 10
(1
), pp. 41
–60
.10.1016/0301-9322(83)90059-917.
Brauner
, N.
, and Maron
, D. M.
, 1989
, “Two-Phase Liquid-Liquid Stratified Flow
,” Phys. Chem. Hydrodyn.
, 11
(4
), pp. 487
–506
.18.
Maron
, D. M.
, Brauner
, N.
, and Rovinsky
, J.
, 1995
, “Analytical Prediction of the Interface Curvature and Its Effects on the Stratified Two-Phase Characteristics
,” Proceedings of the International Symposium Two-Phase Flow Modeling and Experimentation
, 1, pp. 163
–170
.19.
Brauner
, N.
, Maron
, D. M.
, and Rovinsky
, J.
, 1998
, “A Two Fluid Model for Stratified Flows With Curved Interfaces
,” Int. J. Multiphase Flow
, 24
(6
), pp. 975
–1004
.10.1016/S0301-9322(98)00005-620.
Yipping
, L.
, Hua
, Z.
, Shuhua
, W.
, and Jing
, W.
, 2008
, “Prediction of Pressure Gradient and Holdup in Small Eötvös Number Liquid-Liquid Segregated Flow
,” Chin. J. Chem. Eng.
, 16
(2
), pp. 184
–191
.10.1016/S1004-9541(08)60060-921.
Ghosh
, S.
, Das
, G.
, and Das
, P. K.
, 2010
, “Simulation of Core Annular Down Flow Through CFD a Comprehensive Study
,” Chem. Eng. Prog.
, 49
(11
), pp. 1222
–1228
.10.1016/j.cep.2010.09.00722.
Wallis
, G. B.
, 1969
, One Dimensional Two-Phase Flow
, McGraw-Hill
, New York
, Chap. 2 and Chap. 4.23.
Zuber
, N.
, and Findlay
, J. A.
, 1965
, “Average Volumetric Concentration in Two-Phase Flow System
,” ASME J. Heat Transfer
, 87
, pp. 453
–468
.10.1115/1.368913724.
Brauner
, N.
, 1991
, “Two Phase Liquid-Liquid Annular Flow
,” Int. J. Multiphase Flow
, 17
(1
), pp. 59
–76
.10.1016/0301-9322(91)90070-J25.
Arirachakaran
, S.
, Oglesby
, K. D.
, Malinowsky
, M. S.
, Shoham
, O.
, and Brill
, J. P.
,1989
, “An Analysis of Oil/Water Flow Phenomena in Horizontal Pipes
,” SPE Production Operations Symposium
, Oklahoma City, OK, March 13–14, pp. 155
–168
.26.
Malhotra
, A.
, 1995
, “Study of Two and Three-Phase Flows in Large Diameter Horizontal Pipelines
,” M.S. thesis, Ohio University, Athens, OH, 45701, U.S.A.27.
Rodriguez
, O. M. H.
, and Oliemans
, R. V.
2006
, “Experimental Study on Oil–Water Flow in Horizontal and Slightly Inclined Pipes
,” Int. J. Multiphase Flow
, 32
(3
), pp. 323
–343
.10.1016/j.ijmultiphaseflow.2005.11.00128.
Ghosh.
S.
, Das
, G.
, and Das
, P. K.
, 2011
, “Pressure Drop Analysis for Liquid-Liquid Downflow Through Vertical Pipe
,” ASME J. Fluids Eng.
, 133
(1
), pp. 1
–10
.10.1115/1.400335429.
Brauner
, N.
, 1990
, “On the Relation Between Two-Phase Flow Under Reduced Gravity and Earth Experiment
,” Int. Comm. Heat Mass Transf.
, 17
(3
), pp. 271
–282
.10.1016/0735-1933(90)90092-X30.
Bannwart
, A. C.
, 2001
, “Modeling Aspects of Oil-Water Core-Annular Flows
,” J. Petrol. Sci. Eng.
, 32
(1
), pp. 127
–143
.10.1016/S0920-4105(01)00155-331.
Rodriguez
, O. M. H.
, and Baldani
, L. S.
, 2012
, “Prediction of Pressure Gradient and Holdup in Wavy Stratified Liquid–Liquid Inclined Pipe Flow
,” J. Petrol. Sci. Eng.
, 96–97
, pp. 140
–151
.10.1016/j.petrol.2012.09.00732.
Zhang
, H.-Q.
, Vuong
, D. H.
, and Sarica
, C.
, 2012
, “Modeling High-Viscosity Oil/Water Concurrent Flow in Horizontal and Vertical Pipes
,” SPE J.
, 17
, pp. 243
–250
.10.2118/135099-PA33.
Lockhart
, R. W.
, and Martinelli
, R. C.
, 1949
, “Proposed Correlation of Data for Isothermal Two-Phase Two-Component in Pipes
,” Chem. Eng. Prog.
, 45
(1
), pp. 39
–48
.34.
Chisholm
, D.
, 1967
. “A Lockhart Martinelli Basis for the Correlation for Two-Phase Flow
,” Int. J. Heat Mass Transf.
, 10
(18
), pp. 1767
–1778
.10.1016/0017-9310(67)90047-635.
Chisholm
, D.
, 1973
, “Pressure Gradient Due to Friction During the Flow of Evaporating Two Phase Mixtures in Smooth Tubes and Channels
,” Int. J. Heat Mass Transf.
, 16
(29
), pp. 347
–358
.10.1016/0017-9310(73)90063-X36.
Chawla
, J. M.
, 1967
, “Warmeubergang and Druckfall in Waagerechten Rohren Bei Der Stromung Von Verdampfenden Kaltemitteln
,” VDI-Forschungsheft 523, VDI-Verlag, Dusseldorf, Germany, Chapter Lg1-Lg2.37.
Friedel
, L.
, 1980
, “Pressure Drop During Gas/Vapor –Liquid Flow in Pipes
,” Int. Chem. Eng.
, 20
(3
), pp. 352
–367
.38.
Muller-Steinhagen
, H.
, and Heck
, H.
, 1986
, “A Simple Friction Pressure Drop Correlation for Two Phase Flow in Pipes
,” Chem. Eng. Prog.
, 20
(1
), pp. 291
–308
.10.1016/0255-2701(86)80008-339.
Cicchitti
, A.
, Lombardi
, C.
, Silvestri
, M.
, Soldaini
, G.
, and Zavattarelli
, R.
, 1960
, “Two-Phase Cooling Experiments Pressure Drop, Heat Transfer and Burnout Measurements
,” Energ. Nucl.
, 7
(6
), pp. 407
–425
.40.
Bankoff
, S. G.
, 1960
, “A Variable Density Single-Fluid Model Two-Phase Flow With Particular Reference to Steam-Water
,” ASME J. Heat Transfer
, 11
, pp. 265
–272
.10.1115/1.367993041.
Saisoran
, S.
, and Wongwises
, S.
, 2008
, “An Inspection of Viscosity Model for Homogeneous Two-Phase Flow Pressure Drop Prediction in s Horizontal Circular Micro-Channel
,” Int. Comm. Heat Mass Transf.
, 35
(7
), pp. 833
–838
.10.1016/j.icheatmasstransfer.2008.03.01442.
Sun
, L.
, and Mishima
, K.
, 2009
, “Evaluation Analysis of Prediction Methods for Two-Phase Flow Pressure Drop in Mini-Channels
,” Int. J. Multiphase Flow
, 35
(1
), pp. 47
–54
.10.1016/j.ijmultiphaseflow.2008.08.00343.
Muzychka
, Y. S.
, and Awad
, M. M.
, 2010
, “Asymptotic Generalizations of the Lockhart–Martinelli Method for Two Phase Flows
,” ASME J. Fluids Eng.
, 132
(3
), pp. 1
–12
.10.1115/1.400115744.
Samani
, A. R.
, and Borghei
, S. M.
, 2010
, “Pressure Loss in a Horizontal Two-Phase Slug Flow
,” ASME J. Fluids Eng.
, 132
(7
), pp. 1
–8
.10.1115/1.400196945.
Theissing
, P.
, 1980
, “A Generally Valid Method for Calculating Frictional Pressure Drop in Multiphase Flow
,” Chem. Ing. Tech.
, 52
, pp. 344
–345
(in German).10.1002/cite.33052041446.
Stapelberg
, H. H.
, and Mewes
, D.
, 1994
, “The Pressure Loss and Slug Frequency of Liquid-Liquid-Gas Slug Flow in Horizontal Pipes
,” Int. J. Multiphase Flow
, 20
, pp. 285
–303
.10.1016/0301-9322(94)90083-347.
Al-Wahaibi
, T.
, 2012
, “Pressure Gradient Correlation for Oil-Water Separated Flow in Horizontal Pipes
,” Exp. Therm. Fluid Sci.
, 42
, pp. 196
–203
.10.1016/j.expthermflusci.2012.04.02148.
Coleman
, H. W.
, and Steele
, W. G.
, 1981
, Experimentation and Uncertainty Analysis for Engineers
, Second edition, John Wiley & Sons
, New York
, pp. 102
–104
.49.
Dasari
, A.
, Desamala
, A. B.
, Dasmahapatra
, A. K.
, and Mandal
, T. K.
, 2013
, “Experimental Studies and PNN Prediction on Flow Pattern of Viscous Oil-Water Flow Through Circular Horizontal Pipe
,” Ind. Eng. Chem. Res.
, 52
, pp. 7975
–7985
.10.1021/ie301430m50.
Valle
, A.
, and Kvandal
, H.
, 1995
, “Pressure Drop and Dispersion Characteristics of Separated Oil/Water Flow
,” Proceedings of the International Symposium Two-Phase Flow Modeling and Experimentation
2, pp. 583
–592
.51.
Al-Yaari
, M.
, Soleimani
, A.
, Abu-Sharkh
, B.
, Al-Mubaiyedh
, U.
, and Al-Sarkhi
, A.
, 2009
, “Effect of Drag Reducing Polymers on Oil–Water Flow in a Horizontal Pipe
,” Int. J. Multiphase Flow
, 35
(6
), pp 516
–524
.10.1016/j.ijmultiphaseflow.2009.02.01752.
Ullmann
, A.
, and Brauner
, N.
, 2006
, “Closure Relations for Two-Fluid Models for Two-Phase Stratified Smooth and Stratified Wavy Flows
,” Int. J. Multiphase Flow
, 32
(1
), pp. 82
–105
.10.1016/j.ijmultiphaseflow.2005.08.005Copyright © 2014 by ASME
You do not currently have access to this content.
