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

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)00056-2
2.
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-E
3.
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.5450370104
4.
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.5450390106
5.
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-PA
6.
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)00009-2
7.
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)00006-8
8.
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.200500143
9.
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.200500067
10.
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.2008.06.001
11.
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.2008.03.006
12.
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.2008.10.061
13.
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.2011.11.013
14.
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.2011.03.053
15.
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)00081-6
16.
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)90059-9
17.
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)00005-6
20.
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)60060-9
21.
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.2010.09.007
22.
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
.10.1115/1.3689137
24.
Brauner
,
N.
,
1991
, “
Two Phase Liquid-Liquid Annular Flow
,”
Int. J. Multiphase Flow
,
17
(
1
), pp.
59
76
.10.1016/0301-9322(91)90070-J
25.
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.2005.11.001
28.
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
.10.1115/1.4003354
29.
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-X
30.
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)00155-3
31.
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.2012.09.007
32.
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-PA
33.
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)90047-6
35.
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-X
36.
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)80008-3
39.
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
.10.1115/1.3679930
41.
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.2008.03.014
42.
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.2008.08.003
43.
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
.10.1115/1.4001157
44.
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
.10.1115/1.4001969
45.
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.330520414
46.
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)90083-3
47.
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.2012.04.021
48.
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/ie301430m
50.
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.2009.02.017
52.
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.2005.08.005
You do not currently have access to this content.