There is an increasing interest in applying three-dimensional computational fluid dynamics (CFD) for multiphase flow transport in pipelines, e.g., in the oil and gas industry. In this study, the volume of fluid (VOF) multiphase model in a commercial CFD code was used to benchmark the capabilities. Two basic flow structures, namely, the Benjamin bubble and the Taylor bubble, are considered. These two structures are closely related to the slug flow regime, which is a common flow pattern encountered in multiphase transport pipelines. After nondimensionalization, the scaled bubble velocity (Froude number) is only dependent on the Reynolds number and on the Eötvös number, which represent the effect of viscosity and surface tension, respectively. Simulations were made for a range of Reynolds numbers and Eötvös numbers (including the limits of vanishing viscosity and surface tension), and the results were compared with the existing experiments and analytical expressions. Overall, there is very good agreement. An exception is the simulation for the 2D Benjamin bubble at a low Eötvös number (i.e., large surface tension effect) which deviates from the experiments, even at a refined numerical grid.

References

References
1.
Bendiksen
,
K.
,
Malnes
,
D.
,
Moe
,
R.
, and
Nuland
,
S.
, 1991, “
The Dynamic Two-Fluid Model OLGA: Theory and Application
,” SPE Paper No. 19451, pp.
171
180
.
2.
De Schepper
,
S.
,
Heynderickx
,
G.
, and
Marin
,
G.
, 2008, “
CFD Modeling of All Gas-Liquid and Vapor-Liquid Flow Regimes Predicted by the Baker Chart
,”
Chem. Eng. J.
,
138
, pp.
349
357
.
3.
Benjamin
,
T.
, 1968, “
Gravity Currents and Related Phenomena
,”
J. Fluid Mech.
,
31
, pp.
209
248
.
4.
Hager
,
W.
, 1999, “
Cavity Outflow From a Nearly Horizontal Pipe
,”
Int. J. Multiphase Flow
,
25
, pp.
349
364
.
5.
Zukoski
,
E.
, 1966, “
Influence of Viscosity, Surface Tension, and Inclination Angle on Motion of Long Bubbles in Closed Tubes
,”
J. Fluid Mech.
,
25
, pp.
821
837
.
6.
Gardner
,
G.
and
Crow
,
I.
, 1970, “
The Motion of Large Bubbles in Horizontal Channels
,”
J. Fluid Mech.
,
43
, pp.
247
255
.
7.
Clanet
,
C.
,
Heraud
,
P.
, and
Searby
,
G.
, 2004, “
On the Motion of Bubbles in Vertical Tubes of Arbitrary Cross Sections: Some Complements to the Dumitrescu-Taylor Problem
,”
J. Fluid Mech.
,
519
, pp.
359
376
.
8.
Davies
,
R.
and
Taylor
,
S. G.
, 1950, “
The Mechanics of Large Bubbles Rising Through Extended Liquids and Through Liquids in Tubes
,”
Proc. R. Soc. London, Ser. A
,
200
, pp.
375
390
.
9.
Dumitrescu
,
D.
, 1943, “
Strömung an einer Luftblase im senkrechten Rohr
,”
Z. Angew. Math. Mech.
,
23
, pp.
139
149
.
10.
Bendiksen
,
K. H.
, 1985, “
On the Motion of Long Bubbles in Vertical Tubes
,”
Int. J. Multiphase Flow
,
11
, pp.
797
812
.
11.
White
,
E. and Beardmore, R.
, 1962, “
The Velocity of Single Cylindrical Air Bubbles Through Liquids Contained in Vertical Tubes
,”
Chem. Eng. Sci.
,
17
, pp.
351
361
.
12.
Nicklin
,
D.
,
Wilkes
,
J.
, and
Davidson
,
J.
, 1962, “
Two-Phase Flow in Vertical Tubes
,”
Trans. Inst. Chem. Eng.
,
40
, pp.
61
68
. Available at http://archive.icheme.org/cgi-bin/somsid.cgi?session=443875E&page=40ap0061&type=framedpdf
13.
Versteeg
,
H.
, and
Malalasekera
,
W.
, 2007,
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
,
2nd ed.
,
Pearson Education
,
Harlow, England.
14.
Hirt
,
C.
, and
Nichols
,
B.
, 1981, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
, pp.
201
225
.
15.
Wilkinson
,
D.
, 1982, “
Motion of Air Cavities in Long Horizontal Ducts
,”
J. Fluid Mech.
,
118
, pp.
109
122
.
16.
Bendiksen
,
K. H.
, 1984, “
An Experimental Investigation of the Motion of Long Bubbles in Inclined Tubes
,”
Int. J. Multiphase Flow
,
10
, pp.
467
283
.
17.
Mao
,
Z.
, and
Dukler
,
A. E.
, 1990, “
The Motion of Taylor Bubbles in Vertical Tubes. 1. A Numerical Simulation for the Shape and Rise Velocity of Taylor Bubbles in Stagnant and Flowing Liquid
,”
J. Comput. Phys.
,
91
, pp.
132
160
.
18.
Gokcal
,
B.
, 2008, “
An Experimental and Theoretical Investigation of Slug Flow for High Oil Viscosity in Horizontal Pipes
,” Ph.D. thesis, The Graduate School, The University of Tulsa.
19.
Weber
,
M.
, 1981, “
Drift in Intermittent Two-Phase Flow in Horizontal Pipes
,”
Can. J. Chem. Eng.
,
59
, pp.
398
399
.
20.
Spedding
,
P.
, and
Nguyen
,
V.
, 1978, “
Bubble Rise and Liquid Content in Horizontal and Inclined Tubes
,”
Chem. Eng. Sci.
,
33
, pp.
987
994
.
21.
Weber
,
M. E.
,
Alarie
,
A.
, and
Ryan
,
M. E.
, 1986, “
Velocities of Extended Bubbles in Inclined Tubes
,”
Chem. Eng. Sci.
,
41
, pp.
2235
2240
.
22.
Fabre
,
J. and Line, A.
, 1992, “
Modeling of Two-Phase Slug Flow
,”
Annu. Rev. Fluid Mech.
,
24
, pp.
21
46
.
23.
Wallis
,
G.
, 1969,
One Dimensional Two-phase Flow
,
McGraw-Hill
,
New York
.
24.
Nogueira
,
S.
,
Riethmuler
,
M. L.
,
Campos
,
J. B. L. M.
, and
Pinto
,
A. M. F. R.
, 2006, “
Flow in the Nose Region and Annular Film Around a Taylor Bubble Rising Through Vertical Columns of Stagnant and Flowing Newtonian Liquids
,”
Chem. Eng. Sci.
,
61
, pp.
845
857
.
25.
Johansen
,
M.
, 2006, “
An Experimental Study of the Bubble Propagation Velocity in 3-Phase Slug Flow
,” Ph.D. thesis, NTNU, Norway.
26.
Bugg
,
J. D.
, and
Saad
,
G. A.
, 2002, “
The Velocity Field Around a Taylor Bubble Rising in a Stagnant Viscous Fluid: Numerical and Experimental Results
,”
Int. J. Multiphase Flow
,
28
, pp.
791
803
.
27.
Lu
,
X.
, and
Prosperetti
,
A.
, 2009, “
A Numerical Study of Taylor Bubbles
,”
Ind. Eng. Chem. Res.
,
48
, pp.
242
252
.
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