Modeling multiphase flow in porous structures remains a challenge due to the complexity of handling multiple interfaces. This paper presents a one-domain pore-resolved simulation approach for immiscible two-phase flows in porous media, using a monolithic fluid–solid coupling framework to implicitly consider the existence of solid objects, with the fluid–fluid interfaces captured through solving an algebraic volume of fluid equation. Fluid interfacial tension is considered by integrating a continuum surface force, and the wall wettability condition is imposed by modifying the contact angle of the fluid interface at the embedded solid surface. The resulting equations are simple and stable, as there are no empirical models or parameters involved for the interface representation. This approach has been validated through performing a series of test-case simulations, including capillary-dominated flow, capillary rise with gravity, Taylor film formation, and finally two-phase flow in a heterogeneous porous structure. The numerical approach is demonstrated to be well suited for investigating pore-scale two-phase flows in realistic porous media.

1.
R.
Shen
,
X.
Zhang
,
Y.
Ke
,
W.
Xiong
,
H.
Guo
,
G.
Liu
,
H.
Zhou
, and
H.
Yang
, “
An integrated pore size distribution measurement method of small angle neutron scattering and mercury intrusion capillary pressure
,”
Sci. Rep.
11
,
17458
(
2021
).
2.
Y. B.
Tang
,
M.
Li
,
Y.
Bernabé
, and
J. Z.
Zhao
, “
Viscous fingering and preferential flow paths in heterogeneous porous media
,”
JGR Solid Earth
125
,
e2019JB019306
(
2020
).
3.
X.
Lu
,
E.
Tsotsas
, and
A.
Kharaghani
, “
Insights into evaporation from the surface of capillary porous media gained by discrete pore network simulations
,”
Int. J. Heat Mass Transfer
168
,
120877
(
2021
).
4.
S.
An
,
H.
Erfani
,
O. E.
Godinez-Brizuela
, and
V.
Niasar
, “
Transition from viscous fingering to capillary fingering: Application of GPU-based fully implicit dynamic pore network modeling
,”
Water Resour. Res.
56
,
e2020WR028149
, https://doi.org/10.1029/2020WR028149 (
2020
).
5.
L.
Chen
,
A.
He
,
J.
Zhao
,
Q.
Kang
,
Z.-Y.
Li
,
J.
Carmeliet
,
N.
Shikazono
, and
W.-Q.
Tao
, “
Pore-scale modeling of complex transport phenomena in porous media
,”
Prog. Energy Combust. Sci.
88
,
100968
(
2022
).
6.
G.
Smit
,
G.
Diedericks
, and
J.
Du Plessis
, “
Modelling procedure for prediction of flow through porous materials
,”
WIT Trans. Eng. Sci.
18
,
233
240
(
1970
).
7.
Z.
Ou
,
L.
Guo
,
C.
Chi
,
S.
Zhu
,
C.
Ren
,
H.
Jin
, and
D.
Thévenin
, “
Interface-resolved direct numerical simulations of interphase momentum, heat, and mass transfer in supercritical water gasification of coal
,”
Phys. Fluids
34
,
103319
(
2022
).
8.
Z.
Ou
,
C.
Chi
,
L.
Guo
, and
D.
Thévenin
, “
A directional ghost-cell immersed boundary method for low Mach number reacting flows with interphase heat and mass transfer
,”
J. Comput. Phys.
468
,
111447
(
2022
).
9.
C.
Aricò
,
R.
Helmig
,
D.
Puleo
, and
M.
Schneider
, “
A new numerical mesoscopic scale one-domain approach solver for free fluid/porous medium interaction
,”
Comput. Methods Appl. Mech. Eng.
419
,
116655
(
2024
).
10.
F. J.
Carrillo
,
I. C.
Bourg
, and
C.
Soulaine
, “
Multiphase flow modeling in multiscale porous media: An open-source micro-continuum approach
,”
J. Comput. Phys.: X
8
,
100073
(
2020
).
11.
C.
Soulaine
,
S.
Roman
,
A.
Kovscek
, and
H. A.
Tchelepi
, “
Mineral dissolution and wormholing from a pore-scale perspective
,”
J. Fluid Mech.
827
,
457
483
(
2017
).
12.
K.
Wittig
,
P.
Nikrityuk
, and
A.
Richter
, “
Drag coefficient and Nusselt number for porous particles under laminar flow conditions
,”
Int. J. Heat Mass Transfer
112
,
1005
1016
(
2017
).
13.
S.
Haeri
and
J.
Shrimpton
, “
On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows
,”
Int. J. Multiphase Flow
40
,
38
55
(
2012
).
14.
C.
Chi
,
A.
Abdelsamie
, and
D.
Thévenin
, “
A directional ghost-cell immersed boundary method for incompressible flows
,”
J. Comput. Phys.
404
,
109122
(
2020
).
15.
P.
Singh
,
D.
Joseph
,
T.
Hesla
,
R.
Glowinski
, and
T.-W.
Pan
, “
A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows
,”
J. Non-Newtonian Fluid Mech.
91
,
165
188
(
2000
).
16.
Z.
Ou
,
Q.
Xue
,
Y.
Wan
,
H.
Wei
,
C.
Chi
, and
D.
Thévenin
, “
A parameter-free and monolithic approach for multiscale simulations of flow, transport, and chemical reactions in porous media
,”
J. Comput. Phys.
(submitted) (
2024
).
17.
S.
Mirjalili
,
S. S.
Jain
, and
M.
Dodd
, “
Interface-capturing methods for two-phase flows: An overview and recent developments
,”
Cent. Turbul. Res. Annu. Res. Briefs
2017
,
117
135
.
18.
C.
Mulbah
,
C.
Kang
,
N.
Mao
,
W.
Zhang
,
A. R.
Shaikh
, and
S.
Teng
, “
A review of VOF methods for simulating bubble dynamics
,”
Prog. Nucl. Energy
154
,
104478
(
2022
).
19.
S.
Vincent
,
A.
Sarthou
,
J.-P.
Caltagirone
,
F.
Sonilhac
,
P.
Février
,
C.
Mignot
, and
G.
Pianet
, “
Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns
,”
J. Comput. Phys.
230
,
956
983
(
2011
).
20.
R.
Guillaument
,
S.
Vincent
,
J.
Caltagirone
,
M.
Laugier
, and
P.
Gardin
, “
A new volume of fluid model for modeling wetting effects. Application to the impact of emulsion o/w droplets on a moving plate
,” in
7th International Conference on Multiphase Flows
(
2011
).
21.
P.
Horgue
,
M.
Prat
, and
M.
Quintard
, “
A penalization technique applied to the ‘Volume-Of-Fluid’ method: Wettability condition on immersed boundaries
,”
Comput. Fluids
100
,
255
266
(
2014
).
22.
Z.
Ou
,
L.
Guo
,
C.
Chi
,
J.
Zhao
,
H.
Jin
, and
D.
Thévenin
, “
Fully resolved direct numerical simulation of single coal particle gasification in supercritical water
,”
Fuel
329
,
125474
(
2022
).
23.
P.
Bohórquez
, “
Study and numerical simulation of sediment transport in free-surface flow
,” Ph.D. thesis (
University of Malaga
,
Spain
,
2008
).
24.
S.
Mirjalili
,
C. B.
Ivey
, and
A.
Mani
, “
Comparison between the diffuse interface and volume of fluid methods for simulating two-phase flows
,”
Int. J. Multiphase Flow
116
,
221
238
(
2019
).
25.
H.
Marschall
, “
Towards the numerical simulation of multi-scale two-phase flows
,” Ph.D. thesis (
Technische Universität München
,
2011
).
26.
R.
Scardovelli
and
S.
Zaleski
, “
Direct numerical simulation of free-surface and interfacial flow
,”
Annu. Rev. Fluid Mech.
31
,
567
603
(
1999
).
27.
J. U.
Brackbill
,
D. B.
Kothe
, and
C.
Zemach
, “
A continuum method for modeling surface tension
,”
J. Comput. Phys.
100
,
335
354
(
1992
).
28.
A.
Ferrari
and
I.
Lunati
, “
Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy
,”
Adv. Water Resour.
57
,
19
31
(
2013
).
29.
M. M.
Francois
,
S. J.
Cummins
,
E. D.
Dendy
,
D. B.
Kothe
,
J. M.
Sicilian
, and
M. W.
Williams
, “
A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework
,”
J. Comput. Phys.
213
,
141
173
(
2006
).
30.
I.
Lunati
, “
Young's law and the effects of interfacial energy on the pressure at the solid-fluid interface
,”
Phys. Fluids
19
,
118105
(
2007
).
31.
H.
Weller
, “
A new approach to VOF-based interface capturing methods for incompressible, compressible and cavitating flow
,” in
Technical Report
(
OpenCFD Limited
,
2006
).
32.
H.
Rusche
, “
Computational fluid dynamics of dispersed two-phase flow at high phase fractions
,” Ph.D. thesis (
University of London
,
2002
).
33.
R. I.
Issa
, “
Solution of the implicitly discretised fluid flow equations by operator-splitting
,”
J. Comput. Phys.
62
,
40
65
(
1986
).
34.
A. Q.
Raeini
,
M. J.
Blunt
, and
B.
Bijeljic
, “
Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method
,”
J. Comput. Phys.
231
,
5653
5668
(
2012
).
35.
J.-B.
Dupont
and
D.
Legendre
, “
Numerical simulation of static and sliding drop with contact angle hysteresis
,”
J. Comput. Phys.
229
,
2453
2478
(
2010
).
36.
J.
Jurin
, “
An account of some experiments shown before the royal society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes
,”
Philos. Trans. R. Soc. London
30
,
739
747
(
1718
).
37.
Y.
Dimakopoulos
,
G.
Karapetsas
,
N. A.
Malamataris
, and
E.
Mitsoulis
, “
The free (open) boundary condition at inflow boundaries
,”
J. Non-Newtonian Fluid Mech.
187–188
,
16
31
(
2012
).
38.
D.
Gründing
,
M.
Smuda
,
T.
Antritter
,
M.
Fricke
,
D.
Rettenmaier
,
F.
Kummer
,
P.
Stephan
,
H.
Marschall
, and
D.
Bothe
, “
Capillary rise—A computational benchmark for wetting processes
,”
Appl. Math. Modell.
86
,
142
165
(
2020
).
39.
D.
Halpern
and
D.
Gaver
, “
Boundary element analysis of the time-dependent motion of a semi-infinite bubble in a channel
,”
J. Comput. Phys.
115
,
366
375
(
1994
).
40.
P.
Aussillous
and
D.
Quéré
, “
Quick deposition of a fluid on the wall of a tube
,”
Phys. Fluids
12
,
2367
2371
(
2000
).
41.
Y.
Ju
,
W.
Gong
, and
J.
Zheng
, “
Characterization of immiscible phase displacement in heterogeneous pore structures: Parallel multicomponent lattice Boltzmann simulation and experimental validation using three-dimensional printing technology
,”
Int. J. Multiphase Flow
114
,
50
65
(
2019
).
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