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Prediction of spontaneous imbibition with gravity in porous media micromodels

Published online by Cambridge University Press:  18 November 2022

Sheng Li ,
Haihu Liu Open the ORCID record for Haihu Liu [Opens in a new window] ,
Rui Wu ,
Jianchao Cai ,
Guang Xi  and
Fei Jiang
Sheng Li
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Haihu Liu*
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China Heilongjiang Provincial Key Laboratory of Reservoir Physics & Fluid Mechanics in Porous Medium, Daqing 163712, PR China
Rui Wu
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Jianchao Cai
Affiliation:
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, PR China
Guang Xi
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Fei Jiang
Affiliation:
Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Yamaguchi 755-8611, Japan
*
†Email address for correspondence: [email protected]
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Abstract

In this work, theoretical modelling, quasi-three-dimensional (quasi-3D) simulations and micromodel experiments are conducted to study spontaneous imbibition with gravity in porous media micromodels. By establishing the force balance governing the spontaneous imbibition process, we develop a theoretical model for predicting the imbibition length against time in a rectangular capillary. The theoretical model is then extended to the prediction of a compact displacement process in a micromodel by using an equivalent width, which is derived by analogising the micromodel to a rectangular capillary. By simulating spontaneous imbibition in a rectangular capillary with various aspect ratios ($\varepsilon$), we show that the application condition of the quasi-3D method is $\varepsilon \leqslant 1/3$. Next, we simulate spontaneous imbibition in micromodels with various geometries and flow conditions. Fingering and compact displacement are identified for varying viscosity ratios and gravitational accelerations. At low (high) viscosity ratio of wetting to non-wetting fluids, an upward (downward) gravity can promote the stability of the wetting front, favouring the transition from fingering to compact displacement. In addition, we find that the depth-oriented interface curvature dominates the capillary effect during the imbibition, and such a mechanism is considered by introducing an equivalent contact angle into the theoretical model. With the help of equivalent width and contact angle, the theoretical model is shown to provide satisfactory prediction of the compact displacement process. Finally, a micromodel experiment is presented to further verify the developed theoretical model and the quasi-3D simulation.

JFM classification

Low-Reynolds-number flows: Porous media Interfacial Flows (free surface): Capillary flows Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , A9
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© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ajaev, V.S. & Homsy, G.M. 2001 a Steady vapor bubbles in rectangular microchannels. J. Colloid Interface Sci. 240 (1), 259–271.CrossRefGoogle ScholarPubMed
Ajaev, V.S. & Homsy, G.M. 2001 b Three-dimensional steady vapor bubbles in rectangular microchannels. J. Colloid Interface Sci. 244 (1), 180–189.CrossRefGoogle Scholar
Akai, T., Lin, Q., Bijeljic, B. & Blunt, M.J. 2020 Using energy balance to determine pore-scale wettability. J. Colloid Interface Sci. 576, 486–495.CrossRefGoogle ScholarPubMed
Akhlaghi Amiri, H.A. & Hamouda, A.A. 2013 Evaluation of level set and phase field methods in modeling two phase flow with viscosity contrast through dual-permeability porous medium. Intl J. Multiphase Flow 52, 22–34.CrossRefGoogle Scholar
Alinejad, A. & Dehghanpour, H. 2021 Evaluating porous media wettability from changes in Helmholtz free energy using spontaneous imbibition profiles. Adv. Water Resour. 157, 104038.CrossRefGoogle Scholar
Alizadeh, M. & Fatemi, M. 2021 Mechanistic study of the effects of dynamic fluid/fluid and fluid/rock interactions during immiscible displacement of oil in porous media by low salinity water: direct numerical simulation. J. Mol. Liq. 322, 114544.CrossRefGoogle Scholar
Anbari, A., Chien, H.-T., Datta, S.S., Deng, W., Weitz, D.A. & Fan, J. 2018 Microfluidic model porous media: fabrication and applications. Small 14 (18), 1703575.CrossRefGoogle ScholarPubMed
Andersen, P.Ø. & Ahmed, S. 2021 Simulation study of wettability alteration enhanced oil recovery during co-current spontaneous imbibition. J. Petrol. Sci. Engng 196, 107954.CrossRefGoogle Scholar
Anoop, R. & Sen, A.K. 2015 Capillary flow enhancement in rectangular polymer microchannels with a deformable wall. Phys. Rev. E 92, 013024.CrossRefGoogle ScholarPubMed
Armstrong, R.T., Evseev, N., Koroteev, D. & Berg, S. 2015 Modeling the velocity field during Haines jumps in porous media. Adv. Water Resour. 77, 57–68.CrossRefGoogle Scholar
Babchin, A.J., Bentsen, R., Faybishenko, B. & Geilikman, M.B. 2016 On the capillary pressure function in porous media based on relative permeabilities of two immiscible fluids: application of capillary bundle models and validation using experimental data. Adv. Colloid Interface Sci. 233, 176–185.CrossRefGoogle ScholarPubMed
Badalassi, V.E., Ceniceros, H.D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2), 371–397.CrossRefGoogle Scholar
Bell, J.M. & Cameron, F.K. 1906 The flow of liquids through capillary spaces. J. Phys. Chem. 10 (8), 658–674.CrossRefGoogle Scholar
Benavente, D., Lock, P., Del Cura, M.Á.G. & Ordóñez, S. 2002 Predicting the capillary imbibition of porous rocks from microstructure. Transp. Porous Med. 49 (1), 59–76.CrossRefGoogle Scholar
Berg, S., et al. 2013 Real-time 3D imaging of Haines jumps in porous media flow. Proc. Natl Acad. Sci. USA 110 (10), 3755–3759.CrossRefGoogle ScholarPubMed
Blunt, M.J., Alhosani, A., Lin, Q., Scanziani, A. & Bijeljic, B. 2021 Determination of contact angles for three-phase flow in porous media using an energy balance. J. Colloid Interface Sci. 582, 283–290.CrossRefGoogle ScholarPubMed
Blunt, M.J., Lin, Q., Akai, T. & Bijeljic, B. 2019 A thermodynamically consistent characterization of wettability in porous media using high-resolution imaging. J. Colloid Interface Sci. 552, 59–65.CrossRefGoogle ScholarPubMed
Boek, E.S. & Venturoli, M. 2010 Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries. Comput. Maths Applics. 59 (7), 2305–2314.CrossRefGoogle Scholar
Brackbill, J.U., Kothe, D.B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354.CrossRefGoogle Scholar
Cai, J., Jin, T., Kou, J., Zou, S., Xiao, J. & Meng, Q. 2021 Lucas–Washburn equation-based modeling of capillary-driven flow in porous systems. Langmuir 37 (5), 1623–1636.CrossRefGoogle ScholarPubMed
Cai, J., Yu, B., Zou, M. & Luo, L. 2010 Fractal characterization of spontaneous co-current imbibition in porous media. Energy Fuels 24 (3), 1860–1867.CrossRefGoogle Scholar
Chang, C., Kneafsey, T.J., Tokunaga, T.K., Wan, J. & Nakagawa, S. 2021 Impacts of pore network-scale wettability heterogeneity on immiscible fluid displacement: a micromodel study. Water Resour. Res. 57 (9), e2021WR030302.CrossRefGoogle Scholar
Chang, S. & Kim, W. 2020 Dynamics of water imbibition through paper with swelling. J. Fluid Mech. 892, A39.CrossRefGoogle Scholar
Chen, C., Huang, H., Mo, X., Xue, H., Liu, M. & Chen, H. 2021 Insights into the kinetic processes of solute migration by unidirectional freezing in porous media with micromodel visualization at the pore-scale. Sci. Total Environ. 784, 147178.CrossRefGoogle ScholarPubMed
Chen, S. & Doolen, G.D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 (1), 329–364.CrossRefGoogle Scholar
Corapcioglu, M.Y., Chowdhury, S. & Roosevelt, S.E. 1997 Micromodel visualization and quantification of solute transport in porous media. Water Resour. Res. 33 (11), 2547–2558.CrossRefGoogle Scholar
Elizalde, E., Urteaga, R. & Berli, C.L.A. 2015 Rational design of capillary-driven flows for paper-based microfluidics. Lab on a Chip 15, 2173–2180.CrossRefGoogle ScholarPubMed
Fei, L. & Luo, K.H. 2017 Consistent forcing scheme in the cascaded lattice Boltzmann method. Phys. Rev. E 96, 053307.CrossRefGoogle ScholarPubMed
Finch-Savage, W.E., Rowse, H.R. & Dent, K.C. 2005 Development of combined imbibition and hydrothermal threshold models to simulate maize (Zea mays) and chickpea (Cicer arietinum) seed germination in variable environments. New Phytol. 165 (3), 825–838.CrossRefGoogle ScholarPubMed
Fries, N. & Dreyer, M. 2008 An analytic solution of capillary rise restrained by gravity. J. Colloid Interface Sci. 320 (1), 259–263.CrossRefGoogle ScholarPubMed
Gasow, S., Kuznetsov, A.V., Avila, M. & Jin, Y. 2021 A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient. J. Fluid Mech. 926, A8.CrossRefGoogle Scholar
Ginzburg, I. & d'Humières, D. 2003 Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 68, 066614.CrossRefGoogle ScholarPubMed
Gogoi, S. & Gogoi, S.B. 2019 Review on microfluidic studies for EOR application. J. Pet. Tech. 9 (3), 2263–2277.Google Scholar
Golmohammadi, S., Ding, Y., Kuechler, M., Reuter, D., Schlueter, S., Amro, M. & Geistlinger, H. 2021 Impact of wettability and gravity on fluid displacement and trapping in representative 2D micromodels of porous media (2D sand analogs). Water Resour. Res. 57 (10), e2021WR029908.CrossRefGoogle Scholar
Gruener, S., Sadjadi, Z., Hermes, H.E., Kityk, A.V., Knorr, K., Egelhaaf, S.U., Rieger, H. & Huber, P. 2012 Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores. Proc. Natl Acad. Sci. USA 109 (26), 10245–10250.CrossRefGoogle Scholar
Gu, Q., Liu, H. & Wu, L. 2021 Preferential imbibition in a dual-permeability pore network. J. Fluid Mech. 915, A138.CrossRefGoogle Scholar
Gu, Q., Zhu, L., Zhang, Y. & Liu, H. 2019 Pore-scale study of counter-current imbibition in strongly water-wet fractured porous media using lattice Boltzmann method. Phys. Fluids 31 (8), 086602.Google Scholar
Gunstensen, A.K., Rothman, D.H., Zaleski, S. & Zanetti, G. 1991 Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43, 4320–4327.CrossRefGoogle ScholarPubMed
Guo, B., Bandilla, K.W., Nordbotten, J.M., Celia, M.A., Keilegavlen, E. & Doster, F. 2016 A multiscale multilayer vertically integrated model with vertical dynamics for ${\rm CO}_2$ sequestration in layered geological formations. Water Resour. Res. 52 (8), 6490–6505.CrossRefGoogle Scholar
Guo, Z., Zheng, C. & Shi, B. 2002 Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65, 046308.CrossRefGoogle ScholarPubMed
Halliday, I., Hollis, A.P. & Care, C.M. 2007 Lattice Boltzmann algorithm for continuum multicomponent flow. Phys. Rev. E 76, 026708.CrossRefGoogle ScholarPubMed
Horgue, P., Augier, F., Duru, P., Prat, M. & Quintard, M. 2013 Experimental and numerical study of two-phase flows in arrays of cylinders. Chem. Engng Sci. 102, 335–345.CrossRefGoogle Scholar
Hou, D., Zhang, W., Sun, M., Wang, P., Wang, M., Zhang, J. & Li, Z. 2020 Modified Lucas–Washburn function of capillary transport in the calcium silicate hydrate gel pore: a coarse-grained molecular dynamics study. Cement Concrete Res. 136, 106166.CrossRefGoogle Scholar
Hu, R., Lan, T., Wei, G.-J. & Chen, Y.-F. 2019 Phase diagram of quasi-static immiscible displacement in disordered porous media. J. Fluid Mech. 875, 448–475.CrossRefGoogle Scholar
Hu, R., Wan, J., Yang, Z., Chen, Y.-F. & Tokunaga, T. 2018 Wettability and flow rate impacts on immiscible displacement: a theoretical model. Geophys. Res. Lett. 45 (7), 3077–3086.CrossRefGoogle Scholar
Hu, Y., Patmonoaji, A., Zhang, C. & Suekane, T. 2020 Experimental study on the displacement patterns and the phase diagram of immiscible fluid displacement in three-dimensional porous media. Adv. Water Resour. 140, 103584.CrossRefGoogle Scholar
Høgnesen, E.J., Standnes, D.C. & Austad, T. 2004 Scaling spontaneous imbibition of aqueous surfactant solution into preferential oil-wet carbonates. Energy Fuels 18 (6), 1665–1675.CrossRefGoogle Scholar
Ichikawa, N., Hosokawa, K. & Maeda, R. 2004 Interface motion of capillary-driven flow in rectangular microchannel. J. Colloid Interface Sci. 280 (1), 155–164.CrossRefGoogle ScholarPubMed
Jettestuen, E., Helland, J.O. & Prodanović, M. 2013 A level set method for simulating capillary-controlled displacements at the pore scale with nonzero contact angles. Water Resour. Res. 49 (8), 4645–4661.CrossRefGoogle Scholar
Jiang, F. & Tsuji, T. 2015 Impact of interfacial tension on residual ${\rm CO}_2$ clusters in porous sandstone. Water Resour. Res. 51 (3), 1710–1722.CrossRefGoogle Scholar
Joekar-Niasar, V. & Hassanizadeh, S.M. 2012 Analysis of fundamentals of two-phase flow in porous media using dynamic pore-network models: a review. Crit. Rev. Environ. Sci. Technol. 42 (18), 1895–1976.CrossRefGoogle Scholar
Kang, M., Perfect, E., Cheng, C.L., Bilheux, H.Z., Gragg, M., Wright, D.M., Lamanna, J.M., Horita, J. & Warren, J.M. 2013 Diffusivity and sorptivity of berea sandstone determined using neutron radiography. Vadose Zone J. 12 (3), vzj2012.0135.CrossRefGoogle Scholar
Karadimitriou, N.K. & Hassanizadeh, S.M. 2012 A review of micromodels and their use in two-phase flow studies. Vadose Zone J. 11 (3), vzj2011.0072.CrossRefGoogle Scholar
Ladd, A.J.C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.CrossRefGoogle Scholar
Lallemand, P. & Luo, L.-S. 2000 Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61, 6546–6562.CrossRefGoogle ScholarPubMed
Latva-Kokko, M. & Rothman, D.H. 2005 Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys. Rev. E 71, 056702.CrossRefGoogle ScholarPubMed
Lenormand, R., Touboul, E. & Zarcone, C. 1988 Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165–187.CrossRefGoogle Scholar
Li, K. & Zhao, H. 2012 Fractal prediction model of spontaneous imbibition rate. Transp. Porous Med. 91 (2), 363–376.CrossRefGoogle Scholar
Li, S., Liu, H., Zhang, J., Jiang, F. & Xi, G. 2021 Modeling of three-phase displacement in three-dimensional irregular geometries using a lattice Boltzmann method. Phys. Fluids 33 (12), 122108.CrossRefGoogle Scholar
Li, Y., Kazemifar, F., Blois, G. & Christensen, K.T. 2017 Micro-PIV measurements of multiphase flow of water and liquid ${\rm CO}_2$ in 2-D heterogeneous porous micromodels. Water Resour. Res. 53 (7), 6178–6196.CrossRefGoogle Scholar
Lishchuk, S.V., Care, C.M. & Halliday, I. 2003 Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents. Phys. Rev. E 67, 036701.CrossRefGoogle ScholarPubMed
Liu, H., Ba, Y., Wu, L., Li, Z., Xi, G. & Zhang, Y. 2018 A hybrid lattice Boltzmann and finite difference method for droplet dynamics with insoluble surfactants. J. Fluid Mech. 837, 381–412.CrossRefGoogle Scholar
Liu, H., Kang, Q., Leonardi, C.R., Schmieschek, S., Narvaez, A., Jones, B.D., Williams, J.R., Valocchi, A.J. & Harting, J. 2016 Multiphase lattice Boltzmann simulations for porous media applications. Comput. Geosci. 20, 777–805.CrossRefGoogle Scholar
Liu, H., Sun, S., Wu, R., Wei, B. & Hou, J. 2021 Pore-scale modeling of spontaneous imbibition in porous media using the lattice Boltzmann method. Water Resour. Res. 57 (6), e2020WR029219.CrossRefGoogle Scholar
Liu, H., Valocchi, A.J. & Kang, Q. 2013 Pore-scale simulations of gas displacing liquid in a homogeneous pore network using the lattice Boltzmann method. Transp. Porous Med. 99, 555–580.CrossRefGoogle Scholar
Liu, H., Valocchi, A.J. & Kang, Q. 2012 Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations. Phys. Rev. E 85, 046309.CrossRefGoogle ScholarPubMed
Liu, H. & Zhang, Y. 2017 Lattice Boltzmann simulation of the trapping of a microdroplet in a well of surface energy. Comput. Fluids 155, 68–75.CrossRefGoogle Scholar
Lucas, V.R. 1918 Ueber das zeitgesetz des kapillaren aufstiegs von flüssigkeiten. Kolloidn. Z. 23 (1), 15–22.CrossRefGoogle Scholar
Lukyanov, A.V., Sushchikh, M.M, Baines, M.J. & Theofanous, T.G. 2012 Superfast nonlinear diffusion: capillary transport in particulate porous media. Phys. Rev. Lett. 109, 214501.CrossRefGoogle ScholarPubMed
Mason, G. & Morrow, N.R. 2013 Developments in spontaneous imbibition and possibilities for future work. J. Petrol. Sci. Engng 110, 268–293.CrossRefGoogle Scholar
Mohammadi, M., Nikbin-Fashkacheh, H. & Mahani, H. 2022 Pore network-scale visualization of the effect of brine composition on sweep efficiency and speed of oil recovery from carbonates using a photolithography-based calcite microfluidic model. J. Petrol. Sci. Engng 208, 109641.CrossRefGoogle Scholar
Odier, C., Levaché, B., Santanach-Carreras, E. & Bartolo, D. 2017 Forced imbibition in porous media: a fourfold scenario. Phys. Rev. Lett. 119, 208005.CrossRefGoogle ScholarPubMed
Otumudia, E., Hamidi, H., Jadhawar, P. & Wu, K. 2022 Effects of reservoir rock pore geometries and ultrasonic parameters on the removal of asphaltene deposition under ultrasonic waves. Ultrason. Sonochem. 83, 105949.CrossRefGoogle ScholarPubMed
Ouali, F.F., McHale, G., Javed, H., Trabi, C., Shirtcliffe, N.J. & Newton, M.I. 2013 Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels. Microfluid Nanofluid 15 (3), 309–326.CrossRefGoogle Scholar
Pan, C., Prins, J.F. & Miller, C.T. 2004 A high-performance lattice Boltzmann implementation to model flow in porous media. Comput. Phys. Commun. 158 (2), 89–105.CrossRefGoogle Scholar
Porter, M.L., Schaap, M.G. & Wildenschild, D. 2009 Lattice-Boltzmann simulations of the capillary pressure–saturation–interfacial area relationship for porous media. Adv. Water Resour. 32 (11), 1632–1640.CrossRefGoogle Scholar
Prodanović, M. & Bryant, S.L. 2006 A level set method for determining critical curvatures for drainage and imbibition. J. Colloid Interface Sci. 304 (2), 442–458.CrossRefGoogle ScholarPubMed
Qin, C.-Z. & van Brummelen, H. 2019 A dynamic pore-network model for spontaneous imbibition in porous media. Adv. Water Resour. 133, 103420.CrossRefGoogle Scholar
Qin, C.-Z., Wang, X., Hefny, M., Zhao, J., Chen, S. & Guo, B. 2022 Wetting dynamics of spontaneous imbibition in porous media: from pore scale to darcy scale. Geophys. Res. Lett. 49 (4), e2021GL097269.CrossRefGoogle Scholar
Qin, F., Zhao, J., Kang, Q., Derome, D. & Carmeliet, J. 2021 Lattice Boltzmann modeling of drying of porous media considering contact angle hysteresis. Transp. Porous Med. 140, 395–420.CrossRefGoogle ScholarPubMed
Raeini, A.Q., Blunt, M.J. & Bijeljic, B. 2012 Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method. J. Comput. Phys. 231 (17), 5653–5668.CrossRefGoogle Scholar
Riaz, A., Tang, G.-Q., Tchelepi, H.A. & Kovscek, A.R. 2007 Forced imbibition in natural porous media: comparison between experiments and continuum models. Phys. Rev. E 75, 036305.CrossRefGoogle ScholarPubMed
Ruiz-Gutiérrez, É., Armstrong, S., Lévêque, S., Michel, C., Pagonabarraga, I., Wells, G.G., Hernández-Machado, A. & Ledesma-Aguilar, R. 2022 The long cross-over dynamics of capillary imbibition. J. Fluid Mech. 939, A39.CrossRefGoogle Scholar
Sadjadi, Z. & Rieger, H. 2013 Scaling theory for spontaneous imbibition in random networks of elongated pores. Phys. Rev. Lett. 110, 144502.CrossRefGoogle ScholarPubMed
Sharma, J., Inwood, S.B. & Kovscek, A.R. 2012 Experiments and analysis of multiscale viscous fingering during forced imbibition. SPE J. 17 (04), 1142–1159.CrossRefGoogle Scholar
Shi, Y., Yassin, M.R. & Dehghanpour, H. 2018 A modified model for spontaneous imbibition of wetting phase into fractal porous media. Colloids Surf. (A) 543, 64–75.CrossRefGoogle Scholar
Sukop, M.C., Huang, H., Lin, C.L., Deo, M.D., Oh, K. & Miller, J.D. 2008 Distribution of multiphase fluids in porous media: comparison between lattice Boltzmann modeling and micro-x-ray tomography. Phys. Rev. E 77, 026710.CrossRefGoogle ScholarPubMed
Sun, C., McClure, J.E., Mostaghimi, P., Herring, A.L., Berg, S. & Armstrong, R.T. 2020 Probing effective wetting in subsurface systems. Geophys. Res. Lett. 47 (5), e2019GL086151.CrossRefGoogle Scholar
Sun, Y., Kharaghani, A. & Tsotsas, E. 2016 Micro-model experiments and pore network simulations of liquid imbibition in porous media. Chem. Engng Sci. 150, 41–53.CrossRefGoogle Scholar
Tavassoli, Z., Zimmerman, R.W. & Blunt, M.J. 2005 Analytic analysis for oil recovery during counter-current imbibition in strongly water-wet systems. Transp. Porous Med. 58 (1), 173–189.CrossRefGoogle Scholar
Wang, C., Mehmani, Y. & Xu, K. 2021 Capillary equilibrium of bubbles in porous media. Proc. Natl Acad. Sci. USA 118 (17), e2024069118.CrossRefGoogle ScholarPubMed
Wang, F. & Zhao, J. 2021 Mathematical modeling of gravity and buoyancy effect on low interfacial tension spontaneous imbibition in tight oil reservoirs. AIChE J. 67 (9), e17332.CrossRefGoogle Scholar
Washburn, E.W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273–283.CrossRefGoogle Scholar
Wijshoff, H. 2018 Drop dynamics in the inkjet printing process. Curr. Opin. Colloid Interface Sci. 36, 20–27.CrossRefGoogle Scholar
Wu, R., Kharaghani, A. & Tsotsas, E. 2016 Two-phase flow with capillary valve effect in porous media. Chem. Engng Sci. 139, 241–248.CrossRefGoogle Scholar
Wu, R., Zhang, T., Ye, C., Zhao, C.Y., Tsotsas, E. & Kharaghani, A. 2020 Pore network model of evaporation in porous media with continuous and discontinuous corner films. Phys. Rev. Fluids 5, 014307.CrossRefGoogle Scholar
Xiao, J., Cai, J. & Xu, J. 2018 Saturated imbibition under the influence of gravity and geometry. J. Colloid Interface Sci. 521, 226–231.CrossRefGoogle ScholarPubMed
Xiao, L., Zhu, G., Zhang, L., Yao, J. & Sun, H. 2021 Effects of pore-size disorder and wettability on forced imbibition in porous media. J. Petrol. Sci. Engng 201, 108485.CrossRefGoogle Scholar
Xie, C., Lei, W., Balhoff, M.T., Wang, M. & Chen, S. 2021 Self-adaptive preferential flow control using displacing fluid with dispersed polymers in heterogeneous porous media. J. Fluid Mech. 906, A10.CrossRefGoogle Scholar
Xu, D., Bai, B., Wu, H., Hou, J., Meng, Z., Sun, R., Li, Z., Lu, Y. & Kang, W. 2019 Mechanisms of imbibition enhanced oil recovery in low permeability reservoirs: effect of IFT reduction and wettability alteration. Fuel 244, 110–119.CrossRefGoogle Scholar
Xu, M. & Liu, H. 2018 Prediction of immiscible two-phase flow properties in a two-dimensional Berea sandstone using the pore-scale lattice Boltzmann simulation. Eur. Phys. J. E 41, 124.CrossRefGoogle Scholar
Xu, Z., Liu, H. & Valocchi, A.J. 2017 Lattice Boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media. Water Resour. Res. 53 (5), 3770–3790.CrossRefGoogle Scholar
Yang, W., Fu, C., Du, Y., Xu, K., Balhoff, Ma.T., Weston, J. & Lu, J. 2021 Dynamic contact angle reformulates pore-scale fluid-fluid displacement at ultralow interfacial tension. SPE J. 26 (03), 1278–1289.CrossRefGoogle Scholar
Yin, X., Zarikos, I., Karadimitriou, N.K., Raoof, A. & Hassanizadeh, S.M. 2019 Direct simulations of two-phase flow experiments of different geometry complexities using Volume-of-Fluid (VOF) method. Chem. Engng Sci. 195, 820–827.CrossRefGoogle Scholar
Yu, Z. & Fan, L. 2010 Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow. Phys. Rev. E 82, 046708.CrossRefGoogle ScholarPubMed
Zacharoudiou, I., Chapman, E.M., Boek, E.S. & Crawshaw, J.P. 2017 Pore-filling events in single junction micro-models with corresponding lattice Boltzmann simulations. J. Fluid Mech. 824, 550–573.CrossRefGoogle Scholar
Zhang, C., Oostrom, M., Wietsma, T.W., Grate, J.W. & Warner, M.G. 2011 Influence of viscous and capillary forces on immiscible fluid displacement: pore-scale experimental study in a water-wet micromodel demonstrating viscous and capillary fingering. Energy Fuels 25 (8), 3493–3505.CrossRefGoogle Scholar
Zhang, X., Su, Y., Li, L., Da, Q., Hao, Y., Wang, W., Liu, J., Gao, X., Zhao, A. & Wang, K. 2022 Microscopic remaining oil initiation mechanism and formation damage of ${\rm CO}_2$ injection after waterflooding in deep reservoirs. Energy 248, 123649.CrossRefGoogle Scholar
Zhao, B., MacMinn, C.W. & Juanes, R. 2016 Wettability control on multiphase flow in patterned microfluidics. Proc. Natl Acad. Sci. USA 113 (37), 10251–10256.CrossRefGoogle ScholarPubMed
Zhao, B., et al. 2019 Comprehensive comparison of pore-scale models for multiphase flow in porous media. Proc. Natl Acad. Sci. USA 116 (28), 13799–13806.CrossRefGoogle ScholarPubMed
Zhao, B., Pahlavan, A.A., Cueto-Felgueroso, L. & Juanes, R. 2018 Forced wetting transition and bubble pinch-off in a capillary tube. Phys. Rev. Lett. 120, 084501.CrossRefGoogle Scholar
Zhao, J., Qin, F., Fischer, R., Kang, Q., Derome, D. & Carmeliet, J. 2021 Spontaneous imbibition in a square tube with corner films: theoretical model and numerical simulation. Water Resour. Res. 57 (2), e2020WR029190.CrossRefGoogle Scholar
Zheng, J., Ju, Y. & Wang, M. 2018 Pore-scale modeling of spontaneous imbibition behavior in a complex shale porous structure by pseudopotential lattice Boltzmann method. J. Geophys. Res. 123 (11), 9586–9600.CrossRefGoogle Scholar
Zhu, X., Wang, K., Yan, H., Liu, C., Zhu, X. & Chen, B. 2022 Microfluidics as an emerging platform for exploring soil environmental processes: a critical review. Environ. Sci. Technol. 56 (2), 711–731.CrossRefGoogle ScholarPubMed