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Preferential imbibition in a dual-permeability pore network

Published online by Cambridge University Press:  31 March 2021

Qingqing Gu Open the ORCID record for Qingqing Gu [Opens in a new window] ,
Haihu Liu Open the ORCID record for Haihu Liu [Opens in a new window]  and
Lei Wu Open the ORCID record for Lei Wu [Opens in a new window]
Qingqing Gu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Haihu Liu*
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Lei Wu*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

A deep understanding of two-phase displacement in porous media with permeability contrast is essential for the design and optimisation of enhanced oil recovery processes. In this paper, we investigate the forced imbibition behaviour in two dual-permeability geometries that are of equal permeability contrast. First, a mathematical model is developed for the imbibition in a pore doublet, which shows that the imbibition dynamics can be fully described by the viscosity ratio $\lambda$ and capillary number $Ca_m$ which creatively incorporates the influence of channel width and length. Through the finite difference solution of the mathematical model, a $\lambda$–$Ca_m$ phase diagram is established to characterise the imbibition preference in the pore doublet. We then investigate the imbibition process in a dual-permeability pore network using a well-established lattice Boltzmann method, focusing on the competition between the viscous and capillary forces. Like in the pore doublet, the preferential imbibition occurs in high-permeability zone at high $Ca_{m}$ but in low-permeability zone at low $Ca_{m}$. When $Ca_m$ is not sufficiently high, an oblique advancing pattern is observed which is attributed to non-trivial interfacial tension. Using the newly defined capillary number, the critical $Ca_{m}$ curve on which the breakthrough simultaneously occurs in both permeability zones is found to match well with that from the pore doublet and it is the optimal condition for maximising the imbibition efficiency in the entire pore network.

JFM classification

Low-Reynolds-number flows: Porous media Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A138
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Akai, T., Bijeljic, B. & Blunt, M.J. 2018 Wetting boundary condition for the lattice Boltzmann method: validation with analytical and experimental data. Adv. Water Resour. 116, 56–66.CrossRefGoogle Scholar
Akai, T., Blunt, M.J. & Bijeljic, B. 2020 Pore-scale numerical simulation of low salinity water flooding using the lattice Boltzmann method. J. Colloid Interface Sci. 566, 444–453.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
Al-Housseiny, T.T., Hernandez, J. & Stone, H.A. 2014 Preferential flow penetration in a network of identical channels. Phys. Fluids 26, 042110.CrossRefGoogle Scholar
Al-Housseiny, T.T., Tsai, P.A. & Stone, H.A. 2012 Control of interfacial instabilities using flow geometry. Nat. Phys. 8, 747–750.CrossRefGoogle Scholar
Aziz, R., Joekar-Niasar, V. & Martinez-Ferrer, P. 2018 Pore-scale insights into transport and mixing in steady-state two-phase flow in porous media. Intl J. Multiphase Flow 109, 51–62.CrossRefGoogle Scholar
Badalassi, V.E., Ceniceros, H.D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190, 371–397.CrossRefGoogle Scholar
Bahadori, A. 2018 Fundamentals of Enhanced Oil and Gas Recovery from Conventional and Unconventional Reservoirs. Gulf Professional Publishing.Google Scholar
Boek, E.S. & Venturoli, M. 2010 Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries. Comput. Math. Appl. 59, 2305–2314.CrossRefGoogle Scholar
Brackbill, J.U., Kothe, D.B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354.CrossRefGoogle Scholar
Chatzis, I & Dullien, F.A.L. 1983 Dynamic immiscible displacement mechanisms in pore doublets: theory versus experiment. J. Colloid Interface Sci. 91, 199–222.CrossRefGoogle Scholar
Chen, Y., Li, Y., Valocchi, A.J. & Christensen, K.T. 2018 Lattice Boltzmann simulations of liquid CO$_2$ displacing water in a 2D heterogeneous micromodel at reservoir pressure conditions. J. Contam. Hydrol. 212, 14–27.CrossRefGoogle Scholar
Chen, Y., Valocchi, A.J., Kang, Q. & Viswanathan, H.S. 2019 Inertial effects during the process of supercritical CO$_2$ displacing brine in a sandstone: lattice Boltzmann simulations based on the continuum-surface-force and geometrical wetting models. Water Resour. Res. 55, 11144–11165.CrossRefGoogle Scholar
Cinar, Y., Riaz, A. & Tchelepi, H.A. 2009 Experimental study of CO$_2$ injection into saline formations. SPE J. 14, 588–594.CrossRefGoogle Scholar
Fagbemi, S. & Tahmasebi, P. 2020 Coupling pore network and finite element methods for rapid modelling of deformation. J. Fluid Mech. 897, A20.CrossRefGoogle Scholar
Ginzburg, I. & d'Humieres, D. 2003 Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 68, 066614.CrossRefGoogle ScholarPubMed
Gu, Q., Liu, H. & Zhang, Y. 2018 Lattice Boltzmann simulation of immiscible two-phase displacement in two-dimensional Berea sandstone. Appl. Sci. 8, 1497.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, 086602.Google 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
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, 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
Jiang, F. & Tsuji, T. 2015 Impact of interfacial tension on residual CO$_2$ clusters in porous sandstone. Water Resour. Res. 51, 1710–1722.CrossRefGoogle Scholar
Jiang, F. & Tsuji, T. 2016 Numerical investigations on the effect of initial state CO$_2$ topology on capillary trapping efficiency. Intl J. Greenh. Gas Control 49, 179–191.CrossRefGoogle Scholar
Jiang, F. & Tsuji, T. 2017 Estimation of three-phase relative permeability by simulating fluid dynamics directly on rock-microstructure images. Water Resour. Res. 53, 11–32.CrossRefGoogle Scholar
Joekar-Niasar, V., Hassanizadeh, S.M. & Dahle, H.K. 2010 Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling. J. Fluid Mech. 655, 38–71.CrossRefGoogle Scholar
Juanes, R., Spiteri, E.J., Orr, F.M. & Blunt, M.J. 2006 Impact of relative permeability hysteresis on geological CO$_2$ storage. Water Resour. Res. 42, W12418.CrossRefGoogle Scholar
Kibbey, T.C.G. & Chen, L. 2012 A pore network model study of the fluid-fluid interfacial areas measured by dynamic-interface tracer depletion and miscible displacement water phase advective tracer methods. Water Resour. Res. 48, W10519.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
Laidlaw, W.G. & Wardlaw, N.C. 1983 A theoretical and experimental investigation of trapping in pore doublets. Can. J. Chem. Engng 61, 719–727.CrossRefGoogle Scholar
Lake, L.W. 1989 Enhanced Oil Recovery. Prentice Hall.Google 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.CrossRefGoogle ScholarPubMed
Latva-Kokko, M. & Rothman, D.H. 2005 Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys. Rev. E 71, 1–8.CrossRefGoogle ScholarPubMed
Lee, S.L. & Yang, J.H. 1997 Modeling of Darcy-Forchheimer drag for fluid flow across a bank of circular cylinders. Intl J. Heat Mass Transfer 40, 3149–3155.CrossRefGoogle Scholar
Lenormand, R., Touboul, E. & Zarcone, C. 1988 Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165.CrossRefGoogle Scholar
Liu, H., Kang, Q., Leonardi, C.R., Schmieschek, S., Narváez, A., Jones, B.D., Williams, J.R., Valocchi, A.J. & Harting, J. 2015 Multiphase lattice Boltzmann simulations for porous media applications. Comput. Geosci., 777–805.Google Scholar
Liu, H., Valocchi, A.J., Kang, Q. & Werth, C. 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
Ma, K., Liontas, R., Conn, C.A., Hirasaki, G.J. & Biswal, S.L. 2012 Visualization of improved sweep with foam in heterogeneous porous media using microfluidics. Soft Matter 8, 10669–10675.CrossRefGoogle Scholar
Moore, T.F. & Slobod, R.L. 1956 The effect of viscosity and capillarity on the displacement of oil by water. Prod. Monthly 20, 20–30.Google Scholar
Nijjer, J.S., Hewitt, D.R. & Neufeld, J.A. 2019 Stable and unstable miscible displacements in layered porous media. J. Fluid Mech. 869, 468–499.CrossRefGoogle ScholarPubMed
Pan, C., Hilpert, M. & Miller, C.T. 2001 Pore-scale modeling of saturated permeabilities in random sphere packings. Phys. Rev. E 64, 066702.CrossRefGoogle ScholarPubMed
Pan, C., Luo, L.-S. & Miller, C.T. 2006 An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids 35, 898–909.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, 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, 442–458.CrossRefGoogle ScholarPubMed
Raeini, A.Q., Blunt, M.J. & Bijeljic, B. 2014 Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces. Adv. Water Resour. 74, 116–126.CrossRefGoogle Scholar
Ramstad, T., Idowu, N., Nardi, C. & Øren, P.-E. 2012 Relative permeability calculations from two-phase flow simulations directly on digital images of porous rocks. Transp. Porous Med. 94, 487–504.CrossRefGoogle Scholar
Rothman, D.H. 1990 Macroscopic laws for immiscible two-phase flow in porous media: results from numerical experiments. J. Geophys. Res. 95, 8663–8674.CrossRefGoogle Scholar
Sheng, J.J. 2013 Enhanced Oil Recovery Field Case Studies. Gulf Professional Publishing.Google Scholar
Sorbie, K.S., Wu, Y.Z. & McDougall, S.R. 1995 The extended Washburn equation and its application to the oil/water pore doublet problem. J. Colloid Interface Sci. 174, 289–301.CrossRefGoogle Scholar
Soulaine, C., Roman, S., Kovscek, A. & Tchelepi, H.A. 2018 Pore-scale modelling of multiphase reactive flow: application to mineral dissolution with production of CO$_2$. J. Fluid Mech. 855, 616–645.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
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, 3770–3790.CrossRefGoogle Scholar
Yin, X., Zarikos, I., Karadimitriou, N.K., Raoof, A. & Hassanizadeh, S.M. 2018 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
Zhang, C., Oostrom, M., Grate, J.W., Wietsma, T.W. & Warner, M.G. 2011 a Liquid CO$_2$ displacement of water in a dual-permeability pore network micromodel. Environ. Sci. Technol. 45, 7581–7588.CrossRefGoogle Scholar
Zhang, C., Oostrom, M., Wietsma, T.W., Grate, J.W. & Warner, M.G. 2011 b 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, 3493–3505.CrossRefGoogle Scholar
Zhao, B., MacMinn, C.W. & Juanes, R. 2016 Wettability control on multiphase flow in patterned microfluidics. Proc. Natl Acad. Sci. USA 113, 10251–10256.CrossRefGoogle ScholarPubMed
Zheng, Z., Kim, H. & Stone, H.A. 2015 Controlling viscous fingering using time-dependent strategies. Phys. Rev. Lett. 115, 174501.CrossRefGoogle ScholarPubMed
Zheng, Z., Rongy, L. & Stone, H.A. 2015 Viscous fluid injection into a confined channel. Phys. Fluids 27, 062105.CrossRefGoogle Scholar
Zou, Q. & He, X. 1997 On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9, 1591–1598.CrossRefGoogle Scholar