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Investigation of the wetting effects on two-phase fluid flows in a heterogeneous digital core under dynamic conditions

T.R. Zakirov, M.G. Khramchenkov

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The paper studies the wetting effects on the characteristics of two-phase fluid flows in porous media. The originality of paper is a study of displacement under dynamic conditions when the action of viscous forces is significant. As a research tool, the methods of mathematical modeling are used – the lattice Boltzmann equations in a combination with a color-gradient model that describes interphacial interactions. Numerical experiments are carried out in a digital model of a porous medium characterized by a high degree of the pore space heterogeneity. In this work, a map of flow regimes in the coordinates “capillarity number – contact angle” is performed. The identification of four crossover modes between flows with capillary, viscous fingers and with a stable displacement front is carried out. Special attention is paid to the study of the influence of wetting effects on the specific length of the “injected fluid – skeleton” interface.


wetting angle; capillary number; drainage; imbibitions; lattice Boltzmann equations


  • Bakhshian S., Hosseini S.A., Shokri N. (2019). Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method. Scientific Reports, 9(1), 3377. DOI: 10.1038/s41598-019-39741-x
  • Hu R., Lan T., Wei G.J., Chen Y.F. (2019). Phase diagram of quasi static immiscible displacement in disordered porous media. Journal of Fluid Mechanics, 875, pp. 448–475.
  • Cieplak M., Robbins M.O. (1988). Dynamical transition in quasi static fluid invasion in porous media. Physical Review Letters, 60(20), pp. 2042–2045.
  • Cieplak M., Robbins M.O. (1990). Influence of contact angle on quasi static fluid invasion of porous media. Physical Review B, 41(16), pp. 11508–11521.
  • Cottin C., Bodiguel H., Colin A. (2018). Drainage in two-dimensional porous media: From capillary fingering to viscous flow. Phys. Rev. E., 82, 046315.
  • Geistlinger H., Zulfiqar B. (2020). The impact of wettability and surface roughness on fluid displacement and capillary trapping in 2 D and 3 D porous media: 1. Wettability controlled phase transition of trapping efficiency in glass beads packs. Water Resources Research, 56, e2019WR026826. https://
  • Gerke K.M., Korost D.V., Karsanina M.V., Korost S.R., Vasiliev R.V., Lavrukhin E.V., Gafurova D.R. (2021). Modern approaches to pore space scale digital modeling of core structure and multiphase flow. Georesursy = Georesources, 23(2), pp. 197–213. 
  • Jafari I., Masihi M., Zarandi M.N. (2017). Numerical simulation of counter-current spontaneous imbibitions in water-wet fractured porous media: Influences of water injection velocity, fracture aperture, and grains geometry. Physics of Fluids, 29, 113305.
  • Jung M., Brinkmann M., Seemann R., Hiller T., de la Lama M.S., Herminghaus S. (2016). Wettability controls slow immiscible displacement through local interfacial instabilities. Physical Review Fluids, 1, 074202.
  • Holtzman R., Segre E. (2015). Wettability stabilizes fluid invasion into porous media via nonlocal, cooperative pore filling. Physical Review Letters, 115(6), 164501.
  • Hu R., Wan J., Yang Z., Chen Y.-F., Tokunaga T. (2018). Wettability and flow rate impacts on immiscible displacement: A theoretical model. Geophysical Research Letters, 45, pp. 3077–3086.
  • Hu R., Lan T., Wei G.J., Chen Y.F. (2019). Phase diagram of quasi static immiscible displacement in disordered porous media. Journal of Fluid Mechanics, 875, pp. 448–475.
  • Huang H., Huang J.-J., Lu X.-Y. (2014). Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method. Computers & Fluids, 93, pp. 164–172.
  • Lan T., Hu R., Yang Z., Wu D.S., Chen Y.F. (2020). Transitions of fluid invasion patterns in porous media. Geophysical Research Letters, 47, e2020GL089682. 10.1029/2020GL089682
  • Laubie H., Monfared S., Radjaï F., Pellenq R., Ulm F.-J. (2017). Disorder-induced stiffness degradation of highly disordered porous materials. Journal of the Mechanics and Physics of Solids, 106, pp. 207–228.
  • Leclaire S., Reggio M., Trépanier J.-Y. (2012). Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model. Applied Mathematical Modelling, 36, pp. 2237–2252.
  • Leclaire S., Parmigiani A., Malaspinas O., Chopard B., Latt J. (2017). Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media. Physical Review E., 95, 033306. DOI: 10.1103/PhysRevE.95.033306
  • Lenormand R., Touboul E., Zarcone C. (1988). Numerical models and experiments on immiscible displacements in porous media. Journal of Fluid Mechanics, 189, pp. 165–187.
  • Li J., McDougall S.R., Sorbie K.S. (2017). Dynamic pore-scale network model (PNM) of water imbibition in porous media. Advances in Water Resources, 107, pp. 191–211. 
  • 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. Transport in Porous Media, 99, pp. 555–580.
  • Liu H., Kang Q., Leonardi C.R., Schmieschek S., Narváez A., Jones B.D., Williams J.R., Valocchi A.J., Harting J. (2016). Multiphase lattice Boltzmann simulations for porous media applications. Computational Geosciences, 20(4), pp. 777–805. DOI: 10.1007/s10596-015-9542-3
  • Pan C., Luo L.S., Miller C.T. (2006). An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Computers and Fluids, 35, pp. 898–909. DOI: 10.1016/j.compfluid.2005.03.008
  • Porter M.L., Schaap M.G., Wildenschild D. (2009). Lattice-Boltzmann simulations of the capillary pressure-saturation-interfacial area relationship for porous media. Advances in Water Resources, 32, pp. 1632–1640. DOI: 10.1016/j.advwatres.2009.08.009.
  • Primkulov B.K., Talman S., Khaleghi K., Shokri A.R., Chalaturnyk R., Zhao B. Z. (2018). Quasi static fluid fluid displacement in porous media: Invasion percolation through a wetting transition. Physical Review Fluids, 3, 104001. PhysRevFluids.3.104001
  • Primkulov B.K., Pahlavan A.A., Fu X.J., Zhao B.Z., MacMinn C.W., Juanes R. (2019). Signatures of fluid fluid displacement in porous media: Wettability, patterns and pressures. Journal of Fluid Mechanics, 875, R4.
  • Stokes J.P., Weitz D.A., Gollub J.P., Dougherty A., Robbins M.O., Chaikin P.M., Lindsay H.M. (1986). Interfacial Stability of Immiscible Displacement in a Porous Medium. Phys. Rev. Lett. 57, 1718.
  • Succi S. (2001). The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, UK.
  • Tao, L., Min, L., Xueqi, J., Wenlian, X., Qingwu, C. (2019). Influence mechanism of pore-scale anisotropy and pore distribution heterogeneity on permeability of porous media. Petrol. Explor. Develop., 46(3), pp. 594–604.
  • Trojer M., Szulczewski M.L., Juanes R. (2015). Stabilizing fluid-fluid displacements in porous media through wettability alteration. Physical Review Applied, 3(5), 054008.
  • Tsuji T., Jiang F., Christensen K.T. (2016). Characterization of immiscible fluid displacement processes with various capillary numbers and viscosity ratios in 3D natural sandstone. Advances in Water Recourses, 95, pp. 3–15.
  • Zakirov T.R., Galeev A.A., Khramchenkov M.G. (2018). Pore-scale Investigation of Two-Phase Flows in Three-Dimensional Digital Models of Natural Sandstones. Fluid Dynamics, 53(5), pp. 76–91.
  • Zakirov T.R., Galeev A.A. (2019). Absolute permeability calculations in micro-computed tomography models of sandstones by Navier-Stokes and lattice Boltzmann equations. International Journal of Heat and Mass Transfer, 129, pp. 415–426.
  • Zakirov T.R., Khramchenkov M.G. (2020а). Characterization of two-phase displacement mechanisms in porous media by capillary and viscous forces estimation using the lattice Boltzmann simulations. Journal of Petroleum Science and Engineering, 184, 106575. DOI: 10.1016/j.petrol.2019.106575
  • Zakirov T.R., Khramchenkov M.G. (2020b). Simulation of Two-Phase Fluid Flow in the Digital Model of a Pore Space of Sandstone at Different Surface Tensions. Journal of Engineering Physics and Thermophysics, 93 (3), pp. 733–742.
  • Zakirov T.R., Khramchenkov M.G. (2020c). Prediction of permeability and tortuosity in heterogeneous porous media using a disorder parameter. Chemical Engineering Science, 227, 115893.
  • Zakirov T.R., Khramchenkov M.G. (2020d). Pore-scale investigation of the displacement fluid mechanics during two-phase flows in natural porous media under the dominance of capillary forces. Georesursy, 22(1), pp. 4–12.
  • Zakirov T.R., Khramchenkov M.G., Galeev A.A. (2021). Lattice Boltzmann Simulations of the Interface Dynamics During Two-Phase Flow in Porous Media. Lobachevskii Journal of Mathematics, 42(1), pp. 236–255. DOI: 10.1134/S1995080221010297
  • Zhao B., Macminn C. W., Juanes R. (2016). Wettability control on multiphase flow in patterned microfluidics. Proceedings of the National Academy of Sciences of the United States of America, 113(37), pp. 10251–10256.
  • Zou Q., He X. (1997). On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids, 9, pp. 1591–1598. DOI: 10.1063/1.869307

Timur R. Zakirov – PhD (Physics and Mathematics), Associate Professor, Institute of Geology and Oil and Gas Technologies
Kazan Federal University
4/5, Kremlevskaya st., Kazan, 420033, Russian Federation

Maxim G. Khramchenkov – DSc (Physics and Mathematics), Professor, Head of the Department of Mathematical Methods in Geology
Kazan Federal University
4/5, Kremlevskaya st., Kazan, 420033, Russian Federation

For citation:

Zakirov T.R., Khramchenkov M.G. (2022). Investigation of the wetting effects on two-phase fluid flows in a heterogeneous digital core under dynamic conditions. Georesursy = Georesources, 24(1), pp. 16–26. DOI: