Abstract
We develop a rate-dependent network model that accounts for viscous forces by solving for the wetting and non-wetting phase pressure and which allows wetting layer swelling near an advancing flood front. The model incorporates a new time-dependent algorithm by accounting for partial filling of elements. We use the model to study the effects of capillary number, mobility ratio and contact angle distribution on waterflood displacement patterns, saturation and velocity profiles. By using large networks, generated from a new stochastic network algorithm, we reproduce Buckley–Leverett profiles directly from pore-scale modelling thereby providing a bridge between pore-scale and macro-scale transport.
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Aker E., Maløy K.J., Hansen A., Batrouni G.G.: A two-dimensional network simulator for two-phase flow in porous media. Transp. Porous Media 32, 163–186 (1998)
Al-Gharbi M.S., Blunt M.J.: Dynamic network modeling of two-phase drainage in porous media. Phys. Rev. E 71, 016308 (2005)
Bakke S., Øren P.E.: 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2, 136–149 (1997)
Blunt M.J., Scher H.: Pore-level modeling of wetting. Phys. Rev. E 52(6), 6387–6403 (1995)
Blunt M.J., Jackson M.D., Piri M., Valvatne P.H.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 25(8), 1069–1089 (2002)
Bryant S., Blunt M.: Prediction of relative permeability in simple porous media. Phys. Rev. A 46(4), 2004–2011 (1992)
Buckley S.E., Leverett M.C.: Mechanisms of fluid displacement in sands. Trans. AIME 146, 107–116 (1942)
Chen J.-D., Koplik J.: Immiscible fluid displacement in small networks. J. Colloid Interface Sci. 108, 304–330 (1985)
Constantinides G.N., Payatakes A.C.: Effects of precursor wetting films in immiscible displacement through porous media. Transp. Porous Media 38, 291–317 (2000)
Dias M.M., Payatakes A.C.: Network models for two-phase flow in porous media, Part 1. Immiscible microdisplacement of non-wetting fluids. J. Fluid Mech. 164, 305–336 (1986a)
Dias M.M., Payatakes A.C.: Network models for two-phase flow in porous media, Part 2. Motion of oil ganglia. J. Fluid Mech. 164, 337–358 (1986b)
Entov V.M., Musin R.M.: Micromechanics of nonlinear two-phase flows through porous media. Network modeling and percolation analysis. Fluid Dyn. 32, 252–261 (1997)
Hughes R.G., Blunt M.J.: Pore scale modeling of rate effects in imbibition. Transp. Porous Media 40, 295–322 (2000)
Knudsen H.A., Hansen A.: Relation between pressure and fractional flow in two-phase flow in porous media. Phys. Rev. E 65, 056310 (2002)
Knudsen H.A., Aker E., Hansen A.: Bulk flow regime and fractional flow in 2D porous media by numerical simulations. Transp. Porous Media 47, 99–121 (2001)
Lenormand R., Touboul E., Zarcone C.: Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165–187 (1988)
Mogensen K., Stenby E.H.: A dynamic two-phase pore-scale model of imbibition. Transp. Porous Media 32(3), 299–327 (1998)
Nguyen V.H., Sheppard A.P., Knackstedt M.A., Pinczewski W.V.: The effect of displacement rate on imbibition relative permeability and residual saturation. J. Petrol. Sci. Eng. 52(1–4), 54–70 (2006)
Øren P.E., Bakke S.: Process based reconstruction of sandstones and prediction of transport properties. Transp. Porous Media 46, 311–343 (2002)
Øren P.E., Bakke S.: Reconstruction of berea sandstone and pore-scale modeling of wettability effects. J. Petrol. Sci. Eng. 39, 177–199 (2003)
Øren P.E., Bakke S., Arntzen O.J.: Extending predictive capabilities to network models. SPE J. 3, 324–336 (1998)
Panfilov M., Panfilova I.: Phenomenological Meniscus model for two-phase flows in porous media. Transp. Porous Media 58, 87–119 (2005)
Patzek T.W.: Verification of a complete pore network simulator of drainage and imbibition. SPE J. 6, 144–156 (2006)
Pereira G.G., Pinczewski W.V., Chan D.Y.C., Paterson L., Øren P.-E.: Pore-scale network model for drainage dominated three-phase flow in porous media. Transp. Porous Media 24(2), 167–201 (1996)
Ruge J.W., Stueben K.: Algebraic multigrid. In: McComick, S.F. (eds) Multigrid Methods, SIAM Frontiers in Applied Mathematics, vol. 3, SIAM, Philadelphia (1987)
Valvatne P.H., Blunt M.J.: Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. 40, W07406 (2004)
van der Marck S.C., Matsuura T., Glas J.: Viscous and capillary pressures during drainage: network simulations and experiments. Phys. Rev. E 56(5), 5675–5687 (1997)
Vizika O., Avraam D.G., Payatakes A.C.: On the role of the viscosity ratio during low-capillary-numbered forced imbibition in porous media. J. Colloid Interface Sci. 165, 386–401 (1994)
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Idowu, N.A., Blunt, M.J. Pore-Scale Modelling of Rate Effects in Waterflooding. Transp Porous Med 83, 151–169 (2010). https://doi.org/10.1007/s11242-009-9468-0
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DOI: https://doi.org/10.1007/s11242-009-9468-0