Direct numerical simulation of flow on pore-scale images using the phase-field method

Frank F, Liu C, Alpak FO, Berg S, Rivière B (2018)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2018


Book Volume: 23

Pages Range: 1–18

Article Number: SPE-182607-PA

Journal Issue: 5


DOI: 10.2118/182607-PA


Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow on pore structures feasible. In this paper, we describe a two-phase flow simulator that solves mass and momentum balance equations valid at the pore scale, i.e. at scales where the Darcy velocity homogenization starts to break down. The simulator is one of the key components of a molecule-to-reservoir truly multiscale modeling workflow.

A Helmholtz free-energy-driven, thermodynamically-based diffuse-interface/phase-field method is used for the effective simulation of a large number of advecting interfaces, while honoring the interfacial tension. The advective Cahn–Hilliard (mass balance, energy dissipation) and Navier–Stokes (momentum balance, incompressibility) equations are coupled to each other within the phase-field framework. Wettability on rock-fluid interfaces is accounted for via an energy-penalty-based wetting (contact-angle) boundary condition. Individual balance equations are discretized by use of a flexible discontinuous Galerkin (DG) method. The discretization of the mass balance equation is semi-implicit in time using a convex–concave splitting of the energy term. The momentum balance equation is split from the incompressibility constraint by a projection method and linearized with a Picard splitting. Mass and momentum balance equations are coupled to each other via operator splitting and solved sequentially.

We discuss the mathematical model and its DG discretization and briefly introduce nonlinear and linear solution strategies. Numerical validation tests show optimal convergence rates for the DG discretization indicating the correctness of the numerical scheme and of its implementation. Physical validation tests demonstrate the consistency of the phase distribution and velocity fields simulated within our framework. Finally, two-phase flow simulations on two real pore-scale images demonstrate the utility of the pore-scale simulator. The direct pore-scale numerical simulation methodology rigorously takes into account the flow physics by directly acting on pore-scale images of rocks without remeshing. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems.

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Frank, F., Liu, C., Alpak, F.O., Berg, S., & Rivière, B. (2018). Direct numerical simulation of flow on pore-scale images using the phase-field method. Spe Journal, 23(5), 1–18.


Frank, Florian, et al. "Direct numerical simulation of flow on pore-scale images using the phase-field method." Spe Journal 23.5 (2018): 1–18.

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