Physics-preserving IMPES based multiscale methods for immiscible two-phase flow in highly heterogeneous porous media

TL;DR

This paper introduces a physics-preserving multiscale method for simulating immiscible two-phase flow in heterogeneous porous media, combining a novel P-IMPES scheme with MGMsFEM for efficient and accurate computations.

Contribution

The paper presents a new multiscale method that preserves physical laws and improves computational efficiency for two-phase flow in complex porous media.

Findings

The method maintains local mass conservation and bounds for saturation.

It achieves a good balance between accuracy and computational cost.

Numerical experiments verify the robustness and efficiency of the approach.

Abstract

In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme in order to maintain the local conservation of mass for both phases. Besides, this scheme is unbiased and if the time step is smaller than a certain value, the saturation of both phases are bounds-preserving. When updating velocity, MGMsFEM serves as an efficient solver by computing the unknowns on a coarse grid. We follow the operation splitting techinque to deal with the two-phase flow. In particular, we use an upwind strategy to iterate the saturation explicitly and the MGMsFEM is utilized to compute velocity with a decoupled system on a coarse mesh. To show the efficiency and robustness of the proposed method, we design a set of interesting experiments. A rigorous analysis is also included to serve as a theoretical base of the method, which is well verified by the numerical results. Both simulations and analysis indicate that the method attains a good balance between accuracy and computation cost.