Oscillation-free implicit pressure explicit concentration discontinuous Galerkin methods for compressible miscible displacements with applications in viscous fingering

Document Type

Article

Publication Date

11-1-2024

Abstract

The system of compressible miscible displacements is widely adopted to model surfactant flooding in enhanced oil recovery techniques, where a low-viscosity fluid is injected underground to replace the high-viscosity oil. When the mobility ratio of the injected fluid to oil is high, the waterflood front tends to be unstable and exhibits a finger-like growth pattern, known as viscous fingering. Due to its unstable nature, the viscous fingering phenomenon is sensitive to mesh orientation and numerical discretization. Therefore, high-order numerical methods are preferable to reduce numerical artifacts and mesh dependence. In this paper, we propose a high-order discontinuous Galerkin method for the coupled nonlinear system of compressible miscible displacements to simulate the viscous fingering fluid instability in porous media. We adopt the IMplicit Pressure Explicit Concentration time marching approach based on implicit-explicit Runge-Kutta methods to achieve high-order temporal accuracy. Additionally, we introduce an oscillation-free damping term to control the spurious oscillations encountered in the waterflood front due to the large gradient of saturation. We have conducted ample numerical tests in two space dimensions to demonstrate the effectiveness and robustness of the proposed schemes in recovering viscous fingering.

Publication Title

Journal of Computational Physics

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