Coupled Hyperbolic Subsurface Flow (CHSF) Model to Solve Buoyant Two-Phase Flow and Transport in Heterogeneous Porous Media

Abstract

Traditional methods for simulating buoyant two-phase flow and transport in porous media involve solving large systems of tightly coupled discrete equations, which involves non-local operations. In [1], a new approach was proposed which requires no global system to be solved and thus only relies  on local computations. This makes it well-suited for large-scale parallel processing on multiple CPUs and GPUs. The new coupled hyperbolic subsurface flow (CHSF) model for two phase flow and transport, was compared to the Implicit Method and an established general purpose reservoir simulator (GPRS), showing that it is highly efficient and accurate for homogeneous media. However, numerical artifacts appear if it is employed for heterogeneous media. In this work, these artifacts are addressed, and to resolve the deficiencies, a novel multi-dimensional Rankine-Hugoniot-Riemann (MD-RHR) solver is devised. Numerical experiments demonstrate that with this MD-RHR solver the CHSF model can deal with heterogeneous permeability fields and accurately reproduces reference results. 

[1] Jenny, P., Hasanzade, R., & Tchelepi, H. (2023). Tightly coupled hyperbolic treatment of buoyant two-phase flow and transport in porous media. Journal of Computational Physics, 489, 112–205. https://doi.org/10.1016/j.jcp.2023.112205