Hybrid Mimetic Finite Difference and Streamline Methods for Numerical Simulation of Two-phase Flow in Fractured Reservoirs

Abstract

In this work, we present a novel numerical formulation for efficiently modeling two-phase flow in fractured reservoirs. The novel formulation is developed by hybridizing mimetic finite difference and streamline (MFD-SL) methods, in which mimetic finite difference (MFD) is employed to discretize the pressure equation, and the streamline (SL) method is adopted to solve the saturation equation along 1D streamlines. The hybrid formulation is implemented on discrete fracture model (DFM) and is operated in an IMPES-like manner. A simple and practical streamline tracing method is developed on 2D triangular and 3D tetrahedral grids that are commonly implemented in the DFM framework. We benchmark the hybrid MFD-SL formulation with others using various cases with different complexity. Results show the proposed approach could achieve promising results yet with lower computation costs compared to other classical formulations. These achievements benefit from utilizing streamline tracing, which significantly alleviates the numerical diffusion error and improves the computation efficiency. This work, for the first time, incorporates hybrid MFD-SL formulation into DFM in case of triangular and tetrahedral grids and has great potential to be deployed on reservoir-scale simulation workflow.