An efficient method for modeling flow in porous media with immersed faults

TL;DR

This paper introduces a new, efficient modeling method for simulating flow in porous media with faults, significantly reducing computational time while maintaining accuracy, by decoupling pressure and velocity calculations.

Contribution

The paper presents a novel approach that decouples pressure from velocity, reducing degrees of freedom and increasing efficiency in flow modeling with faults.

Findings

Up to 30 times faster than traditional mixed finite element methods.

Maintains comparable accuracy in pressure approximation.

Effective in three-dimensional simulations.

Abstract

Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is to use the mixed finite element method. However, the mixed method could be time consuming due to large number of degree of freedom since both pressure and velocity are considered in the system. A new modeling method is presented in this paper. First, we introduce approximations of pressure based on the relation of pressure and velocity. We furthure decouple the approximated pressure from velocity so that it can be solved independently by continuous Galerkin finite element method. The new problem involves less degree of freedom than the mixed method for a given mesh . Moreover, local problem associated with a small subdomain around the fault is additionally solved to increase the accuracy of approximations around fault. Numerical experiments are conducted to examine the accuracy and efficiency of the new method. Results of three-dimensional tests show that our new method is up to 30$\times$ faster than the the mixed method at given $L^2$ pressure error.