Modelling and discretization of flow in porous media with thin, full-tensor permeability inclusions

TL;DR

This paper introduces a generalized reduced model for simulating fluid flow in fractured porous media with anisotropic, full-tensor permeability, addressing limitations of existing models that assume aligned principal directions.

Contribution

It presents a new mixed-dimensional discretization framework that captures full-tensor permeability effects in faulted porous media, including out-of-plane anisotropy.

Findings

Existing models fail with anisotropic fault zones.

The proposed method converges in 2D and 3D simulations.

Numerical examples demonstrate improved accuracy over traditional approaches.

Abstract

When modelling fluid flow in fractured reservoirs, it is common to represent the fracturesas lower-dimensional inclusions embedded in the host medium. Existing discretizationsof flow in porous media with thin inclusions assume that the principal directions of theinclusion permeability tensor are aligned with the inclusion orientation. While this mod-elling assumption works well with tensile fractures, it may fail in the context of faults,where the damage zone surrounding the main slip surface may introduce anisotropy thatis not aligned with the main fault orientation. In this paper, we introduce a generalizeddimensional reduced model which preserves full-tensor permeability effects also in theout-of-plane direction of the inclusion. The governing equations of flow for the lower-dimensional objects are obtained through vertical averaging. We present a framework fordiscretization of the resulting mixed-dimensional problem, aimed at easy adaptation ofexisting simulation tools. We give numerical examples that show the failure of existingformulations when applied to anisotropic faulted porous media, and go on to show theconvergence of our method in both 2D and 3D