Finite volume method for reduced multi-layer model of compressible Brinkman flow in high-dimensional fractured reservoirs with damage zones

Abstract

This work presents a development in the context of dimensionally reduced multi-layer models in three-dimensional fractured reservoirs, in which the fractures and damage zones are reduced to be surfaces. The single phase flow is governed by fully coupled models with Neumann boundary involving Brinkman equation in two-dimensional hydraulic fractures, Darcy equation in surrounding two-dimensional damage zones and three-dimensional rock matrix. A hybrid-dimensional finite volume method is proposed to demonstrate efficient handling of various multi-layer configurations with Brinkman-type and Darcy-type transmission interface conditions. Additionally, the convergence analysis of proposed numerical method yields fully space-time second-order on staggered nonuniform grids. The sensitivity analysis of effective viscosity is tested by numerical results for three-dimensional problems with intersecting fractures and damage zones to show the performance of the proposed method.