A Darcy-Brinkman Model of Fractures in Porous Media

TL;DR

This paper analyzes the limiting behavior of a coupled Darcy-Stokes system as the channel width approaches zero, deriving a reduced model involving Darcy flow in the porous medium and Brinkman flow along the interface.

Contribution

It introduces a new limiting model for coupled Darcy-Stokes systems with narrow channels, connecting porous media flow with Brinkman flow at the interface.

Findings

The limit problem is a coupled Darcy-Brinkman system.

The model captures the interface behavior as the channel width tends to zero.

Provides a rigorous mathematical characterization of the limiting process.

Abstract

For a fully-coupled Darcy-Stokes system describing the exchange of fluid and stress balance across the interface between a saturated porous medium and an open very narrow channel, the limiting problem is characterized as the width of the channel converges to zero. It is proven that the limit problem is a fully-coupled system of Darcy flow in the porous medium with Brinkman flow in tangential coordinates of the lower dimensional interface.