The narrow fracture approximation by channeled flow

Abstract

The singular problem of non-stationary Darcy flow in a region containing a narrow channel of width O( ) and high permeability O ( 1 ) is shown to be well approximated by a problem with flow concentrated on a weighted Sobolev space over a lower-dimensional interface.The convergence of the solution as → 0 is proved for both the stationary case and the corresponding initial-boundary-value problem. The structure of the limiting problems is dependent on the rate of taper of the channel at its extremities.

First-order indicators for the estimation of discrete fractures in porous media

“…It requires to solve the adjoint limit fault model (31) for λ N and ν E,N , but only on the candidate fault.…”

“…In this model, fractures lie along the edges of the mesh and can be easily opened or closed by adjusting the fracture parameters on edges, which makes it convenient for the purpose of fracture determination. This model has been extended so that one may use non-matching grids [20,33], or disconnect the fracture mesh from that of the domain [31,16]. It has also been extended to treat Forchheimer flow in the fracture [21,27], and multiphase flow [32], but these extensions are not considered in this paper.…”

Analysis of a Coupled Darcy Multiple Scale Flow Model Under Geometric Perturbations of the Interface

“…Consider the solution of the strong problem (5) presented in Morales and Showalter (2012) and in a less general version in Morales and Showalter (2010). Such solution is to be compared with the solution of the system (6) corresponding to a geometric perturbation of the interface…”

Modeling, Analysis and Simulation of Multiscale Preferential Flow - 8/05-8/10 - Final Report

“…Preliminary work involved the analysis of more traditional models in which the channel flow is modeled by a Darcy system with large permeability, as would occur in debris-filled fractures. See [4,5,6,7] below. 3.…”