Compressible flow in fractured porous media with an unbounded density-pressure law

Abstract

We consider a compressible viscous flow in a bounded porous domain which consists of two parts: A system G₁ of fractures antl a system G₂ of porous blocks. It is assumed that the blocks G₂ have a low permeability and the main flow occurs through G₁ whereas the bulk porosity of G₁ is very small cotnparetl to the one of G₂. The material laws relating pressures and densities are supposed to be single-valued (i.e. the local pressure defines the local density and vice versa) but unbountletl thus allowing for power- and exponential laws, e.g. Following the idea of “Two-Compartment” models, separate pressure pi (i = l , 2 ) for the flow in the two compartments and G₁ and G₂Gare introduced. The resulting (possibly) highly nonlinear equations are shown to be well-posed in appropriate Hölder spares. As a by-product one obtains the convergence of a reiteration scheme as well as some sort of a maximum principle for the resulting pseudo-parabolic initial boundary value problem.

Keywords:

• fractured porous media
• evolution problem
• regularity of solutions
• global existence
• uniqueness