Dimensional reduction of a fractured medium for a two-phase flow

Abstract

We consider a porous medium containing a single fracture, and identify the aperture to length ratio as the small parameter ɛ with the fracture permeability and the fracture porosity scaled as exponents of ɛ. We consider a two-phase flow where the flow is governed by the mass balance and the Darcy law. Using formal asymptotic approach, we derive a catalogue of reduced models as the vanishing limit of ɛ. Our derivation provides new models in a hybrid-dimensional setting as well as models which exhibit two-scale behaviour. Several numerical examples confirm the theoretical derivations and provide additional insight.