Summary: THE EXISTENCE OF WEAK SOLUTIONS TO
SINGLE POROSITY AND SIMPLE DUAL-POROSITY MODELS
OF TWO-PHASE INCOMPRESSIBLE FLOW*
Todd Arbogast
Department of Mathematical Sciences,
Rice University, Houston, Texas 77251­1892
Key words and phrases: porous medium, dual-porosity, two-phase, elliptic-parabolic,
integro-differential, degenerate
Abstract. It is shown that there exists a weak solution to a degenerate and singu-
lar elliptic-parabolic partial integro-differential system of equations. These equa-
tions model two-phase incompressible flow of immiscible fluids in either an ordinary
porous medium or in a naturally fractured porous medium. The full model is of
dual-porosity type, though the single porosity case is covered by setting the matrix-
to-fracture flow terms to zero. This matrix-to-fracture flow is modeled simply in
terms of fracture quantities; that is, no distinct matrix equations arise. The equa-
tions are considered in a global pressure formulation that is justified by appealing
to a physical relation between the degeneracy of the wetting fluid's mobility and the
singularity of the capillary pressure function. In this formulation, the elliptic and
parabolic parts of the system are separated; hence, it is natural to consider various
boundary conditions, including mixed nonhomogeneous, saturation dependent ones

Source: Arbogast, Todd - Center for Subsurface Modeling & Department of Mathematics, University of Texas at Austin

Collections: Mathematics; Geosciences