On the singular limit of a two‐phase flow equation with heterogeneities and dynamic capillary pressure

Abstract

We consider conservation laws with spatially discontinuous flux that are perturbed by diffusion and dispersion terms. These equations arise in a theory of two‐phase flow in porous media that includes rate‐dependent (dynamic) capillary pressure and spatial heterogeneities. We investigate the singular limit as the diffusion and dispersion parameters tend to zero, showing strong convergence towards a weak solution of the limit conservation law.

Numerical modeling of the two-phase flow in porous media with dynamic capillary pressure

“…The heterogeneous case of two-phase porous media flow model, in which dynamic effects are taken into account in phase pressure difference is investigated in [33,67]. In [67], the authors investigate the singular limit as the diffusion and dispersion parameters tend to zero, showing strong convergence towards a weak solution of the limit conservation law. In [33], the authors consider a one-dimensional heterogeneous case, with two adjacent homogeneous blocks separated by an interface.…”