Interface conditions for Biot’s equations of poroelasticity

Abstract

Interface conditions at a boundary between two porous media are derived directly from Biot’s equations of poroelasticity by replacing the discontinuity surface with a thin transition layer, in which the properties of the medium change rapidly yet continuously, and then taking the limit as the thickness of the transition layer approaches zero. The interface conditions obtained in this way, the well known “open-pore” conditions, are shown to be the only ones that are fully consistent with the validity of Biot’s equations throughout the poroelastic continuum, including surfaces across which the medium properties are discontinuous. But partially blocked or completely impermeable interfaces exist; these may be looked upon as the case of a thin layer with its permeability taken to be proportional to the layer thickness, again in the limit as layer thickness approaches zero. This approach can serve as a simple recipe for modeling such an interface in any heterogeneous numerical scheme for poroelastic media.