A note on the solution of a poroelastic problem

Abstract

We examine the forced flow through a poroelastic matrix. This apparently simple problem turns out to exhibit some interesting difficulties, and in some circumstances the problem may not be well-posed. It can be regarded as the inverse of that problem where a given pressure difference is applied across a section of poroelastic material. There are two difficulties that arise. In one situation, for certain choices of the function relating permeability to the elastic deformation, compression of the matrix pores results in choking as the underlying matrix permeability deceases. In the second situation, the underlying elastic model fails because the Jacobian of the deformation becomes negative. We examine a sufficient condition on the functional form of the permeability-strain relation for solutions to exist for all flow rates.