Conditions for choking in a poroelastic flow model

We consider a steady Darcy flow of fluid through a section of poroelastic material under an applied pressure difference. In porous media flow, the superficial fluid velocity and applied pressure gradient are related by a permeability such that, when the porous material is rigid, specifying either the flow rate or the applied pressure difference allows the determination of the other quantity and flow will occur for all non-zero applied pressure gradients. When the underlying solid matrix is a deformable elastic material and the fluid permeability can vary with applied strain on the solid matrix, then the permeability can reduce to zero and the solid matrix become impermeable, so that flow is not possible and no steady solution exists. We examine existing steady poroelastic equations for a number of different well-known elastic models and permeability-strain relations and consider solutions for the resulting steady strain and fluid flow. We solve the governing equations numerically for some example situations and propose a sufficient condition on the functional form of the permeability-strain relation for solutions to exist for any specified applied pressure.