Injection of Fluid Into a Layer of Deformable Porous Medium

Abstract

The flow of fluid from a point source into a layer of deformable porous material is considered. The main applications of this work are to subcutaneous injections and subterranean soil flows. The porous material is assumed to be an isotropic, homogeneous, linearly elastic solid. The governing equations are derived for an axisymmetric geometry using linear poro-elasticity and are applied to the situation of a point source at some height z = z0 with a line sink at a distance r = ρ. These are solved analytically using Hankel transform techniques with the Hankel inversion integrals calculated numerically. Results are given for the pressure contours and the displacement of the solid matrix for a variety of source heights and elastic parameters. These indicate the swelling of the medium and subsequent deformation of the free surface. Results indicate regions where one dimensional models may be applicable.