Approximate and Analytic Solutions for Deformation of Finite Porous Filters

Abstract

The deformation, using linear poroelasticity, of a two-dimensional box of porous material due to fluid flow from a line source is considered as a model of certain filtration processes. Analytical solutions for the steady-state displacement, pressure, and fluid velocity are derived when the side walls of the filter have zero solid stress. A numerical solution for the case where the porous material adheres to the side walls is also found. It will be shown, however, that simpler approximate solutions can be derived which predict the majority of the deformation behavior of the filter.