Fluid flow in compressible porous media: I: Steady-state conditions

This is the first of two articles dealing with fluid flow in compressible porous media. In this article a model describing fluid flow and pressure-induced variations in porosity under stationary conditions is developed. In a forthcoming article the dynamic behavior during filtration and wet pressing of compressible porous media are presented. Fluid flow through rigid porous media is generally described by Darcy's law. The corresponding expression for compressible materials is derived in this article. This expression, the steady-state flow (SSF) equation, allows the steady-state flow to be easily calculated, either numerically, or by using the approximative analytical solutions that are also presented here. In the SSF equation optional empirical and/or theoretical permeability and compressibility relationships may be combined. Further, a new compressibility model which also applies for viscoelastic materials is presented. The influence of the compressibility of the material and the influence of precompression is illustrated.