Flow of fluids through porous media.

Abstract

A three-dimensional transient equation for the flow of any time-independent incompressible fluid, Newtonian or non-Newtonian, through compressible porous media has been derived. Equations applicable to Ostwald-de Waele fluids, Bingham fluids, and Newtonian fluids are deduced directly from the general transient equation. It is shown that the one-dimensional filtration equation derived by Tiller is only a special case of the general flow problem. An equation describing the fowl of a compressible fluid (ideal gas) through compressible porous media is also developed. It reduces to the ordinary unsteady flow equation through incompressible porous media when the porosity and specific cake resistance are constant. The usefulness of the integral method in arriving at a reasonable solution to the one-dimensional constant pressure filtration problem is tested utilizing a linear pressure profile through the cake.