Improved Solutions for Porosity and Specific Surface of a Uniform Porous Medium with Attached Film

Abstract

Improved solutions for the porosity and specific surface of uniform porous media with the attached film are provided for four regular packing arrangements. These solutions overcome the limitations of previous solutions, which did not cover the full range of film thicknesses to complete occlusion of the pore space in the porous media. The void spaces within the clogged porous media are analyzed geometrically. The exact solutions for the volume and surface area of overlapping shapes and isolated void spaces are formulated in terms of integrals. New polynomial solutions are proposed to replace the numerical integration in the complete solutions to allow easy implementation in numerical models. With the new solutions, both the porosity and specific surface gradually decrease from the initial values to zero when the film increases to complete pore occlusion. These solutions have application in numerical modeling of the growth of organic mass and deposition of inorganic mass in leachate collection systems and other similar systems in which there maybe growth of a semipermeable film on the surface of the particles in a relatively uniformly graded granular porous medium.