Extension of porosity and surface area models for uniform porous media

The porosity and specific surface of a porous media coated with an accumulating film is evaluated geometrically to take account of limitations to film growth imposed by contact between particles and the film as it develops around the particles. By representing the media with regularly packed spheres, and assuming a uniform film thickness, equations are derived to allow the calculation of porosity and specific surface area as a function of film thickness for each of the four possible regular packing arrangements for both thin and thick films. It is shown that previous models begin to break down at a ratio 2L(t)/d(p) of film thickness, L-t to particle diameter, d(p) of 0.41 for a cubic packing, and 0.15 for an orthorhombic, tetragonal, or rhombohedral packing. Thus, although the previous models may give acceptable results for thin films, such as those encountered in wastewater engineering, they give erroneous porosities and specific surfaces when used to model the thicker films that occur as landfill leachate collection systems clog. Using the new equations it is shown that the porosity is reduced to 10% of its original value (and thus deemed clogged) for dimensionless film thicknesses 2L(t)/d(p) of 0.39, 0.31, 0.20, and 0.18 for the cubic, orthorhombic, tetragonal, and rhombohedral packing arrangements, respectively using the corrected equations. The model is intended for use in estimating the clogging rate of landfill leachate collection systems because of the buildup of thick biological and mineral films.