Biofilm growth and the related changes in the physical properties of a porous medium: 2. Permeability
Growth of a biofilm in a porous medium reduces the total volume and the average size of the pores. The change in the pore size distributions is easily quantified when certain geometric assumptions are made. Existing models of permeability or of relative permeability can be manipulated to yield estimates of the resulting reduction in permeability as a function of biofilm thickness. The associated reductions in porosity and specific surface can be estimated as well. Based on a sphere model of the medium, the Kozeny-Carman permeability model predicts physically realistic results for this problem. Using a cut-and-random-rejoin-type model of the medium, the permeability model of Childs and Collis-George yields qualitatively reasonable results for this problem, as does a generalization of the relative permeability model of Mualem. Permeability models of Kozeny-Carman and of Millington and Quirk lead to unrealistic results for a cut-and-random-rejoin-type medium. The Childs and Collis-George and the Mualem models predict that the permeability reduction for a given volume of biomass is greatest when the porous medium has uniform pore sizes.