An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers

Abstract

Three different conceptual frameworks have been adopted in the past for the development of mathematical models of bacterial growth and biologically reacting solute transport in saturated porous media. Two schools of thought are based upon assuming that the pore scale geometrical configuration of the attached bacteria consists of biofilms or microcolonies; the third school of thought represents the traditional approach where pore scale processes are neglected and the bacteria are assumed to respond to the macroscopic bulk fluid substrate concentration. On the basis of a schematic block diagram representation of a saturated porous medium hosting a microbial population, it is shown that these frameworks share a common theoretical foundation, and that they differ only by the choice of particular constitutive equations for several transfer parameters. Using one possible option in this respect, we derive a mathematical model that involves no unwarranted assumption about the distribution of the microorganisms in the pore space. The governing equations of this latter model are shown to be formally identical to those obtained by F.J. Molz et al. (1986), using the concept of microcolony, and to those that would result from adopting a simple form of biofilm model to describe bacterial growth in the pore space. Some of the consequences of this formal similarity between macroscopic transport equations obtained in different conceptual frameworks are discussed from an operational standpoint and in terms of model validation.