I will present a new macroscopic model for bioremediation which incorporates the decrease in effective porosity due to biomass accumulation and resultant changes in physical and chemical processes. The model consists of advection-reaction-diffusion equations for a sorbing contaminant and a nutrient, a growth and decay differential equation for a native microbial population, Darcy's Law for the velocity, and a constitutive equation for the permeability. By defining a new expression for the relationship between porosity and microbial concentration based on the volume of pore space occupied by biomass, the model is able to capture the important large scale dynamics and provide insight into the onset and control of clogging. The model is validated by reproducing data from an experimental study.
The model also demonstrates the importance of flow boundary conditions on bioclogging. For dense biofilms and the constant inflow conditions which are often imposed in laboratory experiments, the results of the model closely match those of a constant porosity model. The rate of degradation and the speed of the concentration fronts do not vary significantly. Analytical results have been derived for the constant porosity model and we show which results carry over to the new model. Conversely, under constant pressure boundary conditions which are more representative of field studies, the results of the variable porosity model are dramatically different. We explore the parameter regime which leads to clogging and derive expressions for the porosity dependent speeds of the fronts and the percent degraded at a given time.