A dual-porosity theory for solute transport in biofilm-coated porous media

In this work, we derive a Darcy-scale model for solute transport in porous media colonized by biofilms. Biofilms refer to structured communities of microbial cells that grow attached to an aqueous interface, e.g., the pore walls of a water-saturated porous medium. First, we present the pore-scale description of mass transport within and between the phases (water phase and biofilm phase) including the biologically-mediated reactions. Then, a two-equation Darcy-scale mass balance model (classically referred to as dual-porosity model), suitable both for local equilibrium and non-equilibrium conditions, is obtained from the method of volume averaging. Application of this macroscopic model to complex pore geometry of a two-dimensional porous medium supporting biofilms is presented. Comparisons with direct numerical simulation results confirm the large range of validity of the model. Finally, an illustrative example based on a scenario of reactive transport experimental tests is used to point out conditions for when the use of the proposed model is required.