How Can We Account for Micro-scale Biodegradation Processes in Macro-scale Models of Contaminant Transport and Degradation?

Mathematical models for contaminant fate and transport in groundwater are generally defined at the macro-scale, i.e., at spatial scales larger than a single pore or grain of aquifer material. In such models, it is convenient and practical to incorporate mathematical descriptions of chemical reactions that depend upon concentrations defined at similar scales. The problem with this approach is that, for contaminants that undergo biologically- mediated degradation, the actual reaction process depends upon diffusion and reaction in micro-scale (pore- scale or smaller) biofilms or bacterial colonies. Thus, it is not inherently clear how we should account for biodegradation in macroscopic models of contaminant transport. Two approaches may be viable: (1) the microscropic processes may be "upscaled" to a macro-scale mathematical representation that is appropriate for the application of interest, or (2) the microscopic processes may be described explicitly at the appropriate scale, then linked to the macro-scale equations for contaminant transport. In this presentation, we report on our work toward both approaches. Under certain circumstances, micro-scale biodegradation processes may be upscaled to a "lumped" macro-scale reaction rate constant that accounts for several microscopic processes. When this is not feasible, micro-scale equations for diffusion and reaction can be coupled to macro-scale equations for transport by advection and dispersion. Solving these coupled equations can be computationally expensive, especially when the biofilm reaction kinetics are considered to be non-linear. We report on numerical methods that may be employed to solve the coupled system efficiently.