Multiple-scale analysis of transport in porous media with biofilms

摘要

Biodegradation in porous media is most often the consequence of coupled transport phenomena in the presence of biofilms. The description of such transport problems involves different scales: the bacteria scale, the scale of a locally homogenized biofilm, heterogeneous biofilms at a scale lower than the pore-scale, the pore-scale problem, the Darcy-scale description, and, possibly, subsequent scales corresponding to heterogeneities effects. In this paper, various upscaling problems are reviewed. Different models may be built, depending on the amount of local non-equilibrium included in the analysis: equilibrium models, multiple-equations models, asymptotic models. These different models feature different effective properties, which can be estimated from real data through the resolution of several "closure problems" linking averaged variables and lower-scale deviations. The relevance of these different models is discussed based on some theoretical analysis and direct numerical simulation.