ABSTRACT
Any mathematical model is an idealization of a real system at a specified scale. Assumptions and/or simplifications upon which such models are based enable their formulation, analytical and/or numerical treatment and, consequently, their use as predictive tools. The acceptance of a model derives from an optimal balance between simplicity and accuracy in capturing a system’s behavior on the one hand and computational costs on the other. Different models might offer optimal performances, both in terms of fidelity and computation, in various regimes. A further complication in model selection arises when a scale at which predictions are sought is much larger than a scale at which governing equations and first principles are well defined. This situation is particularly common in analysis of flow and transport in porous media: typical scales of interest for predictions are often many orders of magnitude larger than a scale at which most biochemical processes take place. Such complex systems are of particular interest because of their ubiquitous nature: they characterize a variety of environments ranging from geologic formations to biological cells, and from oil reservoirs to nanotechnology products.
