**Effects of Upscaling Nonlinear Processes in Porous Media Flow Systems**
Nonlinear processes govern many porous media phenomena of environmental interest.These include traditional nonlinear relationships that occur in multi-phase flow systems; geochemical reactions in reactive transport systems; and interactions among soils, water, and plants in shallow subsurface ecosystems. In each of these
systems, information on nonlinear relationships is usually given at the local scale, based on measurements or other observations at that scale. For practical simulations, the equations describing the phenomena need to be written at larger averaging scales, and therefore some form of upscaling must be adopted. The process of upscaling has the effect of modifying the local-scale nonlinear relationships such that the upscaling process itself generates some combination of (1) modified nonlinearities, (2) hysteresis, and (3) apparent dynamics. In this presentation I will give examples of each of these effects of upscaling, using the three example systems identified earlier. For traditional
two-phase flow, I will consider upscaling relative permeability functions in a structured heterogeneous domain, as well as the emergence of dynamics in the relationship between capillary pressure and saturation; for reactive transport, I will illustrate the emergence of dynamics in rock-water geochemistry; and for shallow ecosystems, I will demonstrate the emergence of hysteresis in functional relationships that describe water uptake by
plant roots. |