Upscaling Flow and Transport Processes

Abstract

This chapter deals with flow, transport and reaction processes in porous and heterogeneous media characterised by multiple spatial scales. Although the governing equations, at the micro-scale, are simple (and often linear), complex upscaled (effective macro-scale) phenomena can emerge, due to the averaging process. After introducing some general concepts related to multiscale porous media, we present the Darcy’s equation and its assumptions and extensions. A more detailed analysis of dispersion theories for pore-scale and continuum-scale (with Darcy’s flow) solute transport is then carried out, presenting the classical results as well as the most recent research in the field. We then focus on the interaction between dispersion and reaction, through mixing, as well as more complex processes like particle deposition and multiphase flows.