Multi-physics modeling of flow and transport in porous media using a downscaling approach

Multi-phase flow and transport processes generally occur on different spatial and temporal scales. Very often also, within a physical system, they vary in space meaning that different kinds of processes might take place in different parts of the system. In order to account for the variety of processes and to take their scale-dependence into account, the development of multi-scale multi-physics techniques can be envisaged.We extend a recently developed multi-scale multi-physics algorithm by Niessner and Helmig [Niessner J, Helmig R. Multi-scale modeling of three-phase–three-component processes in heterogeneous porous media. Adv Water Resour 2007;11(30):2309–25] where concentration equations were solved in a small part of the domain on a fine scale while pressure and saturation distribution were solved for in the whole physical system. While the saturation equation was upscaled to a coarser scale the pressure equation was still solved time-implicitly and on a fine scale. The new extension of this work is the upscaling of the pressure equation also. Where needed a downscaling approach provides fine-scale velocities.In this technical note, comparisons of the extended algorithm to the original one and to a fine-scale reference solution are shown. The major benefits of this extension are more flexibility with respect to the choice of scale and computational efficiency (the time-implicit solution of the fine-scale pressure equation is very costly) while maintaining a high accuracy.