Upscaling for Multiphase Porous Flow

Ethan Coon, Columbia University

In the study of porous flow, material properties vary widely on very small scales, while the desired computational domain may be many orders of magnitude larger than the scale of this variation. To bridge the gap in scales, upscaling (or homogenization) methods provide a means of taking the important information from fine-scale data to the coarse scale. Variational multigrid provides a natural hierarchy of models on varying grid levels, where, at each level, a correction is determined to minimize error given an interpolation between levels and an operator (or PDE) at the finest level. This allows us to formulate a multilevel upscaling algorithm where equations and data specified on a fine scale are used to generate a physically consistent model on a much coarser scale. Here we will introduce the algorithm and consider its application to multiphase flow in oil reservoirs.

Abstract Author(s): Ethan T. Coon (Columbia University)<br />Scott P. MacLachlan (Delft University of Technology)<br />J. David Moulton (Los Alamos National Laboratory)