Moment Differential Equations, CTRW and Functional Renormalization to Predict Transport in Highly Heterogeneous Porous Media: Theory and Experiments

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

0207988 Sornette Transport in heterogeneous porous media poses formidable challenges to model and predict with good reliability. We propose to develop a microscopic physical basis for effective large scale models such as the continuous-time random walk (CTRW) method, which takes into account extreme fluctuations and anomalous transport paths in the contribution to the large scale transport properties. For this, we will use a combination of renormalization group and functional renormalization techniques to coarse-grain and extrapolate from the microscopic realm to the large-scale description. We also propose to generalize the CTRW model to a multi-scale hierarchical framework with standard local Poissonian-in-time and Gaussian diffusion-in-space describing microscopic processes, to investigate in what sense the coexistence of multiple scales is responsible for the effective anomalous power law properties, such as non-Gaussian distribution of trapping times and of jump sizes captured by the CTRW framework which are usually postulated at a phenomenological level.