A simple velocity random-walk model for macrodispersion in mildly to highly heterogeneous subsurface formations

Recently, we have analytically derived a temporal velocity random-walk model for macrodispersion or transport uncertainty quantification based on velocity statistics from classical first-order perturbation expansions. The applicability of these expansions is limited to mildly heterogeneous formations with log-conductivity variances σY2<1. In this work, we reformulate our model in order to account for velocity skewness and inter-component correlation that emerge as key drivers of non-Fickian dispersion at elevated heterogeneity levels σY. Eventually, we arrive at a light-weight parametrization of macrodispersion that is consistent with our earlier formulation, but at the same time is applicable for formations with multi-Gaussian log-conductivity characterization of variable heterogeneity, i.e. σY from 0 to 1 and beyond.