Relating recent random walk models with classical perturbation theory for dispersion predictions in the heterogeneous porous subsurface

Recently developed stochastic macro-dispersion models enable computationally inexpensive flow and transport predictions for highly heterogeneous formations with statistically non-stationary conductivity and flow statistics. So far, the random processes at the heart of these models have been calibrated numerically based on velocity statistics from Monte Carlo simulation studies. In this work, we provide a more rigorous foundation to some of these models by analytically relating the process definition to given velocity statistics from classical first-order perturbation expansions.