Numerical simulation of solute transport in three‐dimensional, randomly heterogeneous porous media

TLDR

The study develops a 3‑D solute transport model to examine how variable flow fields affect large‑time, large‑scale solute plume development and dispersive behavior in heterogeneous porous media. The model uses a random walk particle method (RWPM) to efficiently simulate multidimensional advection and dispersion in saturated or unsaturated media, with numerical experiments on single realizations of random hydraulic conductivity fields at three heterogeneity levels and varying source locations to probe preasymptotic and nonergodic plume evolution. Simulations show that longitudinal advection and mixing moments agree with stochastic theory, while transverse mixing moments deviate, and reveal pronounced nonergodic effects manifested as large differences in second‑moment evolution across experiments.

Abstract

A three‐dimensional solute transport model has been developed to study detailed contaminant movements through large heterogeneous flow systems in porous media. The model is based upon a random walk particle method (RWPM) which can readily treat multidimensional advection and dispersion processes in saturated or unsaturated media in a computationally efficient manner. The transport simulations are used to examine the large time and spatial effects of the variable flow field on developing solute plumes, and, in particular, to investigate the nature of the large‐scale dispersive behavior. Numerical transport experiments were conducted using single realizations of random hydraulic conductivity fields with three different degrees of heterogeneity. Experiments with different source locations were used to investigate preasymptotic and nonergodic effects that would appear as differences in plume evolution among the experiments. Analyses of the simulations indicate the spatial moments of the particle distributions in statistically isotropic saturated media compare favorably with stochastic theory predictions in terms of longitudinal advection and mixing, but differ markedly from predictions of transverse mixing. The simulations also demonstrate that significant nonergodic effects occur, as reflected in strong differences in the second moment evolution curves among the individual experiments and as predicted from the ensemble stochastic theory.