3 - Nonlocal reactive transport with physical and chemical heterogeneity: linear nonequilibrium sorption with random rate coefficients

Summary

ABSTRACT A nonlocal, first-order, Eulerian, stochastic theory was developed for the mean concentration of a conservative tracer. This was extended to account for nonequilibrium linear sorption with random partition coefficient, K_d, but deterministic rate constant, K_r. Here we extend these results to account for both random K_d and K_r. The basic governing balance law for mean solution-phase concentration is nonlocal in space and time. Nonlocality is manifest in a dispersive flux, an effective convective flux and in sources and/or sinks. The mean concentration balance law is solved exactly in Fourier–Laplace space and numerically inverted to real space. Mean concentration contours and various spatial moments are presented graphically. All results simplify to earlier results under appropriate conditions. The results indicate that there are gaps in existing data sets at major reactive-chemical study sites. The model also suggests the need to design new experiments, and it further suggests that a number of novel correlation functions should be obtained.

INTRODUCTION

Our goals in this work are two-fold. First we highlight the need for nonlocality in transport theory, and secondly we extend our previous reactive transport (Hu, Deng & Cushman, 1995) model to account for both random forward and backward rate coefficients. We limit our attention here to porous media that have two natural scales: a scale on which Darcy's and Fick's laws hold locally (see Dagan, 1989; Gelhar, 1993) and a larger scale defined in terms of the integral scale of the log-fluctuating conductivity. These latter assumptions, while restrictive, are consistent with the main body of literature on transport in porous media.