Nonlocal nonreactive transport in heterogeneous porous media with interregional mass diffusion

Abstract

We present a Eulerian stochastic analysis for nonreactive transport in a heterogeneous, structured medium. A first‐order mass diffusion model (or mobile and immobile model) is applied to describe interregional mass diffusion between advection and nonadvection (mobile and immobile) regions. Spatial variabilities in the media motivate us to treat the interregional mass diffusion coefficient a and hydraulic conductivity K as spatial random variables. The two random variables are assumed to correlate with each other. The analytical solution for mean concentration is given explicitly in Fourier and Laplace transforms and is numerically inverted to real space via fast Fourier transform. Various factors that affect mass diffusion and transport processes are investigated by plotting spatial moments up to third and mean concentration contours. It is shown from the calculation results that interregional mass diffusion will significantly increase plume dispersion in both longitudinal and transverse directions and make the plume negatively skewed and give the breakthrough curve a long tail. In comparison with the case with a deterministic a, randomness of the parameter will increase the plume dispersion and make the plume more skewed, especially for the case where a is negatively correlated with K.