Time‐dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers

Abstract

The expected values of the spatial second‐order moments of a solute body transported by groundwater are derived for flow through heterogeneous formations of a stationary random anisotropic structure. They are based on a general formulation, which reduces to most existing results in the literature as particular cases. Detailed results are given for the spatial variance as a function of time in the case of axisymmetric anisotropy, average flow parallel to the plane of isotropy, first‐order approximation in the log conductivity variance σ Y 2 , and high Peclet numbers. These results fill the gap existing between the studies of Dagan (1982, 1984), on one hand, and those of Gelhar and Axness (1983) and Neuman et al. (1987), on the other. A preliminary investigation of the higher‐order effects in σ Y 2 suggests that the use of the first‐order approximations is warranted, at present, only for σ Y 2 ≪ 1. The impact of the errors of estimation of the parameters on which transport depends is briefly analyzed.