Mass transport: 1. A stochastic analysis of macroscopic dispersion

Conventional modeling of mass transport in groundwater systems usually involves use of the dispersion‐convection equation with large values of porous medium dispersivity to account for macroscopic dispersion. This work describes a modeling concept which accounts for macroscopic dispersion not as a large‐scale diffusion process but as mixing caused by spatial heterogeneities in hydraulic conductivity. The two‐dimensional spatially autocorrelated hydraulic conductivity field is generated as a first‐order nearest‐neighbor stochastic process. Analysis of a variety of hypothetical media shows that over finite domains a population of tracer particles convected through this statistically homogeneous conductivity field does not have the normal distribution and does not yield the constant dispersivity that classic theory would predict. This problem occurs because of insufficient spatial averaging in the macroscopic velocity field by the moving tracer particles. Our analyses suggest that the diffusion model for macroscopic dispersion may be inadequate to describe mass transport in geologic units. Sensitivity analysis with the model has shown that features of transport, such as first arrival of a tracer, are dependent on porous medium structure and that even when the statistical features of porous media are known, considerable uncertainty in the model result can be expected.