Hydraulic conductivity and dispersion upscaling for high-dimensional groundwater flow and transport

Porous geologic formations display complex heterogeneity at various scales. To describe groundwater flow and transport processes more accurately, one must develop models that honor the heterogeneity and anisotropy of porous media as much as possible. Specifically, representing hydraulic conductivity and dispersion coefficients appropriately at different scales is the first step for constructing a numerical groundwater model for use in remediation applications. Here, we will start with widely used groundwater flow and conservative transport (advection-dispersion) models and upscale isotropic hydraulic conductivity and dispersion fields of fine resolution into anisotropic ones, represented through tensors of conductivity and dispersion, at a coarser scale.
Through numerical experiments, we will present how upscaled hydraulic conductivity and macrodispersion coefficients change with respect to different grid size and heterogeneity scale and discuss the role of diffusion and mean velocity. We will also list conditions under which the Fickian dispersion model is justified, then present how a practical Fickian model can approximate what is often thought of as “non-Fickian.”