Analytical solutions for anomalous dispersion transport

Groundwater flow and transport often occur in a highly heterogeneous environment (potentially heterogeneous at multiple spatial scales) and is impacted by geochemical reactions, advection, diffusion, and other pore scale processes. All these factors can give rise to large-scale anomalous dispersive behavior that can make complex model representation and prediction of plume concentrations challenging due to difficulties unraveling all the complexities associated with the governing processes, flow medium, and their parameters. An alternative is to use upscaled stochastic models of anomalous dispersion, and this is the approach used here. Within a probabilistic framework, we derive a number of analytical solutions for several anomalous dispersion models. The anomalous dispersion models are allowed to be either non-Gaussian (α-stable Lévy), correlated, or nonstationary from the Lagrangian perspective. A global sensitivity analysis is performed to gain a greater understanding of the extent to which uncertainty in the parameters associated with the anomalous behavior can be narrowed by examining concentration measurements from a network of monitoring wells and to demonstrate the computational speed of the solutions. The developed analytical solutions are encoded and available for use in the open source computational framework MADS (http://mads.lanl.gov).