Stochastic analysis of contaminant transport in heterogeneous structured porous media: A dual-porosity/permeability approach

Groundwater flow and solute transport in fissured and fractured formations have been the subjects of intensive investigation in the last several decades. Many environmental projects seeking safe repositories for hazardous wastes have been conducted in fractured media. Prediction of the contaminant transport is a critical requirement for waste containment design and evaluation of remediation efforts.; Complex heterogeneity of natural media and scarcity of the available field data preclude use of deterministic models. Therefore, various stochastic approaches have been developed to study the flow and transport in heterogeneous media [Gelhar, 1986; Dagan, 1986]. However, most stochastic studies, particularly analytical studies, are limited to unstructured porous media with mild heterogeneity. Few stochastic studies have been conducted for transport in structured media.; In this dissertation, the nonlocal, Eulerian stochastic perturbation method has been applied to conduct a series of studies on transport of solute in structured/fractured porous media. The dual-porosity/permeability model is adopted to describe flow and transport in structured media. The hydraulic conductivity, sorption coefficients and degradation rates in both flow domains are treated as spatial random variables to describe the heterogeneous nature of the media. A first-order interregional mass transfer model is adopted to describe the diffusive mass transfer between different flow domains. The transfer rate coefficient is also treated as spatial random variable since the transfer process is heterogeneous over all scales. The analytical solutions for the mean concentrations are explicitly expressed in spatial-Fourier and temporal-Laplace transforms and are numerically inverted back into real space via Fast Fourier Transform. The influences of the various random parameters on solute transport are investigated. This dissertation provides a general analytical solution for transport in fractured media undergoing multiple processes, and the general solution is consistent with the solutions under various simplified scenarios.; This dissertation also develops a numerical Monte Carlo simulation approach, including particle-tracking and random walk techniques, to investigate the validity and accuracy of the analytical solutions. The comparison between the two methods reveals that the analytical solution is quite robust in predictions of mean concentrations for structured media with mild heterogeneity within each flow domain.