A spectral stochastic model of virus transport in aquifers

Linda L. Campbell Rehmann

doi:10.17918/00010150

This thesis presents derivation of a spectral stochastic model of field-scale virus transport in heterogeneous, saturated, granular porous media. The effects of small-scale spatial variability in aquifer parameters (e.g., hydraulic conductivity, pore water velocity) as well as virus attachment, detachment, and inactivation parameters on large-scale transport are evaluated. The stochastic mean model is developed from a simple coupled system of local-scale free virus transport and attached virus conservation equations containing transport phenomena expressions obtained from existing literature. The resultant mean equations are found to differ significantly from the local-scale equations, including, for example, modified advection, dispersion, attachment and detachment coefficients, as well as additional macroscopic gradient terms. These macroscopic effective parameters are complex functions of the local-scale transport processes. In order to fully understand the implications of the mean model and its sensitivity to input parameters, numerical simulations of the derived mean equations were conducted. In general, the mean transport model predicts significantly earlier breakthrough than the equivalent local-scale model. As the degree of heterogeneity (variance of the natural-logarithm hydraulic conductivity distribution) is increased, breakthrough occurs successively earlier to such a degree that for a highly heterogeneous aquifer, virus breakthrough can actually precede that of a tracer. Such behaviour has been observed in field and laboratory experiments, and has been attributed to the size exclusion effect. Increasing aquifer heterogeneity also results in decreased model sensitivity to the ratio of free to attached virus inactivation rates, most likely due to decreased residence time resulting from faster transport in higher hydraulic-conductivity lenses. Both the stochastic mean model and the local model are found to be more sensitive to the inactivation rate of the attached viruses than that of the free viruses, indicating that incorporating different rate constants for free and attached viruses is important. As the mean aquifer hydraulic conductivity is increased, the mean model shows less sensitivity to other input parameters such as InK variance and colloid diameter. Mean and modified local breakthrough curves differ the most for the least conductive aquifers studied. Because a more conductive aquifer would experience fewer interactions between colloids and its larger grains (i.e., less filtration), spatial variability would be expected to have less of a role than in a low-conductivity aquifer in which significant interactions occur between colloids and grain surfaces.

A spectral stochastic model of virus transport in aquifers

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A spectral stochastic model of virus transport in aquifers

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