Stochastic analysis of virus transport in aquifers

A large-scale model of virus transport in aquifers is derived using spectral perturbation analysis. The effects of spatial variability in aquifer hydraulic conductivity and virus transport (attachment, detachment, and inactivation) parameters on large-scale virus transport are evaluated. A stochastic mean model of virus transport is developed by linking a simple system of local-scale free-virus transport and attached-virus conservation equations from the current literature with a random-field representation of aquifer and virus transport properties. The resultant mean equations for free and attached viruses are found to differ considerably from the local-scale equations on which they are based and include effects such as a free-virus effective velocity that is a function of aquifer heterogeneity as well as virus transport parameters. Stochastic mean free-virus breakthrough curves are compared with local model output in order to observe the effects of spatial variability on mean one-dimensional virus transport in three-dimensionally heterogeneous porous media. Significant findings from this theoretical analysis include the following: (1) Stochastic model breakthrough occurs earlier than local model breakthrough, and this effect is most pronounced for the least conductive aquifers studied. (2) A high degree of aquifer heterogeneity can lead to virus breakthrough actually preceding that of a conservative tracer. (3) As the mean hydraulic conductivity is increased, the mean model shows less sensitivity to the variance of the natural-logarithm hydraulic conductivity and mean virus diameter. (4) Incorporation of a heterogeneous colloid filtration term results in higher predicted concentrations than a simple first-order adsorption term for a given mean attachment rate. (5) Incorporation of aquifer heterogeneity leads to a greater range of virus diameters for which significant breakthrough occurs. (6) The mean model is more sensitive to the inactivation rate of viruses associated with solid surfaces than to the inactivation rate of viruses in solution.