Multidimenstional Models for Macroscopic Virus Transport in Porous Media
Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace, Fourier, and finite Fourier cosine transform techniques. Instantaneous and continuous/periodic virus loadings from either a point or an elliptic source geometry are examined. Furthermore, porous media with either infinite, semi-infinite, or finite thickness are considered. The effects of virus loading conditions, aquifer boundary conditions, and virus source geometry on virus migration in subsurface porous formations are investigated.
A model for virus transport in one-dimensional, homogeneous, saturated porous media is also developed, accounting for virus sorption and inactivation of liquid phase and adsorbed viruses with different time dependent rate coefficients. The virus inactivation process is represented by a pseudo first-order rate expression. The pseudo first-order approximation is shown to simulate available experimental data from three virus inactivation batch studies better than the frequently employed constant rate inactivation model. Model simulations indicated that the pseudo first-order approximation, compared to the constant inactivation, leads to extended survival of viruses, and consequently more distant migration. Results from a parameter sensitivity analysis demonstrated that estimation of pseudo first-order inactivation rate coefficients from field observations requires data collection near the source of virus contamination during initial stages of virus transport.