The influence of the plume scale on the early time variability in cumulative solute mass in heterogeneous aquifers

The influence of the initial plume scale on the early time variability in cumulative solute mass across a control plane for advection dominated nonreactive solute movement in a heterogeneous three-dimensional aquifer is investigated. Under an assumption of a Gaussian velocity distribution, the closed-form expressions for the early time probability distribution function of travel times and coefficient of variation of cumulative solute mass are derived for the case of statistically isotropic media as functions of the initial plume size, the variance of the log hydraulic conductivity, the correlation scale of the log hydraulic conductivity, and the mean longitudinal velocity. These results are achieved by invoking a modified variance of longitudinal velocity, accounting for the influence of a finite domain size. It is found that at early time, the initial plume size has significant influence on the variability in cumulative solute mass in the case of a finite volume source. The presented methodology can be extended to statistically anisotropic media.