Stochastic analysis of transport and decay of a solute in heterogeneous aquifers

A stochastic analysis of transport and first-order decay for a solute plume in a three-dimensionally heterogenous aquifer shows that a spatially variable decay rate produces effects both in the transient and steady state characteristics of the effective decay rate, effective solute velocity, and longitudinal macrodispersivity. The effective decay rate is found to be less than the mean, which implies that decay predictions that employ spatial averages of observations will tend to overestimate the rates of mass transformation due to decay. The effective solute velocity is found to be the only field scale coefficient dependent on the correlation between decay and log hydraulic conductivity. The longitudinal macrodispersivity is found to be reduced relative to that of a conservative/nondecaying solute. The characteristic timescale of the transient development of all field-scale coefficients is reduced by the presence of a heterogeneous decay rate. All of these trends are accentuated with increasing decay rate variability. Increased peak concentrations, earlier arrival times, and decreased plume spreading are practical consequences of the derived results. The stochastic analysis presented here provides a vehicle to link laboratory-scale measurements with these field-scale predictions.