Transport of sorbing solutes in randomly heterogeneous formations: Spatial moments, macrodispersion, and parameter uncertainty

Abstract

Expressions for the spatial moments and macrodispersion tensor for sorbing solutes in heterogeneous formations were presented using a probabilistic model of a fluid residence time coupled with the particle position analysis. The fluid residence time was defined as a fraction of the actual time during which the particle stayed in the mobile fluid phase of the aquifer. The fluid residence time is a random variable whose variability comes as a result of the non-equilibrium sorption properties. The sorbing solute was assumed to be governed with first-order linear kinetics. The closed-form expressions were based on the stationarity in the kinetic process and on the first-order approximation in the hydraulic conductivity field and in the fluid residence time. The non-equilibrium effects were presented as a function of the spatial variability in hydraulic conductivity and temporal variability in the fluid residence time. The importance of the non-equilibrium processes in the field scale was found to be dependent on reaction rates, retardation factor, mean velocity, and on variance and correlation scale of the hydraulic conductivity. The time needed to reach the asymptotic macrodispersivity is dependent on the degree of non-equilibrium processes and distribution coefficient. The impact from the uncertainty in parameters upon the spatialmore » moments was examined and compared with the organic tracer used in the Borden field experiment.« less