Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers

Abstract

Spatial moment analysis is used in this paper to study the asymptotic, long‐time behavior of the depth‐averaged solute plume for transport in a perfectly stratified aquifer. The solute is assumed to adsorb onto the aquifer solids according to a first‐order reversible kinetic rate law; steady, unidirectional, horizontal flow is assumed with arbitrary vertical variation in pore water velocity, dispersion coefficients, and adsorption reaction parameters. We derive general formulas to calculate the effective dispersion coefficient governing the transport of the depth‐averaged plume. The results demonstrate that overall longitudinal spreading of the plume results from three distinct factors: local Darcy scale longitudinal dispersion, vertical variations in the pore water velocity and retardation factor, and adsorption kinetics. For the example of a two‐layer aquifer, a simple nonequilibrium index is derived which shows that deviations from local equilibrium diminish as the degree of heterogeneity of the retarded pore water velocity increases. It is also demonstrated that enhanced plume spreading can be caused by negative correlation between the vertically varying pore water velocity and retardation factor in addition to slow adsorption kinetics. Thus great caution is warranted in interpreting the results of field scale reactive tracer experiments.