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.

Use of temporal moments to investigate the effects of nonuniform grain‐size distribution on the transport of sorbing solutes

“…The nonequilibrium index is a quantitative measure of when the LEA can be used in place of the LDF model or DSG model and can be defined with either temporal moments [Valocchi, 1985[Valocchi, , 1986[Valocchi, , 1990Parker and Valocchi, 1986] or spatial moments [Valocchi, 1988[Valocchi, , 1989Quinodoz and Valocchi, 1993]. The idea is simple and useful: If the difference between the lower-order moments of the LEA model and the DSG model is small enough, then the intragranular diffusion process is sufficiently fast as to be considered at equilibrium.…”

“…Note that the DSG model as written in (4) does not make any assertion as to the governing mechanism for intragranular diffusion (i.e., pore diffusion or surface diffusion Valocchi, 1985Valocchi, , 1986Valocchi, , 1988Valocchi, , 1989Valocchi, , 1990. The initial and boundary conditions for (1) depend upon the particular application or situation being considered.…”

Spatial moments analysis of kinetically sorbing solutes in aquifer with bimodal permeability distribution

“…[40] The interplay between the first and second terms on the right-hand-side of equation (30) can be studied by analyzing the following nonequilibrium index [Valocchi, 1989]:…”

Evaluation of Health Risks for Contaminated Aquifers

“…Characterizing uncertainty in all of these processes is important for understanding individual susceptibility. [4] where the retardation factor, Rf (dimensionless), for equilibrium sorption is defined as Rf =1+ PB KW [5] If sorption is not an equilbrium process, it can be described by an interphase mass transfer process (12,19,22) as S = iCc, [6] where K is an overall mass transfer coeffi- C(x,y,z,t) = F(Dh,Ksat,AIKC,E,PB) [8] However, some subsurface contaminant transport problems occur in conduit-type flow aquifers (30) that do not behave like flow-through porous media. For these aquifers and flow regimes, equivalent hydraulic characteristics must then be defined and used in Equation 8 to describe the contaminant concentration profile.…”