C. Espinoza et Aj. Valocchi, STOCHASTIC-ANALYSIS OF ONE-DIMENSIONAL TRANSPORT OF KINETICALLY ADSORBING SOLUTES IN CHEMICALLY HETEROGENEOUS AQUIFERS, Water resources research, 33(11), 1997, pp. 2429-2445
A small perturbation approach is used to analyze the impact of chemica
l heterogeneity on the one-dimensional transport of a pollutant that u
ndergoes linear kinetic adsorption. We make an important simplifying a
ssumption that the aquifer is physically homogeneous but chemically he
terogeneous. The aquifer is assumed to be comprised of two distinct zo
nes: reactive and nonreactive; a Bernoulli random process is used to c
haracterize the spatial distribution of reactive zones along the aquif
er. We develop analytical solutions to study the distribution of the e
nsemble mean, standard deviation, and coefficient of variation of the
dissolved concentration after an instantaneous injection of contaminan
t. In addition, numerical solutions based on a Monte Carlo approach ar
e used to determine the validity of the analytical solutions. Finally,
an analysis involving temporal and spatial moments is used to derive
expressions for the large-scale effective parameters (velocity and dis
persion) that capture the impact of chemical heterogeneity. Temporal m
oment analysis provides closed-form analytical expressions for the asy
mptotic effective velocity and dispersion, while spatial moment analys
is explains the effect of chemical heterogeneity on the preasymptotic
value of these effective parameters. A key result from our analysis sh
ows that chemical heterogeneity creates ''pseudokinetic'' or ''macroki
netic'' conditions characterized by a time-dependent effective retarda
tion coefficient even when the local equilibrium assumption is invoked
.