HR: 14:10h
AN: H13H-03    [Abstracts]
TI: Transport Of Reactive Solutes In Bimodal Porous Formations
AU: * Massabo, M
EM: massabo@uiuc.edu
AF: Department of Civil Engineering, University of Illinois, 205 N. Mathews Ave, Urbana, IL 61801 United States
AU: Valocchi, A J
EM: valocchi@uiuc.edu
AF: Department of Civil Engineering, University of Illinois, 205 N. Mathews Ave, Urbana, IL 61801 United States
AU: Bellin, A
EM: bellin@ing.unitn.it
AF: Department of Environmental and Civil Engineering, University of Trento, via Mesiano 77, Trento, TN 38050 Italy
AB: Solute transport in heterogeneous formations is controlled by hydraulic and geochemical property variations over many spatial scales. In order to describe such variability, multi-Gaussian models have been commonly adopted with the justification that they are consistent with field data at a few experimental sites. However, as soon as more detailed studies on the structure of sedimentary formations were completed, a hierarchical structure emerged in which several modes and correlation lengths combine to create a much more complex and heterogeneous structure. Such a complexity is created by the arrangement of lithofacies units, with size, granulometric and textural properties dependent on the energy of the depositional environment. A way to model such complexity is by multi-indicator models. For the simplest case of a bi-modal formation, the logconductivity field can be described as Y(x)=I(x)Y1(x)+[1-I(x)]Y2(x) where I(x) is an indicator stochastic random function (SRF) while Y1(x) and Y2(x) are SRFs representing small- and large-scale variability of respectively. I(x) is a binary function uniformly distributed which assumes the value 1 with probability P$<$1 and the value 0 with probability (1-P), such that P controls the interplay between small and large scale variability. Rubin (1995) discussed the theoretical foundations of this model providing first order approximations in of the longitudinal and transverse macrodispersion coefficient; most of the work that has been done so far is for non-reactive tracers. In this work we extend the work by Rubin to a reactive solute undergoing non-equilibrium reversible adsorption. We obtained semi-analytical solutions for the effective velocity and macro-dispersion coefficients using the stochastic model for adsorption kinetics suggested by Quinodoz and Valocchi (1993). In doing that we focus on the impact of sorption and spatial conductivity variability on the first two spatial moments assuming spatially constant kinetic rate coefficients. Under the validity of the first order approximation, we conclude: (1) the effective velocity is expressed by a time dependent retardation factor composed by two independent terms; the former is time independent and is related to the mean conductivity contrast between the facies, while the second is controlled by the geochemical parameters; (2) the presence of high conductivity inclusions produces higher asymptotic longitudinal dispersion coefficient than low conductivity inclusions and this effect is enhanced by the kinetics; (3) the early time behavior of the longitudinal dispersion coefficient is mainly influenced by the contrast between the mean hydraulic conductivity of the two facies; (4) the kinetics has a much less dramatic effect upon the plume spreading in the transversal direction. Finally we investigate the trustworthiness of the semi-analytical solution for different value of k and P, comparing it with exact results found through numerical simulations.
DE: 1829 Groundwater hydrology
DE: 1831 Groundwater quality
DE: 1832 Groundwater transport
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting