Direct comparison of kinetic and local equilibrium formulations for solute transport affected by surface reactions

Abstract

Modeling transport of reacting solutes in porous media often requires a choice between models based on the local equilibrium assumption (LEA) and models involving reaction kinetics. Direct comparison of the mathematical formulations for these two types of transport models can aid in this choice. For cases of transport affected by surface reaction, such a comparison is made possible by a new derivation procedure. This procedure yields a kinetics-based formulation that is the sum of the LEA formulation and one or more kinetically influenced terms. The dimensionless form of the new kinetics-based formulation facilitates identification of critical parameter groupings which control the approach to transport behavior consistent with LEA model predictions. Results of numerical experiments demonstrate that criteria for LEA applicability can be expressed conveniently in terms of these parameter groupings. The derivation procedure is demonstrated for examples of surface reactions including first-order reversible sorption, Langmuir-type kinetics and binary, homovalent ion exchange. This paper is not subject to U.S. copyright. Published in 1987 by the American Geophysical Union. Paper number 6W4566. Because the LEA is an approximation, its use under certain conditions may result in erroneous predictions of transport behavior. On conceptual grounds, the LEA should apply only under conditions for which the rate of concentration change due to reactions is fast relative to the rate of the flow-induced concentration changes. If the reactions are insufficiently fast as a result of chemical kinetics and/or diffusional limitations, the migration rate of a contaminant front predicted under the LEA will not be correct. For example, simulation results presented by Carnahan and Rerner [1984] demonstrate that an LEA model may significantly underestimate the size of a plume of reacting solute for which the rate of sorption is limited by nonequilibrium mass transfer. Models based on the LEA have proven useful in a variety of solute transport applications. However, an increasing body of experimental evidence reported in the earth science literature indicates that the LEA may not be applicable under certain conditions of interest in the study of solute transport. Valocchi [1985] and Skopp [1986] review a number of studies in which deviations from transport predicted using LEA models, were observed at the scale of laboratory columns. Interpretation of data from recent field experiments [Whiffin and Bahr, 1985' Goltz and Roberts, 1986] suggest that nonequilibrium effects may be important in near field transport of contaminants from sites of disposal or spills. At the regional scale, observed departures from local chemical equilibrium have been used to trace and explain the chemical evolution of groundwater [e.g., Back and Hanshaw, 1971]. The identification of sets of conditions for which the local equilibrium assumption applies is important in choosing between local equilibrium-based and kinetics-based models for solute transport. Several rece...

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