Examples involving six broad reaction classes show that the nature of transport‐affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass‐balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport‐equation system (e.g., whether it involves algebraic, partial‐differential, or integro‐partial‐differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical‐relation (i.e., equilibrium or rate) equations.

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...

A method has been developed to establish steady state flow of water in an unsaturated soil sample spinning in a centrifuge. Theoretical analysis predicts moisture conditions in the sample that depend strongly on soil type and certain operating parameters. For Oakley sand, measurements of flux, water content, and matric potential during and after centrifugation verify that steady state flow can be achieved. Experiments have confirmed the theoretical prediction of a nearly uniform moisture distribution for this medium and have demonstrated that the flow can be effectively one-dimensional. The method was used for steady state measurements of hydraulic conductivity K for relatively dry soil, giving values as low as 7.6 x 10-• • m/s with data obtained in a few hours. Darcy's law was tested by measuring K for different centrifugal driving forces but with the same water content. For the sand at a bulk density of 1.82 Mg/m 3 and 27% saturation, results were consistent with Darcy's law for K equal to 5.22 x 10-•o m/s and forces ranging from 216 to 1650 times normal gravity.

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To improve understanding of hysteretic air permeability relations, a need exists for data on the water content dependence of air permeability, matric pressure, and air trapping (especially for wetting‐drying cycles). To obtain these data, a special instrument was designed. The instrument is a combination of a gas permeameter (for air permeability determination), a suction plate apparatus (for retentivity curve determination), and an air pycnometer (for trapped‐air‐volume determination). This design allowed values of air permeability, matric pressure, and air trapping to be codetermined, i.e., determined at the same values of water content using the same sample and the same inflow‐outflow boundaries. Such data were obtained for two nonswelling soils. The validity of the air permeability determinations was repeatedly confirmed by rigorous tests of Darcy's law. During initial drying from complete water saturation, supplementary measurements were made to assess the magnitude of gas slip. The extended Darcy equation accurately described the measured flux gradient relations for each condition of absolute gas pressure tested. Air permeability functions exhibited zero‐permeability regions at high water contents as well as an abruptly appearing hysteresis at low water contents. Measurements in the zero‐permeability regions revealed that the total amount of air in general exceeded the amount of trapped air. This indicates that the medium' s air space is partitioned into three measurable domains: through‐flowing air, locally accessible air (i.e., air accessible from only one flow boundary), and trapped air. During repeated wetting and drying, the disappearance and reappearance of air permeability coincided closely with the reappearance and disappearance, respectively, of trapped air. The observed relation between critical features of the air permeability functions and those of the air‐trapping functions suggest that water‐based blockages play a significant role in the disruption of gas‐phase connectivity and in preventing air flow, and must be considered in any effectual model of air permeability relations.