Nonequilibrium Transport and Transport-Controlled Reactions

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Porous media are extremely important, not only because they contain most of accessible freshwater, but also because of their biological significance, e.g., hyporheic zones (below rivers or estuaries). Dilution and biochemical reactions control the quality of water in the subsurface, in the sediment of beaches or riverbeds, at groundwater recharge basins, etc. For example, a contaminant plume emanating from a source is gradually diminished through dilution and through chemical reactions in the interior or at the edges of the plume. The success of projects of engineered in-situ remediation often depends on the effectiveness of chemical delivery and mixing of additives, which stimulate native microorganisms to break down contaminants. Equally important to the mixing of reactants may be the removal of reaction products which, if they remain, inhibit reactions because they are deleterious to the microorganisms. Many biochemical reactions that are important in the study of environmental processes are very fast in comparison to transport processes, like advection, diffusion, and mass exchange between aqueous and solid zones. Mixing in porous media is very slow and, thus, is usually the mechanism that controls rates. Reaction rates at scales of interest in practical applications are usually controlled by the rates of transport and mixing within geologic formations, rather than by the rates measured in small and completely mixed reactors. Numerical transport-reaction simulation models are invaluable in describing field-scale processes but there are widespread concerns about their effectiveness, the physical significance of the mathematical expressions and parameters that they employ to describe reaction kinetics, or the extent that these expressions or parameters can be transferred to other sites, or be scaled to sites of different size. This research is a critical reexamination of the fundamentals of transport-limited reactions in order to identify underlying mechanisms and to develop insights into the applicability of commonly used mathematical expressions, appropriate values of parameters, and the importance of scale effects. Existing approaches are revisited and novel approaches are proposed and tested. A new approach is proposed based on the premise that existing parameters like dispersion coefficients or mass-transfer coefficients are inadequate, and occasionally ill-suited, for describing the kinetics of reactions that are controlled by hydrologic transport. Alternative quantities need to be considered, measured, and studied with respect to changes in scale. One approach, which constitutes a drastic departure from available procedures, is based on a rigorous derivation of mixing potentials, which quantify transport-controlled reactions and determine their rates. Critical questions include: what practical tests to perform in the field, how to interpret the results, what accuracy or reliability are practically feasible, and risk-assessment implications. The applicability of various approached is evaluated by examining specific problems from recently completed field studies and experiments and by performing laboratory experiments and detailed numerical simulations.