Jean M. Bahr | Geology Reports

USGS2010

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

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.

Water Resources Research↗

USGS2010

Kinetically influenced terms for solute transport affected by heterogeneous and homogeneous classical reactions

Simulation of transport affected by heterogeneous or homogeneous reversible reactions requires a choice between local equilibrium-based and kinetics-based models. The error associated with the use of equilibrium-based models is equivalent to the error of neglecting certain mathematical terms in the governing kinetics-based transport equations. Identification and evaluation of these kinetically influenced terms can therefore aid in the development of criteria for applicability of local equilibrium- based transport models. This paper extends a four-step derivation procedure, previously presented for cases of transport affected by surface reactions, to transport problems involving homogeneous reactions (solution phase complex formation or oxidation-reduction) and/or precipitation-dissolution reactions. Derivations for these classes of reactions are used to illustrate the manner in which mathematical differences between reaction classes are reflected in the mathematical derivation procedures required to identify kinetically influenced terms. Simulation results for a case of transport affected by a single solution phase complexation reaction and for a case of transport affected by a precipitation-dissolution reaction are used to demonstrate the nature of departures from equilibrium-controlled transport as well as the use of kinetically influenced terms in determining criteria for the applicability of the local equilibrium assumption. A final derivation for a multireaction problem demonstrates the application of the generalized procedure to a case of transport affected by reactions of several classes.

Water Resources Research↗