Local reaction and diffusion in porous media transport models

The problem of when advection-dispersion models apply for reactive transpor t in porous media is addressed. Assuming local mass balances, including arb itrary homogeneous and interfacial chemical reactions, are known, volume av eraging is applied to obtain a set of equations for the average concentrati ons. It is shown that timescale constraints must be satisfied in addition t o the well-known length-scale constraint needed for volume averaging. The t imescale for simulation must be longer than a diffusion timescale in the re presentative elementary volume, t/T-D much greater than 1. In addition, int erfacial reaction timescales must be larger than meaningful diffusion times cales, T-r/T-d much greater than 1. When these constraints are satisfied, t he usual dispersion coefficient exists and is time-invariant and independen t of reactions. Reaction rate expressions and all mass transfer fluxes can be expressed in terms of the average concentrations of the macroscopic mode l. Even when surface reactions are fast, it is shown that the fluid volume can be subdivided into small enough regions such that the appropriate time constraint T-r/T-d much greater than 1 is satisfied. An average model can b e obtained that includes mass transfer resistance expressed in terms df a m ass transfer coefficient. The mass transfer coefficient is defined and is s hown to depend only on the geometry of the porous medium and the flow field . This work provides a theoretical basis for the commonly used advection-di spersion models for reactive transport at the Darcy scale and provides both length-scale and timescale constraints for when they apply.