Local reaction and diffusion in porous media transport models

Abstract

Abstract. The problem of when advection-dispersion models apply for reactive transport in porous media is addressed. Assuming local mass balances, including arbitrary homogeneous and interfacial chemical reactions, are known, volume averaging is applied to obtain a set of equations for the average concentrations. It is shown that timescale constraints must be satisfied in addition to the well-known length-scale constraint needed for volume averaging. The timescale for simulation must be longer than a diffusion timescale in the representative elementary volume, t/To >> 1. In addition, interfacial reaction timescales must be larger than meaningful diffusion timescales, TIT a >> 1. When these constraints are satisfied, the usual dispersion coefficient exists and is timeinvariant and independent of reactions. Reaction rate expressions and all mass transfer fluxes can be expressed in terms of the average concentrations of the macroscopic model. 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 TdTa >> 1 is satisfied. An average model can be obtained that includes mass transfer resistance expressed in terms of a mass transfer coefficient. The mass transfer coefficient is defined and is shown 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-dispersion models for reactive transport at the Darcy scale and provides both length-scale and timescale constraints for when they apply.

Scale dependence of mineral dissolution rates within single pores and fractures

“…This implies that it is only in transport regimes where homogeneous concentration fields form that laboratory-measured reaction rates be used directly. This is consistent with findings from other studies at other spatial scales (Mo and Friedly, 2000;Meile and Tuncay, 2006;Mohamed et al, 2006) where it was demonstrated that relatively fast reaction kinetics combined with low advection and diffusion rates can generate a scaling effect, and thus a discrepancy between lab and field rates.…”

Scale dependence of reaction rates in porous media

“…A distinct impact of reactant segregation, with roughly 20-50% difference between measured rates and those calculated based on average concentrations was observed [21,45]. In diffusion dominated settings, a theoretical analysis suggested only minor effect for reactions taking place in the pore fluid [39]. However, sub-millimeter scale heterogeneity has been observed for O 2 and trace metals in sediments and microbial mats (e.g., [20,16]; see also [12]).…”

Pore‐scale modeling of dissolution from variably distributed nonaqueous phase liquid blobs

“…For Pe approximately equal to 1, the steady state was typically reached in 750,000 time steps. For Pe greater than 40, the error terms in the LB solute transport model become significant and the method is unstable [Noble, 1997].…”