Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity

Abstract

Mass transfer between immobile and mobile zones is a consequence of simultaneous processes. We develop a “multirate” model that allows modeling of small-scale variation in rates and types of mass transfer by using a series of first-order equations to represent each of the mass transfer processes. The multirate model is incorporated into the advective-dispersive equation. First, we compare the multirate model to the standard first-order and diffusion models of mass transfer. The spherical, cylindrical, and layered diffusion models are all shown to be specific cases of the multirate model. Mixtures of diffusion from different geometries and first-order rate-limited mass transfer can be combined and represented exactly with the multirate model. Second, we develop solutions to the multirate equations under conditions of no flow, fast flow, and radial flow to a pumping well. Third, using the multirate model, it is possible to accurately predict rates of mass transfer in a bulk sample of the Borden sand containing a mixture of different grain sizes and diffusion rates. Fourth, we investigate the effects on aquifer remediation of having a heterogeneous mixture of types and rates of mass transfer. Under some circumstances, even in a relatively homogeneous aquifer such as at Borden, the mass transfer process is best modeled by a mixture of diffusion rates.