MULTIPLE-RATE MASS-TRANSFER FOR MODELING DIFFUSION AND SURFACE-REACTIONS IN MEDIA WITH PORE-SCALE HETEROGENEITY

Mass transfer between immobile and mobile zones is a consequence of si multaneous processes. We develop a ''multirate'' model that allows mod eling 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 advec tive-dispersive equation. First, we compare the multirate model to the standard first-order and diffusion models of mass transfer. The spher ical, cylindrical, and layered diffusion models are ail shown to be sp ecific cases of the multirate model. Mixtures of diffusion from differ ent geometries and first-order rate-limited mass transfer can be combi ned and represented exactly with the multirate model. Second, we devel op solutions to the multirate equations under conditions of no flow, f ast flow, and radial flow to a pumping well. Third, using the multirat e model, it is possible to accurately predict rates of mass transfer i n a bulk sample of the Borden sand containing a mixture of different g rain sizes and diffusion rates. Fourth, we investigate the effects on aquifer remediation of having a heterogeneous mixture of types and rat es of mass transfer. Under some circumstances, even in a relatively ho mogeneous aquifer such as at Borden, the mass transfer process is best modeled by a mixture of diffusion rates.