Reversible sorption modeling for multi-zone contaminant dispersal analysis

Mathematical models are presented that account for the mass transport processes associated with isothermal reversible sorption in building materials. These models account for a) the equilibrium limits of reversible sorption processes, b) boundary layer diffusion transport at the adsorbent surface, and/or c) diffusion transport within the adsorbent proper. Three distinct families of models are formulated with individual members of each family distinguished by the sorption equilibrium relation used in their formulation. The first family is based on a discrete or "lumped parameter" idealization of the zone- air/adsorbent system that enforces only the sorption equilibrium constraint. The second family is based on a more complete discrete idealization that adds to the equilibrium constraint a model of boundary layer diffusion. Finally, the third family adds a discretized continuum idealization of diffusion transport within the adsorbent using the Finite Element Method. It is argued that the first model family may be expected to provide reliable predictions of contaminant dispersal in buildings when flow transport processes and source dynamics are slow compared to boundary layer and/or intra-adsorbent transport processes; the second model family is useful for those situations where this is not the case and boundary layer diffusion transport is ratelimiting; the third family provides a means to model those cases where intra-adsorbent transport is rate-limiting. The models are shown to be simple assemblages of dispersal element equations that may be used for general multizone analysis. A comparison the model families is made and measurable criteria are presented to aide in the selection of the model to use. Finally, the results of simple applications of these models are presented that provide some validation of the theory presented.