Equivalence of two models for biodegradation during contaminant transport in groundwater

We compare two models that have been used frequently for describing biodegradation during contaminant transport in groundwater. One is a “simple” model based upon macroscopic properties only, and the other is a “biofilm” model that accounts for contaminant diffusion and reaction in biofilms. Although the simple model has been used frequently, its mathematical formulation appears inadequate to describe the physics of the biodegradation process. Hence it is unclear when the simple model should be considered valid, and analyses predicated upon the simple model are called into question. We resolve this issue by arguing that the simple model should be considered valid when it is mathematically equivalent to the conceptually superior biofilm model. We demonstrate that the two models are exactly equivalent at the macroscopic scale when steady state conditions prevail. Under these conditions the equivalent macroscopic degradation rate coefficient k can be related to microscopic rate parameters that describe mass transfer across a boundary layer, diffusion within the biofilm, and reaction within the biofilm. Under transient (nonsteady state) conditions the two models are not strictly equivalent. However, the error between the two models is negligible in certain cases. In particular, when the rate-limiting step for biodegradation is either mass transfer across the boundary layer or diffusion within the biofilm, there is no distinguishable difference between the predictions of the two models. Thus this paper can be considered a theoretical foundation for use of the commonly employed simple biodegradation model as well as an elucidation of the conditions for its validity.