**2. Model development**

The examination of concurrent sorption and biodegradation in environmental systems is not actually a recent development. The method of volume averaging described by Hassanizadeh and Gray (1979) has frequently been used to examine contaminant transport in porous media. These analyses proceed by defining the groundwater system as containing two phases, the aqueous phase (groundwater) and the solid phase (soils). Of note, in some cases a more elaborate system could be defined with the solid phase actually consisting of multiple phases (i.e. an organic phase along with an inorganic phase), however it is the corollary with the two-phase system that will be used here. In the groundwater systems, the solid phase is stationary with the aqueous phase moving through it, as indicated below in Figure 1.

Fig. 1. Representation of porous media characteristic of groundwater systems

The analysis begins with a microscopic differential volume that is then expanded through volume averaging, with the ultimate result being the series of advection-dispersion-reaction (ADR) equations that are frequently encountered in groundwater research. This underlying methodology will now be applied to an activated sludge basin, with the key difference being that the solid phase will move in conjunction with the aqueous phase, rather than being stationary.
