Analytical modelling of fringe and core biodegradation in groundwater plumes

Biodegradation can be divided into two categories depending on the location at which it occurs within the plume: degradation at the plume fringes, and degradation in the interior (core). Available analytical solutions are limited to the consideration of either fringe or core degradation, which in turn limits the applicability of these solutions. Here, a new analytical approach to modelling plumes with both fringe and core degradation is presented. The approach relies on the use of readily available analytical solutions for solute transport. Using a well-known solution for three-dimensional solute transport from a planar source, an approximate solution is derived for the maximum plume length at steady-state conditions. This is verified through the use of a numerical solution. The solution suggests that the parameters controlling the plume length are: (i) the size of the contaminant source, (ii) electron acceptor to electron donor ratio, (iii) transverse dispersivities and (iv) the ratio between degradation rate constant and velocity (λ/v). The latter term provides a simple check on the relative weights of transport to core degradation and can be used to estimate the importance of core degradation in the overall plume attenuation. The well-documented Bemidji field site has both fringe and core degradation. The new combined degradation model estimates the length of the plume with 10 m of the observed length; core only and fringe only solutions overestimate the length by more than a factor of 2.