Efficient incorporation of microbial metabolic lag in subsurface transport modeling

Abstract

Upon introduction of a degradable substrate into the environment of a microbial community, an appreciable lag may occur before a corresponding increase in microbial activity is observed. Accounting for this metabolic lag may be of importance when modeling subsurface transport of contaminants that undergo reactions mediated by microbes. We present a general technique from mathematical biology that can facilitate incorporation of metabolic lags in subsurface solute transport models involving immobile biomass. By making the metabolic activity of bacteria dependent on the local history of substrate concentrations through a convolution integral, the proposed lag formulation is conceptually related to a previously suggested approach. Computer implementation of transport models with the new lag formulation becomes particularly simple when the numerical scheme (at least partly) reduces the original problem to that of solving systems of ordinary differential equations. Example simulation results show that transport models with this lag formulation can be made to fit real experimental data reasonably well by adjusting the lag parameters. The questions of whether parameter estimates can be generalized across individual model applications and/or whether parameters can be determined by independent experiments could be addressed in future research.