Modelling biodegradation of hydrocarbons in aquifers: when is the use of the instantaneous reaction approximation justified?

In-situ bio-remediation is a viable cleanup alternative for aquifers contaminated by hydrocarbons such as BTEX. Transport models of varying complexity and capabilities are used to quantify their degradation. A model that has gained wide acceptance in applications is BIOPLUME II, which assumes that oxygen-limited biodegradation takes place as an instantaneous reaction. In this work we have employed theoretical analysis, using non-dimensional variables, and numerical modelling to establish a quantitative criterion demarcating the range of validity of the instantaneous reaction approximation against biodegradation kinetics. Oxygen was the limiting species and sorption was ignored. This criterion relates Da o, the Dahmköhler number at oxygen depletion, to Oo*, the ratio of initial to input oxygen concentration, Da o≥0.7(Oo*)2+0.1Oo*+1.8. The derived Da o reflects the intrinsic characteristics of the physical transport and of the biochemical reaction, including the effect of biomass density. Relative availability of oxygen and hydrocarbons exerts a small influence on results. Theory, verified and refined via numerical simulations, showed that significant deviations of instantaneous reactions from kinetics are to be expected in the space–time region s