Linear exchange model for the description of mass transfer limited bioavailability at the pore scale

Reactive transport simulations are a common approach for the quantitative assessment of contaminant biodegradation in the subsurface. To use knowledge on microbial kinetics for the simulation of in situ biodegradation, the mass transfer processes controlling the bioavailability of the contaminants need to be described appropriately. A common approach to account for this problem is using a linear exchange model controlling the link between bulk and bioavailable concentration. Assuming that the subsequent degradation is controlled by the bioavailable concentration, only, these two steps can be combined to an analytical expression for the overall reaction rate know as the Best-Equation. In our work, we evaluate this approach for its ability to describe biodegradation kinetics limited by pore-scale mass transfer. Results from explicit numerical and analytical simulations of mass transport and reactive consumption at the pore scale are used to test the accuracy of results obtained using the Best-Equation. Our analysis shows that strictly spoken the Best-Equation is not valid. However, a good approximation can be achieved with errors of less than 6% in cases of moderate bioavailability and much lower errors in cases of either low or high bioavailability. These results support the description of mass transfer processes used in many reactive transport models. Furthermore, we present a method to obtain an accurate estimate of the unknown rate parameter controlling the diffusive mass transfer processes at the pore scale.