Upscaling of the advection-diffusion-reaction equation with Monod reaction

The need for reliable models for the reactive transport of contaminants in the subsurface is well recognized. The predictive power of these models is determined by the accurate description of bioavailability of contaminants to microorganisms in porous media. Among many other factors influencing bioavailability, diffusive mass transfer processes may limit the substrate availability at the pore scale and hence reduce the effective degradation rate considerably. In this study we used a combination of analytical and numerical methods to upscale surface catalyzed Monod-type reaction rates within a single pore, to obtain effective rate expression at a larger scale. Results show that in the upscaled description Monod kinetics lead to a concentration dependent transition between a reaction and diffusion-limited regime. Strictly, the effective rate repression does not follow Monod-type kinetics. However, we can present appropriate effective parameters relations, which provide an acceptable approximation of degradation dynamics using an effective Monod-type reaction rate.