Upscaling Preasymptotic Reactive Transport with a Spatial Markov Model

Abstract:

Using a semi-analytical solution for the flow field and random walk particle methods we study transport through a channel with wavy boundaries, representing a classical idealization of a pore. There is a reactive biofilm at the edges of the channel that can consume solute as it travels through the channel. While classical apporaches are able to upscale and predict the behavior at asymptotic times, preasymptotic effects will not be well represented. However depending on the timescales of flow, reaction and diffusion as characterized by dimensionless Peclet and Damkohler numbers, preasymptotic effects may be critical to accurately predicting reactive transport in such a system. We propose that an appropriately modified spatial Markov model can achieve this across a broad and representative range of geometries and dimensionless parameter values.