Modelling Reactive Transport in an Upscaled Lagrangian Framework

Abstract:

First, we consider a very simple heterogeneous flow and demonstrate that the Spatial Markov model, an upscaled effective Lagrangian model that has had broad success in upscaling transport across a range of scenarios, can adequately reproduce observations of reactive transport from fully resolved models when reaction rates are heterogeneously distributed within the domain, but only when they are linear in nature. Next, we address how one might incorporate nonlinear reactions into this upscaled framework. To do so we consider recent advances in reactive particle tracking methods, which suggest that the probability of reaction between two particles can be calculated as the product of two thing (i) the probability that both particles collocate and (ii) the probability of reaction given collocation. This naturally decouples the problem as (i) depends only on transport and (ii) only on chemistry. Calculating (i) in advection-diffusion systems is relatively trivial, but here we demonstrate the challenge associated with doing so in an upscaled framework such as the Spatial Markov model and propose some ways around these challenges.