The Spatial Markov Model for Preasymptotic and Anomalous Transport - To correlate or not to correlate?

Abstract:

In the last several years the Spatial Markov model, an anomalous transport model, has been applied with good success to upscale transport in a diverse variety of heterogeneous porous media flows. This model is a random walk model, where a solute plume is represented by a large number of particles, each of which transition through space and time following probabilistic rules designed to effectively describe smaller scale dynamics without explicitly resolving them. It is typically applied by imposing fixed spatial jumps and random time jumps as particles transition, much as is done in various other well known random walk approaches. What distinguishes this approach from other methods is the successive time steps are correlated; that is the current time step a particle takes is still random, but conditioned by the value of its previous step. In certain cases, this correlation has been shown to be critical to accurately reproducing larger scale observations. In this presentation, by considering transport in some simple synthetic heterogeneous flows, where the model can be successfully applied, we will discuss when it is important to consider such correlations and when they can be considered negligible, allowing for the use of a simpler model.