Preasymptotic Approaches to Upscaling of Diffusion Limited Transport of Solutes

We assess the importance of accounting for preasymptotic velocity correlation in upscaling solute transport in a variety of situations. We compare upscaled predictions of the Spatial Markov model which accounts for correlation and upscaled predictions of models which do not account for correlation to high resolution simulations of both reactive and conservative transport. We find that for conservative transport in steady flows velocity correlation plays a major role and cannot be neglected at preasymptotic length scales, yet in unsteady flows this correlation is weak and can be neglected. For reactive transport, we find that velocity correlation is even more important, as accounting for it allows us to accurately model the amount of reactions that take place in the system. Additionally, we find the minimum length scale necessary to use the Spatial Markov model and propose guidelines for the model's use.