Numerical Upscaling of Transport Through Obstructed Regions Over a Broad Range of Reynolds Numbers

Abstract:

While historically flow and transport in porous media has focused on low Reynolds number and Peclet number regimes there are a variety of examples relevant to environmental fluid dynamics where higher Reynolds number flows are important. A common example might include flow and transport through wetlands where plants act as the solid phase of an effective porous medium. In particular, heterogeneity in the flow field due to presence of the solid phases gives rise to complex transport and mixing behaviors that cannot be upscaled at pre-asymptotic times using conventional approaches. We numerically simulate pore-scale flow and transport through obstructed domains over a range of Reynolds numbers from 15 to 280 and then upscale transport. We upscale using a correlated continuous time random walk (correlated CTRW) model, originally introduced in [1]. We then assess the correlated CTRW's ability to predict observables for both asymptotic and pre-asymptotic time scales and compare our results to those of a classical CTRW to determine when velocity correlations must be accounted for.

REFERENCES

[1] T.L. Borgne, M. Dentz, J. Carrera: Lagrangian statistical model for transport in highly heterogeneous velocity fields, Physical Review Letters 101 (2008) 090601.