Upscaled Stochastic Transport Modelling of Hydro-Geologic Systems

In natural hydrologic environments, the surrounding geologic media influences the flow field and associated transport behavior. Specifically, the inherent multi-scale, heterogeneous nature of geological media gives rise to complex fluid flow fields, where the velocity distribution spans several orders magnitude. Modelling the transport of dissolved materials in such multi-scale systems remains a challenge, but has important applications for scientific and engineering problems. In this dissertation, we study transport in hydro-geologic systems with Lagrangian random walk methods. The benefit of random walk methods is that transport behavior can be accurately upscaled, meaning physical process governing transport at a range of scales can be effectively captured in bulk parameters. Here we focus on modifying existing random walk models and improving parameterization schemes, so that they can be applied in more general settings. We consider transport in a variety of hydro-geologic systems, including porous media, fracture networks, and a turbulent channel flow with an underlying sediment bed. This work highlights how transport properties at small scales can be incorporated into effective parameters to predict conservative and reactive transport behavior at larger scales.