Lagrangian Methods to Study Mixing and Reactions in Flows through Heterogeneous Porous Media

Mixing-driven chemical reactions are an important factor to consider in a wide range of natural flowing systems. These flows are in general heterogeneous across a broad range of scales, increasing the complexity of these systems. Non-uniform flows are generally expected to enhance mixing relative to a homogeneous one, which will impact reactions. In reactive transport, the chemicals involved in the reaction must first come into contact before a reaction can occur and mixing is the process that enables this. Many existing models inadequately assume perfect mixing, leading to the overprediction of reaction rates in laboratory and field observations. The effects of incomplete mixing must be properly accounted for in order to accurately predict reactive transport in these systems. In this dissertation, we use Lagrangian particle tracking methods to predict mixing and reactions in flows through idealized two-dimensional heterogeneous porous media. The goal of this work is to identify which aspects of the heterogeneous flows most control mixing and reactions and to develop upscaled models that account for these processes without explicitly resolving them. To do this, we first examine the relationship between reaction numbers and local metrics of flow deformation based on velocity gradients. A link between reactive and conservative transport is also identified. Next, we take what we learned about mixing and reactions from our fully resolved model simulations and work to upscale these processes. We first upscale conservative mixing by modifying the Lagrangian Spatial Markov model (SMM) to predict particle locations that are needed to generate concentration fields that can be used to quantify mixing. Then, we use this modified SMM to extend the LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model to predict upscaled bimolecular reactive transport in flows through idealized heterogeneous porous media.