Characterizing and upscaling transport, mixing and reactions in porous media [electronic resource]
Keywords: Civil and Environmental Engineering.

Reactive transport in porous media is critical to many subsurface environmental issues including the fate and transport of contaminants, nuclear waste disposal, and carbon dioxide sequestration. Often, dilution and mixing are the controlling factors in each of these processes, such as the overlapping of plumes containing different reactants that is necessary for (bio)degradation of a groundwater contaminant. Thus, improved quantification of mixing, including upscaling relationships, parameterizations, and metrics for dilution and reactive mixing, are necessary for enhanced understanding, predictive modeling, and management of resources. There is a crucial need to improve the upscaling of parameters from the pore-scale to the Darcy and field scale, as well as improve our understanding of the phenomena that manifest at the macroscale as a result of the interaction of coupled physical and (bio)chemical processes at the pore scale. In this dissertation, pore-scale numerical models are used in combination with continuum models and lab (bench) scale experiments in order to study the coupled processes of flow, mixing, and reactions in three different studies. Also, a theoretical derivation is provided for the transport of the entropy of a reactive species, and several applications are used to illustrate its potential as a metric for reactive mixing and dilution. In the first study, pore-scale models are used to explore the unresolved question of the impact of using effective versus intrinsic reaction rate constants for predicting reactive transport in porous media. For a case of displacement and mixing of two solutions with irreversible bimolecular reactions, breakthrough curves from multiple locations are analyzed for conservative and reactive transport, as well as the segregation of reactant species along the cross-sections. For a range of Damköhler numbers (Da), effective reaction rate parameters are found and an empirical formula is developed to describe the relationship between the reaction effectiveness factor and $Da$. This helps describe the upscaled system behavior. The pore-scale results confirm the segregation concept advanced by Kapoor et al. (1997); however, for Da> 1, the effective rate constant is much less than the intrinsic rate constant, yet the relative difference in total mass transformation between the pore-scale simulation and what is predicted by the upscaled continuum model using the intrinsic rate constant is rather modest, of the order of about 10%. The explanation for this paradox is the early transition from a rate-limited to a mixing-limited regime, which results in a model that is relatively insensitive to the rate constant because mixing controls the availability of reactants. Thus, the reaction-rate parameter used in the model has limited influence on the rate of product computed. The second and third studies focus on transverse mixing, which often is critical for reactions to occur in porous media. In the second study, multitracer laboratory bench-scale experiments and pore-scale simulations are used to (i) determine a generalized parameterization of transverse hydrodynamic dispersion at the continuum Darcy scale, (ii) improve understanding of basic transport processes at the subcontinuum scale and how they manifest macroscopically, and (iii) quantify the importance of aqueous diffusion for transport of different solutes. In order to capture the observed results from the pore-scale and lab-scale, a nonlinear compound specific parameterization of transverse dispersion is necessary. The pore-scale simulations illustrate that the interplay between advective and diffusive mass transfer results in transverse concentration gradients leading to incomplete mixing in the pore channels. Ultimately, this affects local transverse mixing at the Darcy scale even at high flow velocities. In the third study, different pseudorandom pore-scale porous media are used for both conservative and reactive simulations, and the impact of the choice of transverse dispersion parameterization on predicting mixing-limited reactive transport with a continuum formulation is explored. Again, both pore-scale numerical simulations and flow-through laboratory experiments are used. The nonlinear parameterization of transverse dispersion consistently predicts both product mass flux and reactant plume extents across two orders of magnitude of mean flow velocities. In contrast, the classical linear parameterization of transverse dispersion, assuming a constant dispersivity as a property of the porous medium, could not consistently predict either indicator with great accuracy. Furthermore, the linear parameterization of transverse dispersion predicts an asymptotic (constant) plume length with increasing velocity while the nonlinear parameterization indicates that the plume length increases with the square root of the velocity. Both the pore-scale model simulations and the laboratory experiments of mixing-limited reactive transport show the latter relationship. A final issue this thesis addresses is the need for appropriate metrics that accurately quantify the interplay between mixing and reactive processes. The exponential of the Shannon entropy of the concentration probability distribution has been proposed and applied to quantify the dilution of conservative solutes either in a given volume or in a given water flux via the dilution index and the flux-related dilution index, respectively. In the final study, the transport equation for the entropy of a reactive solute is derived. Using a flux-related framework, it is shown that the degree of uniformity of the solute mass flux distribution for a reactive species and its rate of change are informative measures of physical and (bio)chemical processes and their complex interaction.