David L. Hochstetler

On the importance of diffusion and compound-specific mixing for groundwater transport: an investigation from pore to field scale.

Mixing processes significantly affect and limit contaminant transport and transformation rates in the subsurface. The correct quantification of mixing in groundwater systems must account for diffusion, local-scale dispersion and the flow variability in heterogeneous flow fields (e.g., flow-focusing in high-conductivity and de-focusing in low-conductivity zones). Recent results of multitracer laboratory experiments revealed the significant effect of compound-specific diffusive properties on the physical displacement of dissolved species across a representative range of groundwater flow velocities. The goal of this study is to investigate the role of diffusion and compound-specific mixing for solute transport across a range of scales including: (i) pore-scale (~10⁻² m), (ii) laboratory bench-scale (~10⁰ m) and (iii) field-scale (~10² m). We investigate both conservative and mixing-controlled reactive transport using pore-scale modeling, flow-through laboratory experiments and simulations, and field-scale numerical modeling of complex heterogeneous hydraulic conductivity fields with statistical properties similar to the ones reported for the extensively investigated Borden aquifer (Ontario, Canada) and Columbus aquifer (Mississippi, USA, also known as MADE site). We consider different steady-state and transient transport scenarios. For the conservative cases we use as a metric of mixing the exponential of the Shannon entropy to quantify solute dilution either in a given volume (dilution index) or in a given solute flux (flux-related dilution index). The decrease in the mass and the mass-flux of the contaminant plumes is evaluated to quantify reactive mixing. The results show that diffusive processes, occurring at the small-scale of a pore channel, strongly affect conservative and reactive solute transport at larger macroscopic scales. The outcomes of our study illustrate the need to consider and properly account for compound-specific diffusion and mixing limitations in order to accurately describe and predict conservative and reactive transport in porous media.

The behavior of effective rate constants for bimolecular reactions in an asymptotic transport regime.

Previous research has shown that rate constants measured in batch tests (κ) may over-predict the amount of product formation when used in continuum models, and that these rate constants are often much greater than effective ones (κ(eff)) determined from upscaling studies. However, there is evidence that mixing is more important than the rate constants when using upscaled models. We use a numerical two-dimensional pore-scale porous medium with an approach similar to an experimental column test, and focus on the scenario of the displacement and mixing of two solutions with irreversible bimolecular reactions. Break-through curves of multiple cross-sectional averaged concentrations are analyzed for conservative and reactive transport, as well as the segregation of reactant species along the cross-sections. We compute effective parameters for the continuum scale in order to better understand the impact of using intrinsic rate constants in upscaled models. For a range of Damköhler numbers (Da), we compute effective reaction rate parameters and a reaction effectiveness factor; the latter is described by an empirical formula that depends on the Damköhler number and captures the upscaled system behavior. Our pore-scale results also confirm the segregation concept advanced by Kapoor et al. (1997). We find that for Da>1, κ(eff)<<κ, and yet the relative difference in total mass transformation between the pore-scale simulation and what is predicted by the upscaled continuum model using κ is about 10%. The explanation for this paradox is that the early transition of the regime from rate-limited to mixing-limited 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.