Upscaling reactive transport in porous media : laboratory visualization and stochastic models

Abstract

Solute transport models are essential tools for understanding and forecasting chemical concentrations in groundwater. Advection-dispersion based models can adequately predict spatial averages of conservative solute concentrations without using explicit maps of pore structures or variations in hydraulic conductivity. However, coupling advection-dispersion based transport models to chemical reaction models is inaccurate because it implicitly assumes complete mixing. Mixing in natural porous media is a slow process that can control the overall rate of chemical reactions, and the lack of mixing causes concentrations to be spatially variable. This thesis develops and experimentally validates a new solute transport modeling framework that approximates the correct amount of chemical reaction and provides concentration probability density functions, which are needed to address laws and regulations based on maximum contaminant levels. To study solute mixing and reaction in porous media, we conducted highly detailed lab-scale experiments by digitally imaging the movement of colored dye tracers and colorimetric chemical reactions through illuminated clear homogeneous and heterogeneous porous media.

(cont.) The resulting sequence of solute concentration maps demonstrates the problem of conventional solute transport models and shows that concentrations can be well approximated with Beta distributions. Conservative Beta distributions can be modeled with partial-differential equations for concentration mean and variance. These conservative distributions can then be transformed into joint reactant distributions, which produces product and remaining reactant distributions. This upscaling approach is verified by modeling the product and reactant means, variances, and distributions in heterogeneous media and product means in homogeneous media from our lab-scale experiments. We found that (co)variance production-destruction balances can approximate aqueous species covariance matrixes, which are necessary to form multivariate reactant distributions of complex reactive transport scenarios. Alternatively, these second moments can be used in upscaled reaction expressions derived from a second order Taylor series expansion. Incomplete mixing, parameterized by variance and covariance, causes an upscaled reaction rate to be almost an order of magnitude smaller compared to the conventional reaction rate that implicitly assumes complete mixing.

(cont.) Finally, manipulating the flow field to be perpendicular to its original direction would increase the rate of reactive mixing by an order of magnitude. Thus generating a transient flow field would be a practical way to accelerate natural attenuation and bioremediation.