Fundamental studies on non-classical transport in porous media [electronic resource]
Keywords: Civil and Environmental Engineering.

Finding an appropriate upscaling approach is required for accurate prediction of transport in porous media. Classical macroscopic or continuum-based approaches, such as the advection-dispersion (AD) model for porous media, need greater investigation regarding their implicit assumptions and further discussion of circumstances under which they are applicable. In particular, it is necessary for the upscaled models to adequately consider the effects of heterogeneity, anisotropy, non-equilibrium, and micro-scale degree of mixing on the macroscopic transport in porous media. The primary challenge is to capture the main features of the pore-scale variations of the dependent variables of interest, like solute concentration, in spite of losing most of the small-scale details during the upscaling process. Depending on the objectives of a specific problem, different upscaling approaches are needed to capture different `main features'. This dissertation focuses on rigorous upscaling from the pore scale to the Darcy or laboratory scale to shed light on fundamental aspects of transport: dispersion, non-equilibrium transport, reactive transport, and electrical current in porous media. Pore-scale simulations are used to reveal the implicit assumptions of the classical models and to investigate the applicability of alternative models to non-classical transport based on understanding of physical mechanisms at the micro scale. In the first part of the dissertation, a volume averaging approach based on the scale of a Representative Elementary Volume (REV) is used to emphasize that Fick's Law at the macroscopic level implicitly assumes equilibrium conditions, which often are taken for granted in applications. The second part of the dissertation focuses on equilibrium transport, and applies the method of moments to discuss the properties of the dispersion coefficient and dispersivity. A solid proof indicates that a fourth-order dispersivity tensor is the right way to parameterize dispersion in anisotropic porous media. In addition, the dispersivity tensor may be a function of the fluid velocity, rather than solely dependent on the medium geometry as commonly treated in practical applications. This results in non-linear relationships between the dispersion coefficients and the fluid velocity. Pore-scale simulations in this part also demonstrate different non-linear relationships with the Peclet number (Pe) for the longitudinal and transverse dispersivities and for periodic and randomly-packed porous media. In the third part, detailed evaluation at the pore scale indicates that non-equilibrium between advection and diffusion causes mass transfer limitations between preferential flow paths and slow velocity regions, which manifests as dual-domain transport. When the advection timescale is smaller than the diffusion timescale, the dual-domain mass transfer (DDMT) model captures the non-equilibrium transport more accurately than the AD model. However, the accuracy of the DDMT model is affected by choosing the appropriate values of model parameters, which are dependent on the fluid velocity due to the flow-dependent non-equilibrium behavior. Therefore, column test for model parameterization in the lab are suggested to be conducted in a flow with velocity close to that of the field, and certain adjustments of the parameters according to the difference of velocities in the lab and field are necessary. The fourth part investigates the long-term dissolution and reaction of DNAPL residuals in two representative regimes of the contaminated area. In the entrance regime, the applicability of Gilland-Sherwood correlations to porous media is verified. Pore-scale simulations indicate that the mass transfer increases as a power-law function of Pe and is enhanced by reactions, such as chemical oxidization and bio-reaction. In the regime that is located far from the entrance, the long-term reactions are controlled by the mixing of reactants. With a second-order reaction of the contaminant with some additive, the late-time reactions demonstrate a first-order decay macroscopically with respect to the mass of the additive in an additive-limited scenario. At intermediate time, the additive decays exponentially with the square of time (t^2). The intermediate decay rate is affected by the initial conditions, and increases as the fluid velocity increases and the distance of adjacent DNAPL residuals decreases. The late-time decay rate only depends on the intrinsic reaction rate and the solubility of the contaminant. The fifth part renews the discussion of the parameterization of the bulk electrical conductivity. The upscaling of electrical current in porous media shows that the tortuosity, the most critical parameter in this parameterization, is not well defined at the micro scale. As a macroscopic property to capture all the obstructions of soil grains, the tortuosity is directionally-dependent and does not exhibit intrinsic correlations with porosity.