Thesis (Ph. D.)--Institute of Paper Science and Technology, 1992. / Includes bibliographical references (leaves 187-191).

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 17, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Yuwen Zhang. Vita. Includes bibliographical references.

Dispersivity data compiled over many lengths show that values at typical interwell distances are about two to four factors of ten larger than those measured on cores. Such large dispersivities may represent large mixing zones in the reservoir or they may be a result of convective spreading driven by permeability heterogeneity. This dissertation uses the idea of flow reversal (echo tests) to distinguish between convective spreading and dispersive mixing. Spreading is reversible, mixing is not. A zero or small value of echo dispersivity (estimated after flow reversal) implies little or no mixing and convection dominated transport. An echo dispersivity value equal to the transmission value (estimated after forward flow) would imply well mixed transport. A particle tracking code is developed to simulate echo tests for tracer transport in single phase, incompressible flow through three-dimensional, heterogeneous permeable media. Echo dispersivities are estimated for typical heterogeneity realizations and compared with corresponding transmission values at the field scale. The most important observation is that echo dispersivities are significantly larger than core scale values. They also lie on the overall trend of measured dispersivities and corroborate the large echo dispersivities previously inferred from single well tracer test data. This implies that significant mixing occurs in field scale transport. Echo dispersivities increase with permeability heterogeneity (variance and autocorrelation lengths). This is the effect of local (point or pore scale) mixing in the transverse direction, integrated over long and tortuous flow paths. Transport in typical reservoir formations, with significant autocorrelation in permeabilities, is most likely to be in a pre-asymptotic regime and cannot be described by a unique dispersivity value. This is because the Fickian model for dispersion fails to capture the mixing zone growth correctly in this regime. These results highlight the need to develop representative models for dispersion and improve upscaling methodologies. / text

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Spatial variability of porous media often prevents precise physical characterization of the system. In order to model moisture and solute transport through this media, certain sacrifices in precision must be made. Physical characteristics of the system must be averaged over large scales, lumping the small scale variability into the large scale characterization. Although this precludes a precise definition of the small scale flow characteristics, parameterization is much more attainable. This study addresses methods for determining effective hydraulic conductivity of unsaturated porous media. Effective conductivity is used to describe the large scale behavior of the system. Different methods for calculating the effective conductivity are presented and compared. Results indicate that the unit mean gradient method produces good estimates of the effective conductivity and can be applied using limited field data. The zone of correlation of the hydraulic parameters can be used in experimental design to minimize the errors associated with estimation of the mean pressure. An inverse method for evaluating the optimum effective hydraulic parameters is presented. Results indicate the optimization procedure is more sensitive to wetting than to drying conditions. Because of interaction between the hydraulic parameters, concurrent optimization of more than two of the parameters based on soil pressure data alone is not advised. Anisotropy in an unsaturated soil was found to be a function of the profile mean soil pressure. Results indicate the effective conductivity for flow parallel to soil layering can be estimated from the arithmetic mean of the unsaturated conductivity values for each of the layers and is between the harmonic and geometric means of these data for flow perpendicular to the layering. Estimates of the effective unsaturated hydraulic conductivity obtained through stochastic analysis agreed well with simulation results. Deviations between the stochastic predictions and simulation results are larger when the variability of the soil profile is greater and begin to deviate significantly when the variance of ln K(ψ₀) exceeds 5.0 and the variance of a exceeds 0.02 1/cm².

Several factors which affect the transport of pyridine, quinoline and acridine (aza-arenes) in saturated porous media were investigated in laboratory experiments in order to provide data for input into coupled models that may be applied to predicting the fate of these compounds in groundwater. The effect of pH and ligand type and concentration on acridine solubility was studied in a series of batch and pH-stat experiments. There was a decrease in acridine solubility below the compound's pKₐ due to acridine/ligand precipitate formation. The reaction stoichiometry and solute/sorbent interactions of aza-arene adsorbed to porous silica were determined from batch adsorption and Raman spectroscopy experiments. The neutral aza-arene was hydrogen bonded to surface sites above the compound's pKₐ and there was a cation/ClO₄⁻ complex interacting with surface sites through dipole-dipole interactions below the pKₐ of the compound. The effect of pH, temperature, ligand type, average linear velocity and initial aqueous phase solute concentration on the adsorption of aza-arenes to porous silica was investigated in a series of column experiments. The extent of adsorption followed the trend pyridine < quinoline < acridine due to greater overlap of the molecule with adsorption sites as the number of rings increases. The extent of adsorption was greater below the compound's pKₐ than above because the complex was able to optimize its orientation with the surface. The extent of adsorption of neutral acridine was enhanced when carbonate was used as a buffer relative to phosphate due to carbonate's more exothermic hydration enthalpy. The isotherms were non-linear above and below the pKₐ of acridine. The enthalpy of the adsorption reaction was less exothermic below the compound's pKₐ than above due to the stronger hydrogen bonds formed between the surface and the neutral molecule compared to the dipole-dipole interactions that bond the complex to the surface below the pKₐ. Non-equilibrium effects on the adsorption reaction were minor. Adsorption-desorption was on the order of seconds to minutes. Kinetic effects became more important as temperature decreased.

The effectiveness of a cyclodextrin (sugar-based) solution for enhancedsolubilization removal of multicomponent nonaqueous phase organic liquid (NAPL) contamination from an aquifer is tested in a pilot-scale field experiment. This effort is the first field test of this innovative technology, termed a "Complexing Sugar Flush" (CSF). The saturated zone within an enclosed cell was flushed with 8 pore volumes of 10wt% cyclodextrin solution. The cyclodextrin solution increased the aqueous concentrations of all the target contaminants to values from about 100 to more than 20,000 times the concentrations obtained during a water flush conducted immediately prior to the CSF. The degree of solubility enhancement was greater for the morehydrophobic contaminants. Conversely, the relative mass removal was greater for the less-hydrophobic compounds due to their generally higher apparent solubilities. The average reduction in NAPL mass for the target contaminants was about 41%. A relationship is developed to describe enhanced dissolution of a multiple-component NAPL, and is used to analyze the field data. The effluent concentrations for most of the target contaminants during the cyclodextrin flush were within a factor of two of the equilibrium values predicted using this theory. Deviations from ideal dissolution behavior were also observed. Finally, the cyclodextrin solution appeared to significantly enhance both the magnitude and the rate of NAPL dissolution compared to a water flush conducted prior to the cyclodextrin flush. These results contribute to a better understanding of the important physicochemical processes involved in using enhancedsolubilization agents for the remediation of multiple-component NAPLs.

We consider steady state unsaturated flow in bounded randomly heterogeneous soils under influence of random forcing terms. Our purpose is to predict pressure heads and fluxes and evaluate uncertainties associated with these predictions, without resorting to Monte Carlo simulation, upscaling or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. Following Tartakovsky et al. [1999], by assuming that the Gardner model is valid and treating the corresponding exponent a as a random constant, the steady-state unsaturated flow equations can be linearized by means of the Kirchhoff transformation. This allows us develop exact integro-differential equations for the conditional first and second moments of transformed pressure head and flux. The conditional first moments are unbiased predictions of the transformed pressure head and flux, and the conditional second moments provide the variance and covariance associated with these predictions. The moment equations are exact, but they cannot be solved without closure approximations. We developed their recursive closure approximations through expansion in powers of σᵧ and σᵦ, the standard deviations of Y = lnK(s), and β = ln α, respectively, where K(s), is saturated hydraulic conductivity. Finally, we solve these recursive conditional moment equations to second-order in σᵧ and σᵦ, as well as second-order in standard deviations of forcing terms by finite element methods. Computational examples for unsaturated flow in a vertical plane, subject to deterministic forcing terms including a point source, show an excellent agreement between our nonlocal solutions and the Monte Carlo solution of the original stochastic equations using finite elements on the same grid, even for strongly heterogeneous soils.

It has been shown by Neuman [1990], Di Federico and Neuman [1997, 1998a,b] and Di Federico et al. [1999] that observed multiscale behaviors of subsurface fluid flow and transport variables can be explained within the context of a unified stochastic framework, which views hydraulic conductivity as a random fractal characterized by a power variogram. Any such random fractal field is statistically nonhomogeneous but possesses homogeneous spatial increments. When the field is statistically isotropic, it is associated with a power variogram γ(s) = Cs²ᴴ where C is a constant, s is separation distance, and If is a Hurst coefficient (0 < H< 1). If the field is Gaussian it constitutes fractional Brownian motion (fBm). The authors have shown that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or Gaussian vario grams of overlapping, homogeneous random fields (modes) having mutually uncorrelated increments and variance proportional to a power 2H of the integral (spatial correlation) scale. Low- and high-frequency cutoffs are related to length scales of the sampling window (domain) and data support (sample volume), respectively. Intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy, created by a hiatus of modes associated with discrete ranges of scales. In this dissertation, I investigate the effects of domain and support scales on the multiscale properties of random fractal fields characterized by a power variogram using real and synthetic data. Neuman [1994] and Di Federico and Neuman [1997] have concluded empirically, on the basis of hydraulic conductivity data from many sites, that a finite window of length-scale L filters out (truncates) all modes having integral scales λ larger than λ = μL where μ ≃ 1/3. I confii in their finding computationally by generating truncated fBm realizations on a large grid, using various initial values of μ, and demonstrating that μ ≃ 1/3 for windows smaller than the original grid. My synthetic experiments also show that generating an fl3m realization on a finite grid using a truncated power variogram yields sample variograms that are more consistent with theory than those obtained when the realization is generated using a power variogram. Interpreting sample data from such a realization using wavelet analysis yields more reliable estimates of the Hurst coefficient than those obtained when one employs variogram analysis. Di Federico et al. [1997] developed expressions for the equivalent hydraulic conductivity of a box-shaped support volume, embedded in a log-hydraulic conductivity field characterized by a power variogram, under the action of a mean uniform hydraulic gradient. I demonstrate that their expression and empirically derived value of μ ≃ 1/3 are consistent with a pronounced permeability scale effect observed in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona. I then investigate the compatibility of single-hole air permeability data, obtained at the ALRS on a nominal support scale of about 1 m, with various scaling models including fBm, fGn (fractional Gaussian noise), fLm (fractional Lévy motion), bfLm (bounded fractional Lévy motion) and UM (Universal Multifractals). I find that the data have a Lévy-like distribution at small lags but become Gaussian as the lag increases (corresponding to bfLm). Though this implies multiple scaling, it is not consistent with the UM model, which considers a unique distribution. If one nevertheless applies a UM model to the data, one obtains a very small codimension which suggests that multiple scaling is of minor consequence (applying the UM model to permeability rather than log-permeability data yields a larger codimension but is otherwise not consistent with these data). Variogram and resealed range analyses of the log-permeability data yield comparable estimates of the Hurst coefficient. Resealed range analysis shows that the data are not compatible with an fGn model. I conclude that the data are represented most closely by a truncated fBm model.

This dissertation examines three different aspects of groundwater contamination by immiscible liquids, both at laboratory and field scale. The first component incorporates a study of denser than water immiscible-liquid dissolution at the laboratory scale that aims to describe the effects of immiscible liquid source-zone saturation, distribution, and length on dissolution rates. It was observed that overall immiscible-liquid saturation, distribution, and source zone length did not influence initial dissolution rates under the condition of the experiments. However, transient phase dissolution behavior, primarily observed by the heterogeneously packed columns, was significantly different to that of the homogeneously packed columns. This indicates that initial dissolution rates are comparable for these different systems, however it is demonstrated that immiscible liquid distributions (e.g., heterogeneity) can significantly effect transient dissolution rates. The second component investigates the effectiveness of a field-scale partitioning tracer test (PTT) for the measurement of the amount of denser than water immiscible liquid in the subsurface. It was demonstrated that the effectiveness of partitioning tracer test may be significantly limited by factors contributing to nonideal transport such as sorption, tracer mass, and immiscible liquid distribution. The third component examines the effectiveness of a field-scale remediation technology for the enhanced removal of denser than water immiscible liquid in the subsurface. An important component of this project was the implementation of reagent recovery and reuse, which improved the efficiency of the technology. It was demonstrated that the effectiveness of enhanced solubilization technologies for groundwater remediation may be significantly limited by the distribution of immiscible liquid in the subsurface. However, the nature of cyclodextrin (enhanced-solubilization agent) makes it an attractive option for subsurface remediation of immiscible-liquid contaminants, especially for situations where mobilization is undesirable and where the use of higher-toxicity agents is not possible.