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Secondary structures (e.g., fractures, sand lenses, kimberlite intrusions) can compromise the ability of clay-rich bedrock aquitards to protect underlying aquifers from near-surface contamination. To date, the effects of secondary structures on water migration and solute transport in these deposits have been poorly characterized. This study characterized the water migration and solute transport mechanisms at both a geologically simple and a geologically complex late-Cretaceous shale aquitard, with the field sites located 5 km apart in central Saskatchewan, Canada. The geotechnical properties and hydrogeologic properties of the complex aquitard were altered by kimberlite volcanism and subsequent hydrothermal alteration during its deposition (99 to 112 Ma BP). High-resolution, 1-D vertical profiles of conservative δ2H and Cl were collected from both sites (203 and 353 m deep, respectively) to define the vertical solute transport mechanisms. The shape of the 1-D tracer profiles and associated solute transport modeling from the geologically simple site suggest diffusion is the dominant transport mechanism through the entire thickness of the Lower Colorado shale aquitard (330 to 246 m above sea level, asl). Similarly, profiles through the complex, fractured, Cretaceous shale and associated modeling suggest diffusion is the dominant transport mechanism through the entire profile despite the presence of fractures; however, hydrothermal alteration during cooling of the kimberlite volcaniclastic material reduce the effective porosity (ne) of the kimberlite material from 40% to 1-5%. Results also suggest that, despite kimberlite emplacement in the study area, water migration and solute transport in the overlying and underlying Cretaceous shale may be unaffected by kimberlite volcanism and associated fracturing and alteration.

This dissertation is composed of five chapters and three major contributions are presented in Chapter II, III and IV. Chapter I provided a review of studies on solute transport in aquifer-aquitard system. If the aquitard is considered, two categories of methods address the diffusive flux between the aquifer and aquitard: the old method treats the diffusive flux as a volumetric source in the governing equation of the solute transport in the aquifer; the new method treats the aquifer-aquitard boundary as a strict physical boundary with the requirement of continuity of solute concentration and the vertical flux. The new method is adopted throughout this study. In Chapter II, a review of numerical techniques on Inverse Laplace Transform is provided. By careful comparison between several popular algorithms, the multiple precision Stehfest algorithm is chosen as the method to inverse out solutions on solute transport in Laplace domain throughout this dissertation. In Chapter III, solutions were obtained for two dimensional solute transport in an aquifer-aquitard system with a divergent radial flow field, which can treat different types of solute input function and advection, longitudinal and transverse dispersion in the aquifer, vertical diffusion in the aquitard, retardation and radioactive decay in the aquifer and aquitard are taken into account. Mass exchange via diffusion between the aquifer and aquitard are investigated. The effects of hydrologic properties of the aquitard on solute transport are analyzed. Comparisons were made between the results from this study and those from previous studies. The diffusion along the aquifer-aquitard boundary was treated as a volumetric source term, and proved these solutions yield more accurate solute concentration, while those from previous studies tend to overestimate solute concentration in the aquitard, and underestimate the concentration in the aquifer. In Chapter IV, solutions were derived for the transport of radioactive isotopes in an aquifer-aquitard system with regional flow field. This study focused on the effects of different solute transport processes on the results of groundwater age dating using radiometric techniques. Chapter V summarized the remaining problems in this study and directions for future researches.

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The impact of the soil structure on flow and transport in partially water saturated soils is currently still a matter of scientific debate. The major aim of this thesis was to investigate the relation between heterogeneity and transport for a natural unsaturated heterogeneous Tertiary sand deposit. In the first part, we analyzed the flow and transport at the scale of an undisturbed monolith. Chloride breakthrough curve experiments were used to derive an apparent dispersion coefficient at the TDR sampling and monolith scale. Application of a Brilliant Blue pulse allowed further the visualization of flow distribution within the monolith. Small undisturbed soil cores were sampled throughout the monolith and the hydraulic characteristic curves at the scale of the cores were determined. Textural variability and structure as inferred from the inspection of the Brilliant Blue pattern and analysis of the small core sampling were subsequently implemented in a 3-D model and transport was simulated. The simulations clearly revealed the importance of the macro-structure on the transport behavior of the soil. We also showed that the micro-variability heterogeneity component was needed to assess the scaling of the effective and local scale dispersivity. In the second part, we studied in-situ chloride transport in the vadose formation separating the bottom of a lake and an unconfined aquifer. First the uncertainty generated by the undersampling of the lake chloride concentration time series were investigated. Subsequently, velocity and dispersivity profiles were assessed by inverse modeling of the soil chloride concentration time series. We observed that the clay layers induced an increase of the dispersivity below them. We hypothesize that fingering flow or convergence phenomena, occurring below sand-clay interfaces, lead to non-representative artificially high dispersivity values. Velocity and dispersivity values just above the clay layers however seem more reliable due to convergence phenomena and better lateral mixing induced by a larger water content. In this formation, the transport behavior could be characterized considering a hierarchical structure of the subsoil heterogeneity. In this model, the flow field micro-variability is influenced by pore structure (possibly characterized by scaling factors). The next complexity level is induced by the slight layering resulting from the sedimentation process (not investigated in this work). Then, the third hierarchical level is assessed by the macro-structure and the sequence of clay layers in the sand. Each of these levels is assumed to have an effect on the solute mixing process and effective macro-dispersivity.

The primary focus of the research is to extend the principles of Nanofiltration(NF) to non-aqueous systems using solvent-resistant NF membranes. Several differentlevels of interaction are introduced when organic solvents are used with polymericmembranes and thus quantification of polymer-solvent interactions is critical. Puresolvent permeation studies were conducted to understand the mechanism of solventtransport through polymeric membranes. Different membrane materials (hydrophilic andhydrophobic) as well as different solvents (polar and non-polar) were used for the study.For example, hexane flux at 13 bar through a hydrophobic silicone based NF membranewas ~ 0.6 x 10-4 cm3/cm2. s. and that through a hydrophilic aromatic polyamide based NFmembrane was ~ 6 x 10-4 cm3/cm2. s. A simple model based on a solution-diffusionapproach which uses solvent physical properties (molar volume, viscosity) andmembrane properties (surface energy, etc) is used for correlating the pure solventpermeation through hydrophobic polymeric membranes.Solute transport studies were performed using organic dyes and triglycerides inpolar and non-polar solvents. For example, the rejection of Sudan IV (384 MW organicdye) in n-hexane medium is about 25 % at 15 bar and that in methanol is about –10 % atabout 20 bar for a hydrophobic (PDMS-based) membrane. However, for a hydrophilicpolyamide based NF membrane, the direction of separation is reversed (86 % in methanoland 43 % in n-hexane). From our experimental data with two types of membranes it isclear that coupling of the solute and solvent fluxes cannot be neglected. Two traditionaltransport theories (Spiegler-Kedem and Surface Force-Pore Flow model) that considercoupling were evaluated with literature and our experimental solute permeation data. Amodel based on a fundamental chemical potential gradient approach has been proposedfor explaining solute separation. The model uses solute, solvent and membrane physicalproperties and uses the Flory-Huggins and UNIFAC theories as activity coefficientmodels. This model has been used to obtain a correlation for the diffusion coefficients ofsolutes in hexane through a hydrophobic membrane. This correlation along withconvective coupling can be used to predict separation behavior for different solutes and atdifferent temperatures.

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Geological carbon dioxide (CO₂) storage in deep geological formations can only lead to significant reductions in anthropogenic CO₂ emissions if large amounts of CO₂ can be stored safely. Determining the storage capacity, which is the volume of CO₂ stored safely, is essential to determine the feasibility of geological CO₂ storage. One of the main constraints for the storage capacity is the physical mechanisms of fluid flow in heterogeneous formations, which has not been studied sufficiently. Therefore, I consider two related problems: a) the evolution of injection-induced overpressure that determines the area affected by CO₂ storage and b) the rate of buoyant fluid flow along faults that determines the leakage of CO₂. I use a layered model of a sandstone reservoir embedded in mudrocks to quantify the increase in storage capacity due to dissipation of overpressure into the mudrocks. I use a model of a fault surface with flow barriers to constrain the reduction in the buoyancy-driven leakage flux across the fault. Using the layered model with injection at constant rate, I show that the pressure evolution in the reservoir is controlled by the amount of overpressure dissipated into ambient mudrocks. A main result of this study is that the pressure dissipation in a layered reservoir is controlled by a single dissipation parameter, M, that is identified here for the first time. I also show that lateral pressure propagation in the storage formation follows a power-law governed by M. The quick evaluation of the power-law allows a determination of the uncertainty in the estimate of the storage capacity. To reduce this uncertainty it is important to characterize the petrophysical properties of the mudrocks surrounding the storage reservoir. The uncertainty in mudrock properties due to its extreme heterogeneity or limited data available can cause large variability in these estimates, which emphasizes that careful characterization of mudrock is required for a reliable estimate of the storage capacity. The cessation of the injection operation will reduce overpressure near the injector, but regional scale pressure will continue to diffuse throughout the whole formation. I have been able to show that the maximum radius of the pressure plume in the post-injection period is approximately 3.5 times the radius of the pressure plume at the cessation of injection. Two aquifers can be hydraulically connected by a fault cutting across the intermediate aquitard. If the upper aquifer contains denser fluid, an exchange flow across the fault will develop. The unstable density stratification leads to a fingering pattern with localized zones of upwelling and downwelling along the fault. Due to the small volume of the fault relative to the aquifers, the exchange-flow will quickly approach a quasi steady state. If the permeability of the fault plane is homogeneous, the average number of the quasi-steady plume fingers, (nu), scales with the square root of the Rayleigh number Ra and the exchange flux measured by dimensionless convective flux, the Sherwood number, Sh, is a linear function of Ra. The dispersive flux perpendicular to the flow direction induces the formation of wider fingers and subsequently the less convective flux parallel to the flow direction. In the flow system with larger Ra, even the same increase in transverse dispersivity [alpha]T causes stronger impact of the mechanical dispersion on the vertical exchange flow so that (nu) and Sh reduce more with larger [alpha]T . Both measured characteristics, however, follow the same scaling for the non-dispersive homogeneous case by using a modified Rayleigh number, Ra*, considering the mechanical dispersion. The presence of flow barriers along the fault triggers unsteady exchange flow and subsequently controls the growth of the plume fingers. If the barriers are sufficiently wide to dominate the flow system, they create preferential pathways for exchange flow that determines the distribution of the quasi-steady fingers, and (nu) converges to a constant value. In addition, wider barriers induce substantial lateral spreading and enhance the efficiency of structural trapping, and reduce the exchange rate but still follows a linear relationship function of the effective Rayleigh number, Raeff , defined by the vertical effective permeability. This study is motivated by geological CO₂ storage in brine-saturated aquifer, but the effect of geological heterogeneity is also important in many other geological and engineering applications, in particular the risk assessment of the injection operations or the migration of hydrocarbons in tectonic-driven or hydraulically developed faults in reservoirs. Better understanding of fluid flow in geologically heterogeneous formations will allow more precise estimate of the reservoir capacity as well as more efficient operation of injection or production wells. / text

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The feasibility of simulating solute transport in a channel impregnated witha biofilm is investigated. Biofilm factors relevant for numerical simulation arestudied to determine a suitable range of simulation. Inside the feasable rangeseveral cases are simulated to gain insight of how different factors influence thesolute transport in and around biofilms.