Many conceptual models have been proposed to explain the fluid-flow mechanism responsible for the origin of carbonate-hosted lead-zinc deposits such as those in the Mississippi Valley and at Pine Point. This study is devoted to the quantitative investigation of one ore-genesis mechanism: gravity-driven groundwater-flow systems. Numerical modeling techniques are used to develop a self-contained computer code for two-dimensional simulation of regional transport processes along cross sections through sedimentary basins. The finite-element method is applied to solve the steady-state, fluid-flow and heat-transport equations, and a moving-particle random-walk model is developed to predict the dispersion and advection of aqueous components. The program EQ3/EQ6 is used to compute possible reaction-path scenarios at the ore-forming site. Full integration of geochemical calculations into the transport model is currently impractical because of computer-time limitations. Results of a sensitivity analysis indicate that gravity-driven ground-water-flow systems are capable of sustaining favorable fluid-flow rates, temperatures, and metal concentrations, for ore formation near the thin edge of a basin. Dispersive processes render long-distance transport of metal and sulfide in the same fluid an unlikely process in the genesis of large ore deposits, unless metal and sulfide are being added to the fluid along the flow path. The transport of metal in sulfate-type brines is a more defensible model, in which case the presence of reducing agents control the location of ore deposition. Hydrodynamic conditions that could result.--in ore formation through mixing of two fluids are rare. The theoretical approach is a powerful tool for gaining insight into the role of fluid flow in ore genesis and in the study of specific ore districts. A preliminary model of the Pine Point deposit suggests paleoflow rates on the order of 1.0 to 5.0 m³/m² yr, paleoconcentrations of zinc on the order of 1.0 to 5.0 mg/kg • H₂O, and paleotemperatures in the range 60°C to 100°C. Under these conditions, the time required for the formation of Pine Point would be on the order of 0.5 to 5.0 million years. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.

A theory is presented which accounts for a particular aspect of nonlinearity caused by the deviation of plume "particles" from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities. Quasilinear expressions for the time-dependent nonlocal dispersivity and spatial covariance tensors of ensemble mean concentration are derived, as a function of time, variance σᵧ² of log hydraulic conductivity, degree of anisotropy, and flow direction. One important difference between existing linear theories and the new quasilinear theory is that in the former transverse nonlocal dispersivities tend asymptotically to zero whereas in the latter they tend to nonzero Fickian asymptotes. Another important difference is that while all existing theories are nominally limited to situations where σᵧ² is less than 1, the quasilinear theory is expected to be less prone to error when this restriction is violated because it deals with the above nonlinearity without formally limiting σᵧ². The theory predicts a significant drop in dimensionless longitudinal dispersivity when σᵧ² is large as compared to the case where σᵧ² is small. As a consequence of this drop the real asymptotic longitudinal dispersivity, which varies in proportion to σᵧ² when σᵧ² is small, is predicted to vary as σᵧ when σᵧ² is large. The dimensionless transverse dispersivity also drops significantly at early dimensionless time when σᵧ² is large. At late time this dispersivity attains a maximum near σᵧ² = 1, varies asymptotically at a rate proportional to σᵧ² when σᵧ² is small, and appears inversely proportional to σᵧ when σᵧ² is large. The actual asymptotic transverse dispersivity varies in proportion to σᵧ⁴ when σᵧ² is small and appears proportional to σᵧ when σᵧ² is large. One of the most interesting findings is that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the orientation of longitudinal spread is generally offset from μ toward the direction of largest log hydraulic conductivity correlation scale. When local dispersion is active, a plume starts elongating parallel to μ. With time the long axis of the plume rotates toward the direction of largest correlation scale, then rotates back toward μ, and finally stabilizes asymptotically at a relatively small angle of deflection. Application of the theory to depth-averaged concentration data from the recent tracer experiment at Borden, Ontario, yields a consistent and improved fit without any need for parameter adjustment.

Many environmental studies of water transport through the vadose zone require a field determination of saturated hydraulic conductivity. The purpose of this dissertation is to analyze the reliability of existing methods to determine saturated hydraulic conductivity, K(s), in the vadose zone from constant head borehole infiltration test data. In methods developed by the U. S. Bureau of Reclamation [USBRI, and in lesser known ones, K(s) is computed knowing the height of water in the borehole, length open to the formation, borehole radius, distance above the water table, and steady flow rate. The mathematical formulas on which these methods rest are derived on the basis of numerous simplifying assumptions. The free surface approach is used as the conceptual model of flow from a borehole. Results of numerical simulations are used to compare with the analytical solutions. Simulations with a steady-state finite element computer program, FREESURF, show that the Nasberg-Terletskata solution most closely approximates flow from a borehole with the free surface approach. The influence of capillarity is simulated for saturated-unsaturated porous media in four soils using a finite element computer program, FLUMP, and an integrated finite difference program, TRUST. Contrary to what one finds with the free surface approach, only a small portion of the flow field near the borehole is saturated at steady-state and the cross sectional area normal to the flow path increases with depth below the borehole. For deep water table conditions in fine textured soils, values of K(s) computed using the USBR open-hole equations may be more than 160% greater than the true values; and in coarse sands the USBR solutions may under-estimate the actual value by more than 35%. Mostly because of the influence of unsaturated soil properties there is no unique relationship between K(s), borehole conditions, and steady flow rate, as implied in the analytical solutions. Steady-state simulations demonstrate that existing solutions for borehole infiltration tests in anisotropic or nonuniform soils may also lead to significant errors. Time dependent simulations show that the time to reach a steady flow rate may be more than several days in very dry, low-permeable soils. The time to reach a steady flow rate can be significantly reduced by decreasing the open area between the borehole and formation while increasing the height of water in the borehole. Two methods are proposed to minimize the time, water volume requirements, and cost of conducting constant head borehole infiltration tests. Simulations show that a plot of the inverse of flow rate versus logarithm of time departs from a straight line after about 80% of the steady rate is achieved for various soil and borehole conditions; the steady rate is approximately 0.8 times the rate at the break in slope. In the second method flow rate is plotted versus the inverse of the square root of time and the steady rate is estimated within about 10% by linear extrapolation of early time measurements. USBR field data generally support this linear relationship. Two empirical equations are proposed to compute K(s). The first is applicable for a range of borehole conditions and approximately accounts for capillary effects with a single parameter. The second applies if the height of water in the borehole is I meter, and is based on the time to reach 80% of the steady rate and saturation deficit of the field soil.

Solute transport studies frequently rely on numerical solutions of the classical advection-diffusion equation. Unfortunately, solutions obtained with traditional finite difference and finite element techniques typically exhibit excessive numerical diffusion or spurious oscillation when advection dominates, especially when velocity field is highly variable. One recently developed technique, the finite analytic method, offers an attractive alternative. Finite analytic methods utilize local analytic solutions in discrete elements to obtain the algebraic representations of the governing partial differential equations, thus eliminating the truncation error in the finite difference and the use of approximating functions in the finite element method. The finite analytic solutions have been shown to be stable and numerically robust for advection-dominated transport in heterogeneous velocity fields. However, the existing finite analytic methods for solute transport in multiple dimensions have the following disadvantages. First, the method is computationally inefficient when applied to heterogeneous media due to the complexity of the formulation. Second, the evaluation of finite analytic coefficients is when the Peclet number is large. Third, the method introduces significant numerical diffusion due to inadequate temporal approximation when applied to transient problems. This thesis develops improved finite analytic methods for two-dimensional steady as well as unsteady solute transports in steady velocity fields. For steady transport, the new method exploits the advantages of the existing finite analytic and finite difference methods. The analytically difficult diffusion terms are approximated by finite difference and numerically difficult advection and reaction terms are treated analytically in a local element in deriving the numerical schemes. The new finite analytic method is extended to unsteady transport through application of Laplace transformation. Laplace transformation converts the transient equation to a steady-state expression that can be solved with the steady version of the improved finite analytic method. Numerical inversion of the transformed variables is used to recover solute concentration in the physical space-time domain. The effectiveness and accuracy of the new finite analytic method is demonstrated through stringent test examples of two dimensional steady-state transport in highly variable velocity fields. The results clearly demonstrated that the improved finite analytic methods are efficient, robust and accurate.

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A computer model simulating moisture migration in soil from a drip source considering root water extraction (RWE) was developed. The model was formulated using Continuous System Modeling Program (CSMP). / A two-dimensional non-linear unsaturated transient flow equation was solved using the principle of mass conservation and Darcy's law on soils of dwarf-apple orchards located in southwestern Quebec. A finite axisymmetric cylinder with homogeneous, isotropic and non-swelling soil was considered for the simulations. No flow conditions across the boundaries of the cylinder were fixed. The initial soil moisture contents in the soil profile observed in the field were input for the simulations. / The macroscopic approach was used to compute RWE as a function of (THETA), Z and t. The RWE was assumed to be equal to evapotranspiration (EP) which was estimated using temperatures and the solar radiation index of the location. / The moisture contents in the soil profile observed at the termination of emitter discharge were in close agreement with the simulated values. The soil moisture distribution was found to depend on the amount of water remaining in the soil and soil moisture retention characteristics. It is independent of the rate of emitter discharge, the depth of root zone and method of application.

A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.