Emil O. Frind

Migration of contaminants in groundwater at a landfill: A case study: 4. A natural-gradient dispersion test

Abstract A natural-gradient tracer test using a chloride solution with an initial injection volume of 0.7 m 3 was performed in the sandy aquifer at the Borden site. The solution was injected into five well points set ∼1 m below the water table in an uncontaminated zone situated above the contaminant plume at a location ∼450 m downflow from the landfill. Under conditions of natural groundwater flow, the tracer slug was monitored for a period of 4 months by withdrawing small-volume samples from points in a three-dimensional array of bundle-type multilevel samplers. Measurements of hydraulic head were obtained from a network of miniature piezometers. Soon after injection, the tracer slug gradually split into two halves, one half moving horizontally at an average velocity of 2.9 · 10 −6 ms −1 and the other horizontally at 8.2 · 10 −7 ms −1 . Although the split has been attributed to local lateral heterogeneity, the nature of the heterogeneity and its influence on the hydraulic-head distribution were not clearly distinguishable in the field data obtained before, during or after the test. The chloride patterns for each of the two halves of the tracer slug evolved into Gaussian forms although the patterns demonstrated some irregularity at early time. The relatively smooth Gaussian forms were unexpected because the aquifer has numerous small-scale heterogeneities observed in vertical cores obtained from the tracer zone and because the glaciofluvial origin of the aquifer suggests that heterogeneities are not laterally continuous. Simulated chloride distributions from a three-dimensional analytical solution to the advection-dispersion equation were fitted to the field data to obtain best-fit estimates of the values of longitudinal, transverse-horizontal and transverse-vertical dispersivity at various travel distances for each of the two halves of the tracer zone. This is the first known field test that has permitted the estimation of three principal dispersion coefficients in layered media. The longitudinal dispersivity was found to increase from 0.01 m at a distance of 0.75 m from the source to 0.08 m at 11.0 m. The transverse-horizontal dispersivity increased also to a value of 0.03 m at 11.0 m. Transverse-vertical dispersion was very weak and was accounted for by molecular diffusion. The relative lack of vertical dispersion is consistent with the shape of the plume of leachate contamination from the landfill. It was concluded that the observed increase in dispersivity along the path of migration is likely caused by heterogeneities. Information on the dispersion-controlling heterogeneities is not yet available as practical field methodologies for their identification and description have not yet been developed. Until such information is incorporated into mass-transport models, a realistic solution of the dispersion problem in heterogeneous media will remain elusive.

Two-phase flow in heterogeneous porous media. 1. Model development

A two-dimensional finite difference model to study the simultaneous movement of a dense, nonaqueous phase liquid and water in heterogeneous porous media is developed. A distinctive feature of the solution is that the primary variables solved for, wetting phase pressure and wetting phase saturation, are both existent throughout the solution domain regardless of whether the nonwetting phase is present. This eliminates the need to specify small, fictitious saturations of nonwetting fluid ahead of the advancing front where only wetting fluid is present, as is often required in conventional simulators. The model is therefore well suited for the simulation of ground water contamination problems involving the advance of immiscible liquids into previously uncontaminated groundwater systems. The finite difference equations are solved fully implicitly using Newton-Raphson iteration. In order to minimize computer storage and execution time a Dupont-Kendall-Rachford iterative solver utilizing Orthomin acceleration has been incorporated. The numerical model is verified against an exact analytical solution which incorporates fully the effects of both relative permeability and capillary pressure. The model is validated through comparison to a parallel-plate laboratory experiment involving the infiltration of tetrachloroethylene into a heterogeneous sand pack.

Numerical simulation of biodegradation controlled by transverse mixing

Abstract Microbial activity in aquifers is controlled by the mixing between the reacting substrates. Conventional modelling methods that are commonly used to analyze reactive transport of organics in heterogeneous systems may give erroneous results because mixing is often over-represented in the model. This effect will be strongest when the reaction is controlled by transverse dispersion as in the case of aerobic degradation of waste-water introduced into an aquifer by an injection well. We show that fictitious transverse mixing can be created by a numerical model based on rectangular grids, and that this problem can be controlled by formulating the problem in streamline-oriented coordinates. In both model formulations, nonlinear high-resolution techniques minimizing the amount of artificial diffusion were applied, so that fictitious mixing is exclusively due to grid-orientation effects. Additionally it is shown that applying dispersivity values based on the second spatial moment transverse to the direction of flow leads to an overestimation of mixing. The fictitious degradation produced by model-dependent transverse dispersion caused the modelled plume to degrade much faster, and therefore appear much shorter, than the actual plume. Thus, the choice of appropriate dispersivity values as well as the control of artificial transverse diffusion is crucial when modelling mixing-controlled reactive transport.

Modeling of multicomponent reactive transport in groundwater: 1. Model development and evaluation

MINTRAN is a new model for simulating transport of multiple thermodynamically reacting chemical substances in groundwater systems. It consists of two main modules, a finite element transport module (PLUME2D), and an equilibrium geochemistry module (MINTEQA2). Making use of the local equilibrium assumption, the inherent chemical nonlinearity is confined to the chemical domain. This linearizes the coupling between the physical and chemical processes and leads to a simple and efficient two-step sequential solution algorithm. The advantages of the coupled model include access to the comprehensive geochemical database of MINTEQA2 and the ability to simulate hydrogeological systems with realistic aquifer properties and boundary conditions under complex geochemical conditions. The model is primarily targeted toward groundwater contamination due to acidic mine tailings efiiuents but is potentially also applicable to the full range of geochemical scenarios covered by MINTEQA2. The model is tested with respect to ion exchange chemistry and with respect to precipitation/dissolution chemistry involving multiple sharp fronts. The companion paper presents two-dimensional simulations of heavy metal transport in an acidic mine tailings environment, focusing on environmental implications.

Two-phase flow in heterogeneous porous media: 2. Model application

The migration of a dense, nonaqueous phase liquid through heterogeneous porous media is examined using numerical simulation. Laboratory measurements of capillary pressure-saturation curves were performed on samples obtained from a sand aquifer and scaled to permeability to provide a data base of model input parameters. Numerical simulations incorporating 25,200 finite difference cells are carried out in a spatially correlated, random permeability field to illustrate the influence of fluid properties on the migration of a nonwetting liquid below the water table. The simulation results are characterized by spatial moments to reflect the relative degrees of lateral spreading exhibited by the migrating nonwetting body in the presence of lenses of differing permeability. In addition, numerical simulations were performed in a solution domain containing a single lens of lower permeability material in order to examine the local-scale sensitivity to porous media and fluid properties. The results of the study show the migration of a nonwetting liquid to be extremely sensitive to subtle variations in the capillary properties of the porous medium and to be influenced strongly by the fluid physical properties.

Sulfide mineral oxidation and subsequent reactive transport of oxidation products in mine tailings impoundments: A numerical model

A versatile numerical model that couples oxygen diffusion and sulfide-mineral oxidation (PYROX) has been developed to simulate the oxidation of pyrite in the vadose zone of mine tailings. A shrinking-core oxidation model and a finite element numerical scheme are used to simulate the transport of oxygen and oxidation of pyrite grains. The rate of pyrite oxidation is assumed to be limited by the transport of oxygen to the reaction site. The model determines the spatially variable bulk diffusion coefficient for oxygen on the basis of moisture content, porosity, and temperature, all of which are variable input parameters. The model PYROX has been coupled to an existing reactive transport model (MINTRAN), which uses a finite element scheme for transport of contaminants and MINTEQA2 to solve for the equilibrium geochemistry. The reactions described by MINTRAN are subject to the local equilibrium assumption. The resulting model, MINTOX, is capable of simulating tailings impoundments where the oxidation of pyrite or pyrrhotite is causing acidic drainage and where acid neutralization and attenuation of dissolved metals can be attributed to equilibrium reactions. Because MINTOX uses realistic boundary conditions and hydrogeological properties, the potential benefits of various remediation schemes, such as moisture-retaining covers, can be quantitatively evaluated.

Reactive transport modeling of an in situ reactive barrier for the treatment of hexavalent chromium and trichloroethylene in groundwater

Multicomponent reactive transport modeling was conducted for the permeable reactive barrier at the Coast Guard Support Center near Elizabeth City, North Carolina. The zero-valent iron barrier was installed to treat groundwater contaminated by hexavalent chromium and chlorinated solvents. The simulations were performed using the reactive transport model MIN3P, applied to an existing site-specific conceptual model. Reaction processes controlling the geochemical evolution within and down gradient of the barrier were considered. Within the barrier, the treatment of the contaminants, the reduction of other electron acceptors present in the ambient groundwater, microbially mediated sulfate reduction, the precipitation of secondary minerals, and degassing of hydrogen gas were included. Down gradient of the barrier, water-rock interactions between the highly alkaline and reducing pore water emanating from the barrier and the aquifer material were considered. The model results illustrate removal of Cr(VI) and the chlorinated solvents by the reactive barrier and highlight that reactions other than the remediation reactions most significantly affect the water chemistry in the barrier. In particular, sulfate reduction and iron corrosion by water control the evolution of the pore water while passing through the treatment system. The simulation results indicate that secondary mineral formation has the potential to decrease the porosity in the barrier over the long term and illustrate that the precipitation of minerals is concentrated in the upgradient portion of the barrier. Two-dimensional simulations demonstrate how preferential flow can affect the reduction of electron acceptors, the consumption of the treatment material, and the formation of secondary minerals. In addition, the model results indicate that deprotonation and the adsorption of cations down gradient of the barrier can potentially explain the observed pH buffering.

Nonequilibrium mass transfer between the vapor, aqueous, and solid phases in unsaturated soils during vapor extraction

Vapor extraction is a commonly used method for removing nonaqueous phase liquid volatile organic compounds (VOC) from the vadose zone. Experience indicates that in the absence of liquid VOC, the efficiency of vapor extraction systems decreases dramatically with time as effluent concentrations approach zero asymptotically. When such systems are restarted after a temporary shutdown, effluent concentrations are often found to recover for a short period before dropping back to preshutdown levels. This behavior is generally attributed to kinetic processes which limit the transfer of contaminant into the moving air. A numerical model is developed to simulate the rate-limited extraction of volatile compounds governed by first-order kinetic mass transfer processes. A sensitivity analysis is performed to identify model responses to various kinetic and equilibrium partitioning processes. The model is calibrated using experimental data collected from a pilot-scale experiment involving vapor extraction of trichloroethylene from fine sand. An analysis of the relationships between airflow rates and the kinetic mass transfer coefficients under various pumping schemes shows that for a given condition, increasing the flow rate has little effect beyond a certain point. It is also shown that pulsed pumping is generally less efficient than continuous pumping at a low rate.

Thermal energy storage in an unconfined aquifer: 2. Model development, validation, and application

A fully three-dimensional numerical model for simulating coupled density-dependent groundwater flow and thermal energy transport is developed and validated. The transport solution is based on a finite element time integration algorithm which generates a symmetric coefficient matrix while retaining second-order accuracy in time. The use of a symmetric conjugate gradient solver for both the flow and transport matrices results in a high degree of computational efficiency. Three-dimensional deformable block elements are used to allow the model to conform to domains with irregular geometry. The thermal transport model is validated against the results of the Borden thermal injection field experiment presented in the companion paper. The model simulations provide an excellent match with the observed temperature distribution over time, with the effects of thermal buoyancy and losses across the ground surface accurately reproduced by the model. The model is shown to be a practical tool for simulating the type of low-temperature thermal transport problems that arise in connection with seasonal aquifer thermal energy storage and ground source heat extraction systems.

Comparative error analysis in finite element formulations of the advection-dispersion equation

Abstract The behaviour of numerical solutions of the one-dimensional advection-dispersion equation is investigated and comparisons between the consistent and the lumped formulations of Galerkin finite element schemes are made. Well-known criteria for the control of accuracy in the lumped (finite difference) formulation are reviewed. It is found that, because the numerical error produced by the consistent formulation is generally less than that produced by the lumped formulation, these criteria can also be used for the control of numerical dispersion in the consistent formulation. However, because the error in both types of solutions decreases in time when the discretization is invariant, the criteria can be relaxed with advancing simulation time. For the consistent formulation it is found that beyond some initial time period, the numerical error depends only on the temporal discretization. This suggests that constant accuracy can be maintained throughout the simulation period while allowing the time step length to grow.