Investigation of Consolidation-Induced Solute Transport. II: Experimental and Numerical Results

This paper presents an experimental and numerical investigation of consolidation-induced solute transport. Diffusion and large strain consolidation tests were performed on composite specimens of kaolinite clay consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Experimental measurements of effluent concentration, solute mass outflow, and final concentration profiles were obtained for a variety of initial, boundary, and loading conditions, including unload/reload. Numerical simulations were conducted using a computational model in which solute transport occurs by advection, dispersion, and sorption and is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. Large strains were taken into account as well as variation of effective diffusion coefficient with porosity and nonlinear nonequilibrium sorption effects. The numerical simulations are in good to excellent agreement with the experimental measurements. Results indicate that, depending on conditions, diffusion and consolidation-induced advection can make important contributions to solute transport and mass outflow. Thus, both mechanisms should be considered for transport analyses involving soft contaminated clays undergoing large volume change. Results also indicate that nonequilibrium sorption effects were not significant for the materials and test conditions used in this study.     

Model for Consolidation-Induced Solute Transport with Nonlinear and Nonequilibrium Sorption

A numerical model, called CST2, is presented for coupled large strain consolidation and solute transport in saturated porous media. The consolidation and solute transport algorithms include the capabilities of a previous model, CST1, with the addition of a variable effective diffusion coefficient during consolidation and nonlinear nonequilibrium sorption. The model is based on a dual-Lagrangian framework that tracks separately the motions of fluid and solid phases. Verification checks of CST2 show excellent agreement with analytical and numerical solutions for solute transport in rigid porous media. A parametric study illustrates that, for the test cases considered, variation of effective diffusion coefficient during consolidation has an important effect on solute transport, whereas nonlinearity of the sorption isotherm has a less important effect. Additional simulations show that nonequilibrium sorption can have a strong effect on consolidation-induced solute transport and that this effect becomes more important as the rate of consolidation increases. The simulations also corroborate previous findings that consolidation can have a lasting effect on solute migration because transient advective flows change the distribution of solute mass which then becomes the initial condition for subsequent transport processes.     

Coupled Large Strain Consolidation and Solute Transport. I: Model Development

The development of a numerical model, CST1, for coupled large strain consolidation and solute transport in saturated porous media is presented. The consolidation algorithm is one-dimensional and includes the capabilities of a previous code, CS2, with the addition of time-dependent loading, unload/reload effects, and an externally-applied hydraulic gradient. The solute transport algorithm is two-dimensional and accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Solute transport is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. The key to the transport model is the definition of two Lagrangian fields of elements that follow the motions of fluid and solid phases separately. This reduces numerical dispersion and simplifies transport calculations to that of dispersion mass flow between contiguous fluid elements. The effect of relative numerical resolution of fluid and solid elements on the accuracy of sorption/desorption is also discussed. This paper presents the theoretical and numerical development of the CST1 model. A companion paper presents verification checks of CST1 and the results of simulations that illustrate the significance of consolidation-induced solute transport for some interesting numeric examples.     

Parametric Study of One-Dimensional Solute Transport in Deformable Porous Media

Formulation for the effect of dissipation of excess pore water pressure on one-dimensional advective-diffusive transport of solutes in clays is presented. The formulation is based on the effect of the rate of consolidation or swelling and excess pore pressure or suction dissipation on transient, nonlinear advective component of transport through clay. One partial differential equation is presented for advective diffusive transport that is dependent upon soil/solute properties and transient hydraulic head gradient, which is calculated from the Terzaghi consolidation equation. Finite difference method is used to solve the system of partial differential equations for consolidation and solute transport. Four hypothetical cases are evaluated to demonstrate the effect of consolidation under loading and swelling under hydraulic gradient on advective-diffusive transport and breakthrough in single and double drainage clay layer. The results show that consolidation in doubly drained clay impacts concentration profiles, but does not significantly impact breakthrough of the diffusive flux. Consolidation under single drainage conditions, significantly impacts the diffusional flux. When drainage path is the same as the diffusional flux, consolidation accelerates transport and breakthrough time can be less than 5% of the diffusional breakthrough time under no consolidation. Swelling under hydraulic gradient application can either accelerate or retard the advective diffusive flux, depending upon the ratio of the effective diffusion coefficient relative to the coefficient of consolidation. Higher the effective diffusion coefficient and lower the coefficient of consolidation result in an increase in the effect of pressure dissipation on transport.     

Coupled Large Strain Consolidation and Solute Transport. II: Model Verification and Simulation Results

The results of numerical simulations for coupled large strain consolidation and solute transport, obtained using the CST1 model, are presented. CST1 accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Verification checks of CST1 show excellent agreement with analytical solutions for one-dimensional (1D) transport in rigid porous media, including various Peclet numbers and concentration boundary conditions. Similarly excellent agreement is observed for two-dimensional advection-dispersion transport in rigid media and 1D advection-dispersion transport in compressible media undergoing large strain consolidation. CST1 is then used to investigate consolidation-induced solute transport for a single composite liner system and a confined disposal facility for dredged contaminated sediments. In both cases, solute transport was found to be strongly affected by consolidation-induced advection both during and after the consolidation period. Consolidation has a lasting effect on solute migration because transient advective flows change the distribution of solute mass, which then becomes the initial condition for subsequent transport processes.     

Coupled Consolidation and Contaminant Transport in Compressible Porous Media

This paper presents an experimental and numerical investigation of coupled consolidation and contaminant transport in compressible porous media. Numerical simulations were performed using the CST2 computational model, in which a dual-Lagrangian framework is used to separately follow the motions of fluid and solid phases during consolidation. Diffusion and large strain consolidation-induced transport tests were conducted on composite specimens of kaolinite slurry consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Assessment of the importance of the consolidation process on solute transport is based on measured and simulated solute breakthrough curves and final contaminant concentration profiles. CST2 simulations closely match the experimental data for three different loading conditions. Diffusion and consolidation-induced advection made important contributions to solute transport and mass outflow in this study. Additional simulations indicate that consolidation-induced contaminant transport may also be affected by specimen boundary drainage and initial concentration conditions.     

Volatile Organic Compound (VOC) Transport through Compacted Clay

Movement of volatile organic compounds (VOCs) through compacted clay liners was investigated using laboratory-scale column and tank tests. Hydraulic conductivity of the compacted clay was not significantly impacted by the introduction of VOCs in concentrations up to 20 mg∕L. Soil-water partition coefficients of the seven VOCs tested had a strong logarithmic relationship with the octanol-water partition coefficient. Partition coefficients from batch tests were in good agreement with those measured directly on soil samples at the termination of the column∕tank tests. The VOCs were degraded in the clay, with estimated half-lives ranging from 2 to 116 days. Mechanical dispersion was not significant in the range of the hydraulic conductivities of the test specimens (i.e., <10?7 cm∕s). Effective molecular diffusion coefficients were mostly in 10?6 cm2∕s and generally decreased with increasing aqueous solubility. Mass transport parameters of VOCs in clay liners can be estimated from laboratory batch tests and properly prepared small-scale column tests. However, accounting for degradation of VOCs and minimizing the number of transport parameters that are simultaneously estimated from a single response-time record are important considerations for accurate determination of transport parameters.     

Evaluation of Multidimensional Transport through a Field-Scale Compacted Soil Liner

A field-scale compacted soil liner was constructed at the University of Illinois at Urbana-Champaign by the U.S. Environmental Protection Agency (USEPA) and Illinois State Geological Survey in 1988 to investigate chemical transport rates through low permeability compacted clay liners (CCLs). Four tracers (bromide and three benzoic acid tracers) were each added to one of four large ring infiltrometers (LRIs) while tritium was added to the pond water (excluding the infiltrometers). Results from the long-term transport of Br? from the localized source zone of LRI are presented in this paper. Core samples were taken radially outward from the center of the Br? LRI and concentration depth profiles were obtained. Transport properties were evaluated using an axially symmetric transport model. Results indicate that (1) transport was diffusion controlled; (2) transport due to advection was negligible and well within the regulatory limits of ksat ? 1×10?7?cm/s; (3) diffusion rates in the horizontal and vertical directions were the same; and (4) small positioning errors due to compression during soil sampling did not affect the best fit advection and diffusion values. The best-fit diffusion coefficient for bromide was equal to the molecular diffusion coefficient multiplied by a tortuosity factor of 0.27, which is within 8% of the tortuosity factor (0.25) found in a related study where tritium transport through the same liner was evaluated. This suggests that the governing mechanisms for the transport of tritium and bromide through the CCL were similar. These results are significant because they address transport through a composite liner from a localized source zone which occurs when defects or punctures in the geomembrane of a composite system are present.     

Chloride Transport through Cement-Bentonite Barriers

This paper presents experimental results from a number of column tests on cement-bentonite (CB) mixtures permeated with chloride (Cl?). Factors influencing the hydraulic conductivity (k), the hydrodynamic dispersion coefficient (D) and the retardation factor (Rd) are investigated. The significant factors considered are the curing period, seepage velocity (v), reference concentration (CR), and mean particle size (d50). Other factors such as porosity (n) and mix design are also discussed. Results show that a longer curing period lowers all three transport parameters. Furthermore, as the seepage velocity increases, Rd decreases and D increases. The yielding velocity at which mechanical dispersion (Dmd) starts prevailing is observed at about 0.0001?cm/s. Both Rd and D are seen to reduce with increasing CR. Thus, the concept of CR could be used to explain the data scattering in a CB hydrodynamic curve.     

Evaluation of Metal Attenuation through Paper Clay Utilized for Containment of Contaminated Groundwater

Paper clay has several properties that make its use in vertical barriers very promising. In this paper the characteristics of two paper sludges (which will also be referred to as paper clays) one from the Erving Paper Company and one from the International Paper Company are considered. To determine the feasibility of paper clay for heavy metal attenuation, batch tests, column tests, hydraulic conductivity tests, and pressure filtration tests were performed. Batch testing showed that the metal, the distribution coefficient (Kd) ranged from as low as 0.002 L/g for manganese to as high as 6.7 L/g for lead in International paper clay. In the Erving paper clay the Kd ranged from 0.007 L/g for manganese to 1.9 L/g for cadmium, while the International paper clay Kd ranged from 0.002 L/g for manganese to 6.7 L/g for lead. Chemisorption was established as the predominant metal binding mechanism in both clays with the only exceptions being manganese adsorption on International paper clay that indicated a constant partitioning, and copper and lead on Erving paper clay that indicated constant partitioning and cooperative adsorption, respectively. Both hydraulic conductivity and pressure filtration tests revealed permeabilities ranging from 10?5 to 10?7?cm/s. Chloride testing showed that the coefficient of hydrodynamic dispersion (D) within paper clay is on the order of 10?7?cm2/s.     

Predicting Solute Flux through a Clay Membrane Barrier

Measured solute flux breakthrough curves (FBCs) from column tests performed on a semipermeable clay membrane subjected to KCl solutions are compared with predicted FBCs using independently measured flow and transport properties. The predicted FBCs are based on three scenarios: (1) Advective–dispersive transport that neglects membrane behavior; (2) advective–dispersive transport that accounts for the concentration dependency of the effective salt-diffusion coefficient (Ds?) resulting from membrane behavior, referred to as partially coupled transport; and (3) fully coupled transport that includes both the explicit coupling terms (e.g., hyperfiltration, chemico-osmosis) associated with clay membrane behavior and the concentration dependency of Ds?. The FBCs predicted by fully coupled transport agree best with the measured FBCs. However, for the diffusion-controlled conditions of the column tests, the steady-state solute fluxes predicted by partially coupled transport are only 23–69% higher than the measured steady-state fluxes. The results imply that the advective–dispersive transport theory can be used to provide reasonably accurate, albeit somewhat conservative, estimates of steady-state solute flux through clays that behave as semipermeable membranes, provided diffusion is a significant, if not dominant, solute transport process and the concentration dependency of Ds? are taken into account.     

Diffusive Transport of Permanganate during In Situ Oxidation

The transport of permanganate in low permeability media (LPM) and its ability to degrade trichloroethylene (TCE) in situ were studied through diffusive transport experiments with intact soil cores. A transport cell was developed to measure the effective diffusion coefficient (Deff) of a Br? tracer through intact cores of silty clay LPM obtained from a field site and enable calculation of the apparent tortuosity (τa) of the medium. Then, 5000 mg?L?1 of KMnO4 was added to the cell and diffusive transport and soil matrix interactions were observed. After three months, the soil cores were dissected for morphologic examination and characterization of matrix ions, total organic carbon, MnO4?, and manganese oxides (MnO2). The experiment was then repeated after 2 μL of pure phase TCE were delivered into the center of each of two intact cores. Permanganate transport was observed for one month and then an extraction of the entire soil core was made to determine the extent of TCE degradation. This research demonstrated that permanganate can migrate by diffusion and yield reactive zones that can be predicted based on the properties of the LPM and the oxidant source. Under the experimental conditions examined, permanganate had little effect on the LPM’s pore structure or continuity, and appreciable soil organic matter remained even after 40–60 days of exposure to the oxidant. MnO2 solids, an oxidation by-product, were observed in the LPM, but not at levels sufficient to cause pore filling or alter the apparent matrix tortuosity, even when TCE was present. During diffusive transport of permanganate, TCE in the silty clay LPM was degraded by 97%.     

Migration of Heavy Metals in Saturated Sand and Bentonite/Soil Admixture

Heavy metal migration through compacted, saturated sand and bentonite/soil admixtures were investigated using kinetic, batch sorption tests, and column tests. Sorption of Pb, Zn, and Cd at pH 5 by bentonite is found to be 411.2, 163.4, and 71.8 mL/g, respectively. The permeability of the compacted sand (8×10?4?cm/s) is found to be 6 orders of magniture higher than that of bentonite/soil admixture (about 8×10?10?cm/s) when permeated with metal solutions under an effective stress of 34.5 kPa (5 psi). The permeation of metal solutions into bentonite/soil admixture columns does not result in a significant increase in permeability. Experimental results of batch sorption and hydraulic conductivity tests were also analyzed with a computer-based simulation model, POLLUTE, to determine the transport parameters (effective porosity, dispersion coefficient, retardation) of chloride ions and heavy metals in a homogeneous compacted sand and bentonite/soil admixture using a curve fitting technique.     

Solute Transport Modeling in Overland Flow Applied to Fertigation

A model of solute transport in overland flow is developed and applied to the simulation of surface fertigation. Water flow is simulated using the depth-averaged, 1D shallow water equations. Solute flow is represented by an advection-diffusion model. The resulting set of three partial differential equations is sequentially solved at each time step. First, water flow is computed using the explicit two-step McCormack method. Based on the obtained velocity field, solute transport is explicitly determined from the advection-diffusion equation using the operator split technique. Four field experiments involving fertigation events on an impervious free-draining border were performed to validate the proposed model and to obtain estimates of Kx, the longitudinal dispersion coefficient. A value of Kx = 0.075 m2 s?1 satisfactorily reproduces the field experiments. The model is also applied to the simulation of a fertigation event on a pervious border. A sensitivity analysis is performed to assess the dependence of fertilizer distribution uniformity on the value of Kx. Finally, the proposed model is compared with a previous model based on pure advection.     

Long-Term Tritium Transport through Field-Scale Compacted Soil Liner

A 13-year study of tritium transport through a field-scale earthen liner was conducted by the Illinois State Geological Survey to determine the long-term performance of compacted soil liners in limiting chemical transport. Two field-sampling procedures (pressure-vacuum lysimeter and core sampling) were used to determine the vertical tritium concentration profiles at different times and locations within the liner. Profiles determined by the two methods were similar and consistent. Analyses of the concentration profiles showed that the tritium concentration was relatively uniformly distributed horizontally at each sampling depth within the liner and thus there was no apparent preferential transport. A simple one-dimensional analytical solution to the advective–dispersive solute transport equation was used to model tritium transport through the liner. Modeling results showed that diffusion was the dominant contaminant transport mechanism. The measured tritium concentration profiles were accurately modeled with an effective diffusion coefficient of 6×10?4?mm2/s, which is in the middle of the range of values reported in the literature.     

Conservative Semi-Lagrangian Algorithm for Pollutant Transport in Rivers

A conservative semi-Lagrangian numerical method for solute transport in steady nonuniform flows is presented. The method is an extension of earlier work on the authors' DISCUS method. Numerical results are compared against an exact solution for solute transport in a nonuniform flow with a linearly varying velocity coefficient and a quadratically varying dispersion coefficient. The method is stable and fully conservative at large Courant and grid Péclet numbers. Accuracy is also good and appears to be primarily related to spatial resolution and grid Péclet number. The method is significantly more computationally efficient than Eulerian numerical methods.     

Appropriate Material Properties for Advective–Diffusive Solute Flux in Membrane Soil

A generalized advective–diffusive equation for describing electrolytic solute transport in fine-grained soil (clay) membranes is presented. Clarification is made between the current theory and the widely cited coupled-flow theory by Yeung and Mitchell. Results of recently published experimental data are evaluated to demonstrate that the effective diffusion coefficient associated with Fick’s first law is not an appropriate independent material property for solute transport considerations in membrane soil. Three independent and experimentally attainable material properties are identified, specifically: osmotic efficiency, membrane diffusion coefficient, and hydraulic conductivity. Simple physical experiments by which these properties may be measured are described.     

Coupled Surface–Subsurface Solute Transport Model for Irrigation Borders and Basins. I. Model Development

Surface fertigation is widely practiced in irrigated crop production systems. Lack of design and management tools limits the effectiveness of surface fertigation practices. The availability of a process-based coupled surface–subsurface hydraulic and solute transport model can lead to improved surface fertigation management. This paper presents the development of a coupled surface–subsurface solute transport model. A hydraulic model described in a previous paper by the writers provided the hydrodynamic basis for the solute transport model presented here. A numerical solution of the area averaged advection–dispersion equation, based on the split-operator approach, forms the surface solute transport component of the coupled model. The subsurface transport process is simulated using HYDRUS-1D, which also solves the one-dimensional advection–dispersion equation. A driver program is used for the internal coupling of the surface and subsurface transport models. Solute fluxes calculated using the surface transport model are used as upper boundary conditions for the subsurface model. Evaluation of the model is presented in a companion paper.     

Consolidation of a Geosynthetic Clay Liner under Isotropic States of Stress

The consolidation behavior of a geosynthetic clay liner (GCL) was evaluated by consolidating duplicate specimens of the GCL in a flexible-wall cell to a final effective stress, σ′, of 241 kPa (35.0 psi). The hydraulic conductivity, k, also was measured at the end of each loading increment. The results indicated that the GCL was normally consolidated for values of σ′ greater than 34.5 kPa (5.0 psi), which correlates well with limited consolidation data reported in the literature for GCLs based on confined compression using oedometers. Values of the coefficient of consolidation, cv, for the GCL ranged from 5.2×10?10?m2/s to 2.1×10?9?m2/s, and generally decreased with increasing σ′, albeit only slightly. Values of the measured k, kmeasured, for the GCL were low ( ? 5.0×10?9?cm/s) due to the sodium bentonite content of the GCL, and were within a factor of about two of the values of k calculated on the basis of classic (Terzaghi) small-strain consolidation theory, ktheory (i.e., 0.5 ? ktheory/kmeasured ? 2.0), suggesting that the theory is appropriate for describing the consolidation behavior of the GCL. The results also are consistent with the results of previous studies based on one-dimensional consolidation of sodium montmorillonite, suggesting that there would be little difference in the consolidation behavior of the GCL under confined compression.     

Estimation of Mass Transport Parameters of Organic Compounds through High Density Polyethylene Geomembranes Using a Modifield Double-Compartment Apparatus

A modified double-compartment apparatus (MDCA) is used to estimate mass transport parameters of organic compounds through high density polyethylene (HDPE) geomembranes and to investigate the effects of aging and external tension of HDPE geomembranes on the mass transport of organic compounds. A developed one-dimensional partition–diffusion mass transport model successfully explains the mass transport of the organic compounds through the HDPE geomembranes in a dilute aqueous solution–geomembrane system. Similar to batch immersion tests, the HDPE–water partition coefficient (KHDPE–W) values of organic compounds are found to have close relationships with the octanol–water partition coefficient and the aqueous solubility; furthermore, the diffusion coefficient (D) values decrease with the increase of their molecular diameter. For HDPE geomembranes served in the landfill liner for 5 years and stretched by 8% of their initial length, KHDPE–W values for organic compounds increase by 5–58%, D values for organic compounds increase by 10–86%, and breakthrough times are faster, indicating more amounts of organic compounds may break through the HDPE geomembrane in fields than expected. The mass transport parameters from MDCA tests could be used with those from batch immersion tests interchangeably after mass loss and immobilization of organic compounds in MDCA tests are considered.