Advective-dispersive Solute Transport Research Articles

General analytical solutions of multispecies advective-dispersive solute transport equations coupled with a complex reaction network

Stepwise reductive dechlorination of tetrachloroethene (PCE) to trichloroethene (TCE), three dichloroethylene (DCE) isomers (1,1-DCE, cis −1,2- DCE, and trans −1,2- DCE), vinyl chloride (VC), and ethane (ETH) may proceed under anaerobic conditions. However, most multispecies transport models for describing the plume migration of a chemical mixture comprising the original chlorinated solvent and its dechlorinated byproducts in the literature are often simplified to a sequential first-order reaction network which cannot account for the divergent reactions from TCE to the three DCE isomers and convergent reactions from the three DCE isomers to VC. In this study, general analytical solutions to multispecies transport equations with a complex reaction network were derived for a combination of semi-infinite and finite systems. The developed analytical solutions were robustly verified against a semi-analytical solution that can consider the same complex reaction network. The verification results indicated that the derived analytical solutions were accurate and robust. The general solutions derived in the present study were also used to investigate the effects of the outlet boundary conditions on solute transport involving a complex reaction network. The results showed that the analytical solution derived for infinite outlet BCs predicted lower concentrations of contaminants near the outlet boundary than those for finite outlet BCs. Moreover, a straight decay chain model may over- or under- estimate the DCE and VC concentrations compared to the multiple branching isomer reaction model. The developed analytical solutions with a complex reaction network provide more realistic and efficient tools for assessing the movement of chlorinated solvents and their degradation-related byproducts in soil–water systems.

Semi-analytical model for solute transport in a three-dimensional aquifer with dual porosity and a volumetric source term

A new solution for advective–dispersive solute transport is developed for three-dimensional aquifer of finite thickness and width, infinite extent along the direction of flow, dual porosity, equilibrium linear sorption and first-order decay of both the sorbed and dissolved mass with coefficients that may differ in the mobile and immobile domains, and with initial concentration distribution or with source represented by a volumetric mass generation term of arbitrary time-dependence. The analytical Laplace domain solution is numericaly inverted into the time domain. The model is benchmarked against MT3DMS and simpler analytical models. The model is sensitive to transport parameters describing the dual domain, suggesting it may be used for evaluating tracer tests. The model is suitable for checking accuracy of numerical models and identifying ranges of key transport parameters.

Well Rate and Placement for Optimal Groundwater Remediation Design with A Surrogate Model

A new surrogate-assisted optimization formulation for groundwater remediation design was developed. A stationary Eulerian travel time model was used in lieu of a conservative solute transport model. The decision variables of the management model are well locations and their flow rates. The objective function adjusts the residence time distribution between all pairs of injection-production wells in the remediation system. This goal is achieved by using the Lorenz coefficient as an effective metric to rank the relative efficiency of many remediation policies. A discrete adjoint solver was developed to provide the sensitivity of the objective function with respect to changes in decision variables. The quality management model was checked with simple solutions and then applied to hypothetical two- and three-dimensional test problems. The performance of the simulation-optimization approach was evaluated by comparing the initial and optimal remediation designs using an advective-dispersive solute transport simulator. This study shows that optimal designs simultaneously delay solute transport breakthrough at pumping wells and improve the sweep efficiency leading to smaller cleanup times. Well placement optimization in heterogeneous porous media was found to be more important than well rate optimization. Additionally, optimal designs based on two-dimensional models were found to be more optimistic suggesting a direct use of three-dimensional models in a simulation-optimization framework. The computational budget was drastically reduced because the proposed surrogate-based quality management model is generally cheaper than one single solute transport simulation. The introduced model could be used as a fast, but first-order, approximation method to estimate pump-and-treat capital remediation costs. The results show that physically based low-fidelity surrogate models are promising computational approaches to harness the power of quality management models for complex applications with practical relevance.

Investigation of permeability alteration of fractured limestone reservoir due to geothermal heat extraction using three-dimensional thermo-hydro-chemical (THC) model

Heat extraction by cold water circulation disturbs the thermo-chemical equilibrium of a geothermal reservoir, activating the dissolution/precipitation of minerals in the fractures. Calcite being a more reactive mineral than other rock minerals composing the earth curst, we investigate the permeability alteration during geothermal heat production from carbonate reservoirs. In this study the simulations are performed using the code FEHM with coupled thermo-hydro-chemical (THC) capabilities for a three dimensional domain. The computational domain consists of a single fracture connecting the injection and production wells. For reactive alteration of aperture, the model considers that the kinetics of dissolution/precipitation is coupled to the equilibrium interactions among the aqueous species/ions. The reaction rate predominantly depends on the temperature dependent solubility and advective–dispersive solute transport in the fracture. Due to the nonuniform flow fields resulting from injection and production, the coupled thermo-hydro-chemical processes initiate significant variation of the aperture alteration rate over the fracture. We have considered different operating conditions such as different mass injection rate, injection temperature and concentration of minerals. Our simulations show that dissolution and precipitation can occur simultaneously at different locations in fracture. Furthermore the reaction rate varies with time and the reaction rate can also switch between dissolution and precipitation. To illustrate this interesting behavior, the variations of shape and size of zero reaction rate contours with time are shown. An interesting outcome is a non-monotonic evolution of the overall transmissivity between the wells. The alteration of overall transmissivity largely depends on the concentration of mineral in the injected water with respect to the solubility at the initial fracture temperature. For both dissolution and precipitation controlled cases, the rapid changes in transmissivity provide challenges for maintaining circulation of water at constant mass flow rate.

Dual-tracer, non-equilibrium mixing cell modelling and uncertainty analysis for unsaturated bromide and chloride transport

A model is presented for simulating one-dimensional advective dispersive solute transport in the vadose zone. The finite-volume, mixing-cell model uses drainage flux intervals as the index variable, which are calculated by a soil water balance model. The modelling approach considers solute transport from two different regions as well as a slow and a fast transport domain in each region as parallel transport processes. The model is applied to breakthrough curves of Cl− and Br− measured at different locations and different depths in the volcanic vadose zone of the Tutaeuaua subcatchment of Lake Taupo, New Zealand, following a dual tracer application. Estimates of transport parameter and model predictive uncertainty were derived using the differential evolution adaptive metropolis, DREAMZS adaptive Markov chain Monte Carlo algorithm, a formal Bayesian likelihood function, observed leachate volumes, and Cl− breakthrough curves. The model was subsequently evaluated using Br− breakthrough curves from the dual tracer experiment and a previously conducted Br− tracer-only experiment. Uncertainty bounds derived by this MCMC method simultaneously capture the observed Br− and Cl− breakthrough curves and corresponding drainage volumes. Results suggest that the slow transport domain properties are relatively similar for different locations in the vadose zone and that the variability in contaminant fluxes is predominantly driven by structural variability of the vadose zone causing lateral flow.

Errata to ‘Analytical solutions for advective-dispersive solute transport in double-layered finite porous media’, International Journal of Numerical and Analytical Methods in Geomechanics, 2011; 35:438-460 , DOI: 10.1002/nag.903

Errata to ‘Analytical solutions for advective-dispersive solute transport in double-layered finite porous media’, <i>International Journal of Numerical and Analytical Methods in Geomechanics, 2011; 35:438-460</i> , <i>DOI: 10.1002/nag.903</i>

Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media

AbstractAnalytical solutions for advection and dispersion of a conservative solute in a one‐dimensional double‐layered finite porous media are presented. The solutions are applicable to five scenarios that have various combinations of fixed concentration, fixed flux and zero concentration gradient conditions at the inlet and outlet boundaries that provide a wide number of options. Arbitrary initial solute concentration distributions throughout the media can be considered via explicit formulations or numerical integration. The analytical solutions presented have been verified against numerical solutions from a finite‐element‐based approach and an existing closed‐form solution for double‐layered media with an excellent correlation being found in both cases. A practical application pertaining to advective transport induced by consolidation of underlying sediment layers on contaminant movement within a capped contaminated sediment system is presented. Comparison of the calculated concentrations and fluxes with alternative approaches clearly illustrates the need to consider advection processes. Consideration of the different features of contaminant transport due to varying pore‐water velocity fields in primary consolidation and secondary consolidation stages is achieved via the use of non‐uniform initial concentration distributions within the proposed analytical solutions. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Use of finite element method as a simulation technique for bioremediation of naphthalene, anthracene and pyrene contaminated soil in a fixed bed reactor

In this work, the finite element method was applied to solve one-dimensional advective-dispersive solute transport model with linear equilibrium sorption and first-order degradation. This mathematical approach was adopted to adequately predict the effluent concentrations and breakthrough profiles of naphthalene, anthracene and pyrene. Simulation results showed that the concentrations of naphthalene, anthracene and pyrene within a contact period of 49 days, decreased in the direction of flow from 100 mg/l at the surface to zero at 9 cm subsurface depth. The residual concentrations of naphthalene, anthracene and pyrene were found to be 0, 35.79 and 0% respectively by the 49th day of exposure. The theoretical predictions when compared with actual experimental results from the soil column showed an average deviation of 3.92%, an indication of a reasonable agreement between the model and data from experiment. The finite element method has been found to be satisfactory as a predictive tool to show the distribution of the contaminant solutes. This is significant as it displays the capacity of ascertaining the behaviour of these contaminants over long spatial and temporal scales and predicting the extent of bioremediation of the contaminated sites.

Optimal Extraction of Groundwater in Gaza Coastal Aquifer

Two multi-objective management models are applied on a local area selected from the regional Gaza coastal aquifer. The objectives and constraints of these management scenarios include maximizing the total volume of water pumped, minimizing the salt concentration of the pumped water, and controlling the drawdown limits. The physical model is based on the CODESA-3D density-dependent advective-dispersive solute transport model. Genetic algorithm is used as the optimization tool. The models are tested on a part of the aquifer ( ) with 9 existing pumping wells located at various depths. The results of the optimization show that the optimization/simulation approach can give better decision if there is enough information to feed to the model. It confirms that the use of the concept of safe yield alone is not enough for sustainable develop-ment of the coastal aquifer. It shows that the optimum pumping rate is in the range of 26%–34% of the total natural replenishment. The application shows that the proposed technique is a powerful tool for solving this type of management problems.

A meshless method to simulate solute transport in heterogeneous porous media

We derive a meshless numerical method based on smoothed particle hydrodynamics (SPH) for the simulation of conservative solute transport in heterogeneous geological formations. We demonstrate that the new proposed scheme is stable, accurate, and conserves global mass. We evaluate the performance of the proposed method versus other popular numerical methods for the simulation of one- and two-dimensional dispersion and two-dimensional advective–dispersive solute transport in heterogeneous porous media under different Pèclet numbers. The results of those benchmarks demonstrate that the proposed scheme has important advantages over other standard methods because of its natural ability to control numerical dispersion and other numerical artifacts. More importantly, while the numerical dispersion affecting traditional numerical methods creates artificial mixing and dilution, the new scheme provides numerical solutions that are “physically correct”, greatly reducing these artifacts.

Analytical Advection–Dispersion Model for Transport and Plant Uptake of Contaminants in the Root Zone

In regulatory and risk management analyses of environmental contaminants, the vadose zone may be treated as a subcomponent within a larger environmental modeling framework. For the complexity of the larger system model to remain at manageable levels, it is desirable that subcomponent models be relatively simple and require few input parameters. In this work, we develop an advective–dispersive solute transport equation that includes plant uptake of water and solute and present an analytical solution. Assumptions underlying the transport model include linear solute sorption, first‐order uptake, and a uniform soil water content. We examine the latter assumption in detail and demonstrate the effects of rooting depth, soil texture, and leaching fraction on the uniformity of the root‐zone water content. The new analytical advection–dispersion model should be useful for estimating the transport and uptake of strongly sorbing and persistent contaminants, where the timescale relevant for assessing environmental impacts is long (decades) and short‐term fluctuations caused by, for example, precipitation can be averaged. As an illustration, model predictions are made for the uptake of cadmium (Cd) by wheat (Triticum aestivum L.) grown in sludge‐amended soil. The predictions are compared with those of a “one‐compartment” model that has been proposed previously for risk analysis and regulatory studies. The comparison shows that the one‐compartment model overestimates the long‐term, steady‐state Cd concentration in harvested wheat grain. The analytical advection–dispersion model is recommended as a tool for environmental risk assessment of strongly sorbing, persistent contaminants.

Optimal and sustainable extraction of groundwater in coastal aquifers

Four examples are investigated for the optimal and sustainable extraction of groundwater from a coastal aquifer under the threat of seawater intrusion. The objectives and constraints of these management scenarios include maximizing the total volume of water pumped, maximizing the profit of selling water, minimizing the operational and water treatment costs, minimizing the salt concentration of the pumped water, and controlling the drawdown limits. The physical model is based on the density-dependent advective-dispersive solute transport model. Genetic algorithm is used as the optimization tool. The models are tested on a hypothetical confined aquifer with four pumping wells located at various depths. These solutions establish the feasibility of simulating various management scenarios under complex three-dimensional flow and transport processes in coastal aquifers for the optimal and sustainable use of groundwater.

Streamline-based simulation of advective–dispersive solute transport

We extend the streamline method to model diffusion and dispersion in solute transport problems using an operator splitting technique. Fluid is moved along streamlines ignoring dispersion, and then component concentrations are mapped onto the underlying grid. Dispersion is included by solving the dispersive portion of the conservation equation on the grid. We quantify the effects of numerical dispersion resulting from remapping solutions from streamlines to the grid. We verify the method by comparison with one-dimensional analytical solutions and by predicting the results of a tracer test in a heterogeneous sand pack. We show the ability of our formulation to handle finely resolved geological models by running a 1.122 million cell field-scale problem. At both the laboratory and field scales we find long tails in the breakthrough curves. The average behavior is consistent with anomalous or non-Gaussian transport where wide variations in permeability result in a large spread of flow velocities. Local mixing caused by dispersion or diffusion can impact the overall recovery of tracer but does not significantly affect the late-time behavior of the plumes.

Modeling depth-variant and domain-specific sorption and biodegradation in dual-permeability media

A dual-permeability model (S_1D_DUAL) was developed to simulate the transport of land-applied pesticides in macroporous media. In this model, one flow domain was represented by the bulk matrix and the other by the preferential flow domain (PFD) where water and chemicals move at faster rates. The model assumed the validity of Darcian flow and the advective–dispersive solute transport in each of the two domains with inter-domain transfer of water and solutes due to pressure and concentration gradients. It was conceptualized that sorption and biodegradation rates vary with soil depth as well as in each of the two flow domains. In addition to equilibrium sorption, kinetic sorption was simulated in the PFD. Simulations were conducted to evaluate the combined effects of preferential flow, depth- and domain-variant sorption, and degradation on leaching of two pesticides: one with strong sorption potential (trifluralin) and the other with weak sorption potential (atrazine). Simulation results for a test case showed that water flux in the PFD was three times more than in the matrix for selected storm events. When equilibrium sorption was considered, the simulated profile of trifluralin in each domain was similar; however, the atrazine profile was deeper in the PFD than in the bulk matrix under episodic storm events. With an assumption of negligible sorption in the PFD, both the atrazine and the trifluralin profiles moved twice deeper into the PFD. The simulated concentrations of the chemicals were several orders higher in the PFD than in the matrix, even at deeper depths. The volume fraction of the macropores and the sorption and biodegradation properties of the chemicals could also affect the amount of pesticides leaving the root zone. For an intense storm event, slow sorption reaction rates in the PFD produced higher breakthrough concentrations of atrazine at the bottom of the simulated soil profile, thus posing the risk for breakthrough of chemicals from the root zone.

Application of the method of temporal moments to interpret solute transport with sorption and degradation

In this note, we applied the temporal moment solutions of [Das and Kluitenberg, 1996. Soil Sci. Am. J. 60, 1724] for one-dimensional advective–dispersive solute transport with linear equilibrium sorption and first-order degradation for time pulse sources to analyse soil column experimental data. Unlike most other moment solutions, these solutions consider the interplay of degradation and sorption. This permits estimation of a first-order degradation rate constant using the zeroth moment of column breakthrough data, as well as estimation of the retardation factor or sorption distribution coefficient of a degrading solute using the first moment. The method of temporal moment (MOM) formulae was applied to analyse breakthrough data from a laboratory column study of atrazine, hexazinone and rhodamine WT transport in volcanic pumice sand, as well as experimental data from the literature. Transport and degradation parameters obtained using the MOM were compared to parameters obtained by fitting breakthrough data from an advective–dispersive transport model with equilibrium sorption and first-order degradation, using the nonlinear least-square curve-fitting program CXTFIT. The results derived from using the literature data were also compared with estimates reported in the literature using different equilibrium models. The good agreement suggests that the MOM could provide an additional useful means of parameter estimation for transport involving equilibrium sorption and first-order degradation. We found that the MOM fitted breakthrough curves with tailing better than curve fitting. However, the MOM analysis requires complete breakthrough curves and relatively frequent data collection to ensure the accuracy of the moments obtained from the breakthrough data.

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\U-4 mm²/s, which is in the middle of the range of values reported in the literature.

Optimal Identification of Ground-Water Pollution Sources and Parameter Estimation

An optimization-based methodology for identifying unknown sources of ground-water pollution is presented. The proposed methodology utilizes an optimization model in which the flow and transport equations are embedded as constraints. A nonlinear programming algorithm is used to obtain as solution the optimal estimates of unknown source characteristics. The input to this model includes measured pollutant concentration at observation sites. The source identification methodology is further extended to the simultaneous estimation of aquifer parameters as well as identification of unknown pollutant sources. Performance of the developed methodology is evaluated for illustrative examples considering two-dimensional flow and advective-dispersive solute transport. Different cases including variability in data availability, single and multiple potential source locations, and errors in measurement data are considered. These performance evaluations demonstrate that at least for the illustrative example problems, the p...

Modeling of heavy metal migration in sand/bentonite and the leachate pH effect

Numerical simulations were carried out using a multicomponent reactive solute transport model to study the migration of four heavy metals (Cd 2+, Pb 2+, Cu 2+ and Zn 2+) in a sand/bentonite mixture. The numerical model is capable of simulating simultaneous processes of water flow, advective–dispersive solute transport, and chemical reactions such as acid–base reaction, complexation, ion exchange, precipitation and dissolution. The migration of the heavy metals was simulated in a hypothetical sand/bentonite clay column which was assigned realistic physical and chemical properties and boundary conditions to model one-dimensional contaminant transport through a landfill barrier. The input leachate properties used in the model were modified from those of an actual leachate containing the heavy metals. The numerical simulations were focused on the concentration profiles of these heavy metals in the simulated barrier and the effect of the leachate pH on their mobilities. Numerical results indicate that under a nearly neutral leachate, the mobility of the four heavy metals follows the order Cu 2+>Zn 2+>Pb 2+>Cd 2+. Under a more acidic leachate, the mobility order changes to: Cd 2+>Zn 2+>Cu 2+>Pb 2+. However, the differences in mobility of the four heavy metals were relatively small. The leachate pH has a significant effect on the migration of Cd 2+ and Pb 2+, but has only limited effect on the mobility of Cu 2+ and Zn 2+.

Mixing-cell boundary conditions and apparent mass balance errors for advective–dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective–dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RI−), or as the value when it is approached from the column side (MC-RI+). Solutions of these injection types with constant or—in one case—distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Péclet numbers. For most real situations, the model for resident injection MC-RI+ is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI+ model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI+ defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections.