A field experiment on cation exchange-affected multicomponent solute transport in a sandy aquifer

A field experiment was performed in an aquifer in order to study multicomponent cation-exchange processes under natural flow conditions. The aquifer is a glacial outwash plain with sandy aquifer material having a cation-exchange capacity (CEC) of 1.0 meg/100 g. A continuous injection of groundwater spiked with sodium and potassium as chlorides was accomplished over 37 days to resemble leachate contamination from landfills. The plume was monitored by sampling in a dense spatial network (length 100 m, width 20 m) over a period of 2.5 years in order to obtain breakthrough curves and spatial contour maps of the chemical compounds. Na and especially K showed a substantial retardation caused by cation-exchange processes despite the low CEC of the aquifer material. The average velocity of K⁺ was only 10% of the velocity of chloride (0.7 m day⁻¹). The relative migration velocity of Na⁺ was not a constant in the plume, but apparently influenced by dilution. Ca²⁺ and Mg²⁺ were expelled from the cation-exchange sites of the aquifer material and subsequently transported with the same velocity as chloride. The breakthrough curves of the various compounds showed multiple peaks and low concentration zones. It was concluded by calculations with PHREEQE that changes in calcite equilibrium may occur in the lower part of the aquifer, while complexation processes seem to be of no importance. Cation exchange is then the most important process in this field experiment, and further evaluation of the data by a geochemical transport model including cation exchange is recommended.     

Dimensionless analysis of two analytical solutions for 3-D solute transport in groundwater

Analytical solutions are widely used as screening tools for estimating the potential for contaminant transport in groundwater, or for interpreting tracer tests or groundwater quality data. A solution for three-dimensional solute migration from a plane-source source that is frequently used in practice is the approximate solution of Domenico [J. Hydrol. 91 (1987) 49-58]. A more rigorous solution to the same problem was provided by Sagar [ASCE, J. Hydraul. Div. 108, no. HY1 (1982) 47-62]. A comprehensive and unambiguous comparison between these two solutions is provided using dimensionless analysis. The solutions are first cast in terms of dimensionless parameters and then used to provide type curves covering a wide range of dimensionless parameter values. Results show that while discrepancies between the two solutions are relatively negligible along the plume centreline (for flow regimes dominated by advection and mechanical dispersion), large concentration differences can be observed as lateral distance from the centreline increases, especially in the presence of solute decay.     

Reactive solute transport in macroscopically homogeneous porous media: analytical solutions for the temporal moments

In this work, we investigate one-dimensional solute transport affected by rate-limited sorption, first-order mass transfer, and first-order transformation. Analytical expressions are obtained for the temporal moments of the solute in the solution phase. The effect of various rate coefficients on the temporal moments is examined. It was found that, in the presence of transformation reactions, the mean arrival time, and the spread and skewness of the breakthrough curves, are not monotonic functions of the rate coefficients. These solutions will be useful as a preliminary analysis tool for ascertaining the relative importance of various processes under given conditions. They may also be used to analyze the accuracy of various numerical techniques used for simulation of reactive transport.     

Analytical solution of two-dimensional solute transport in an aquifer–aquitard system

This study deals with two-dimensional solute transport in an aquifer–aquitard system by maintaining rigorous mass conservation at the aquifer–aquitard interface. Advection, longitudinal dispersion, and transverse vertical dispersion are considered in the aquifer. Vertical advection and diffusion are considered in the aquitards. The first-type and the third-type boundary conditions are considered in the aquifer. This study differs from the commonly used averaged approximation (AA) method that treats the mass flux between the aquifer and aquitard as an averaged volumetric source/sink term in the governing equation of transport in the aquifer. Analytical solutions of concentrations in the aquitards and aquifer and mass transported between the aquifer and upper or lower aquitard are obtained in the Laplace domain, and are subsequently inverted numerically to yield results in the real time domain (the Zhan method). The breakthrough curves (BTCs) and distribution profiles in the aquifer obtained in this study are drastically different from those obtained using the AA method. Comparison of the numerical simulation using the model MT3DMS and the Zhan method indicates that the numerical result differs from that of the Zhan method for an asymmetric case when aquitard advections are at the same direction. The AA method overestimates the mass transported into the upper aquitard when an upward advection exists in the upper aquitard. The mass transported between the aquifer and the aquitard is sensitive to the aquitard Peclet number, but less sensitive to the aquitard diffusion coefficient.     

Evaluating non-equilibrium solute transport in small soil columns

Displacement studies on leaching of bromide and two pesticides (atrazine and isoproturon) were conducted under unsaturated steady state flow conditions in 24 small undisturbed soil columns (5.7 cm in diameter and 10 cm long) each collected from two sites differing in soil structure and organic carbon content in North Germany. There were large and irregular variabilities in the characteristics of both soils, as well as in the shapes of breakthrough curves (BTCs) of different columns, including some with early breakthrough and increased tailing, qualitatively indicating the presence of preferential flow. It was estimated that one preferential flow column (PFC) at site A, and four at site B, contributed, respectively to 11% and 58% of the accumulated leached fraction and to more than 80% of the maximum observed standard deviation (SD) in the field-scale concentration and mass flux of pesticides at two sites. The bromide BTCs of two sites were analyzed with the equilibrium convection-dispersion equation (CDE) and a non-equilibrium two-region/mobile-immobile model. Transport parameters of these models for individual BTCs were determined using a curve fitting program, CXTFIT, and by the time moment method. For the CDE based equilibrium model, the mean values of retardation factor, R, considered separately for all columns, PFCs or non-preferential flow columns (NPFCs) were comparable for the two methods; significant differences were observed in the values of dispersion coefficients of two sites using the two estimation methods. It was inferred from the estimated parameters of non-equilibrium model that 5-12% of water at site A, and 12% at site B, was immobile during displacement in NPFCs. The corresponding values for PFCs of two sites were much larger, ranging from 25% to 51% by CXTFIT and from 24% to 72% by the moment method, suggesting the role of certain mechanisms other than immobile water in higher degrees of non-equilibrium in these columns. Peclet numbers in PFCs of both sites were consistently smaller than five, indicating the inadequacy of the non-equilibrium model to incorporate the effect of all forms of non-equilibrium in PFCs. Overall, the BTCs of individual NPFCs, PFCs and of field average concentration at the two sites were better reproduced with parameters obtained from CXTFIT than by the moment method. The moment method failed to capture the peak concentrations in PFCs, but tended to describe the desorption and tail branches of BTCs better than the curve fitting approach.     

An overview of uncertainties in modelling groundwater solute transport

Model predictions are uncertain because of uncertainties on future and/or anthropogenic stresses, parameter values and conceptual models. The first two groups of problems can be addressed through rather systematic methods (scenario analysis, error transmission techniques, automatic calibration algorithms, etc.). However, conceptual uncertainties are rarely given adequate attention. The objective of this paper is to synthesize conceptual difficulties associated with transport. These include: (1) processes that are significant at small scales may not be relevant at large scales; (2) inversely, new processes (e.g., dispersion) emerge in response to increase in scale and the way to represent them may depend on the assumed model structure; (3) the observed shapes of both breakthrough curves and pollutant plumes are not well represented by the classical transport equation; (4) porosities and dispersivities derived from field tracer tests often exhibit a directional dependence; etc. Though not directly related to solute transport, scale effects on hydraulic conductivity may also affect solute transport modelling. When these anomalies are examined, it is concluded that they are directly or indirectly caused by heterogeneity. Current approaches for dealing with heterogeneity can be divided into stochastic and deterministic. Stochastic methods have been successful in explaining qualitatively some anomalies of solute transport, but they appear to be far from reaching a stage at which they can be used routinely for solving realistic field problems. On the other hand, when applied with care, deterministic methods have been successfully used in actual problems. Yet, it can be argued that they fail to account for small-scale variability of concentrations so that they would become ineffective when dealing with nonlinear processes, such as chemical reactions. Relevance of on-going research for overcoming these difficulties is discussed.     

Simulation of solute transport across low-permeability barrier walls

Low-permeability, non-reactive barrier walls are often used to contain contaminants in an aquifer. Rates of solute transport through such barriers are typically many orders of magnitude slower than rates through the aquifer. Nevertheless, the success of remedial actions may be sensitive to these low rates of transport. Two numerical simulation methods for representing low-permeability barriers in a finite-difference groundwater-flow and transport model were tested. In the first method, the hydraulic properties of the barrier were represented directly on grid cells and in the second method, the intercell hydraulic-conductance values were adjusted to approximate the reduction in horizontal flow, allowing use of a coarser and computationally efficient grid. The alternative methods were tested and evaluated on the basis of hypothetical test problems and a field case involving tetrachloroethylene (PCE) contamination at a Superfund site in New Hampshire. For all cases, advective transport across the barrier was negligible, but preexisting numerical approaches to calculate dispersion yielded dispersive fluxes that were greater than expected. A transport model (MODFLOW-GWT) was modified to (1) allow different dispersive and diffusive properties to be assigned to the barrier than the adjacent aquifer and (2) more accurately calculate dispersion from concentration gradients and solute fluxes near barriers. The new approach yields reasonable and accurate concentrations for the test cases.     

Dual-domain solute transfer and transport processes: evaluation in batch and transport experiments

Soil macropore networks establish a dual-domain transport scenario in which water and solutes are preferentially channeled through soil macropores while slowly diffusing into and out of the bulk soil matrix. The influence of macropore networks on intra-ped solute diffusion and preferential transport in a soil typical of subsurface-drained croplands in the Midwestern United States was studied in batch- and column-scale experiments. In the batch diffusion studies with soil aggregates, the estimated diffusion radius (length) of the soil aggregates corresponded to the half-spacing of the aggregate fissures, suggesting that the intra-ped fissures reduced the diffusion impedance and preferentially allowed solutes to diffuse into the soil matrix. In the column-scale solute transport experiments, the average diffusion radius (estimated from HYDRUS-2D simulations and a first-order diffusive transfer term) was nearly double that of the batch-scale study. This increase may be attributed to a loss of pore continuity and a compounding of the small diffusion impedance through macropores at the larger scale. The column-scale solute transport experiments also suggest that two preferential networks exist in the soil. At and near soil saturation, a primary network of large macropores (possibly root channels and earthworm burrows) dominate advective transport, causing a high degree of physical and sorption nonequilibrium and simultaneous breakthrough of a nonreactive (bromide) and a reactive (alachlor) solute. As the saturation level decreases, the primary network drains, while transport through smaller macropores (possibly intra-ped features) continues, resulting in a reduced degree of nonequilibrium and separation in the breakthrough curves of bromide and alachlor.     

Fluid flow and solute transport in a network of channels

A new model to describe flow and transort in fractured rocks is proposed. It is based on the concept of a network of channels. The individual channel members are given stochastically selected conductances and volumes. Flow-rate calculations have been performed. For large standard deviations in conductances, channeling becomes pronounced with most of the water flowing in a few paths. The effluent patterns and flow-rate distributions obtained in the simulations have been compared to three field measurements in drifts and tunnels of flow-rate distributions. Standard deviations of channel conductances were between 1.6 and 2.4 in some cases. A particle-following technique was used to simulate solute transport in the network. Non-sorbing as well as sorbing solute transport can be simulated. By using a special technique, solutes that diffuse into the rock matrix can also be simulated.     

Prediction of mass-transfer coefficient for solute transport in porous media

Several previously reported laboratory studies related to transport of solutes through packed columns were utilized to develop predictive relationships for mass-transfer rate coefficient. The data were classified into two groups: those obtained under rate-limited mass transfer between mobile and immobile water regions (physical nonequilibrium conditions), and those derived from rate-limited mass transfer between instantaneous and slow sorption sites (sorption nonequilibrium conditions). The mass-transfer coefficient in all these studies was obtained by fitting breakthrough data to a transport model employing a first-order rate limitations with a "constant" mass-transfer coefficient, independent of flow conditions. This study demonstrated that the mass-transfer coefficient in these models is dependent on system parameters including pore-water velocity, length-scale, retardation coefficient, and particle or aggregate size. Predictive relationships were developed, through regression analysis, relating mass-transfer coefficient to residence time. The developed relationships adequately estimated previously reported field mass-transfer values. Successful simulations of field desorption data reported by Bahr [J. Contam. Hydrol. 4 (1989) 205] further demonstrate the potential applicability of the developed relationships.     

Flow transiency on analytical modeling of subsurface solute transport

Environmental Science and Pollution Research - Groundwater flow velocity and dispersivity might be temporally or spatially variable rather than constant. In this paper, linearly-asymptotically or...     

Theory for reactive solute transport through clay membrane barriers

The theoretical development for one-dimensional, coupled migration of solutes with different ionic mobilities through clay soils that behave as ion-restrictive membranes, referred to as clay membrane barriers (CMBs), is presented. The transport formulation is based on principles of irreversible thermodynamics and accounts explicitly for coupling effects of hyperfiltration (ultrafiltration) and chemico-osmotic counter-advection associated with clay membrane behavior in the absence of electrical current. Since, by definition, no solute can enter a "perfect" or "ideal" membrane, the concept of an implicit coupling effect, such that the effective salt-diffusion coefficient, Ds* approaches zero as the chemico-osmotic efficiency coefficient, omega approaches unity is introduced. The theoretical development also illustrates that, even in the absence of membrane behavior, traditional advective-dispersive transport theory based on a constant value of Ds* for the solutes may not be appropriate for simulating transient transport in reactive (ion exchanging) systems. This potential limitation is illustrated through simulations for solute mass flux involving the migration of a binary salt solution (KCl) through a clay barrier with exchange sites saturated with a single exchangeable cation (e.g., Na+) that enters the pore solution upon ion exchange with the salt cation (K+).     

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability–possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.     

Large-scale modeling of reactive solute transport in fracture zones of granitic bedrocks

Final disposal of high-level radioactive waste in deep repositories located in fractured granite formations is being considered by several countries. The assessment of the safety of such repositories requires using numerical models of groundwater flow, solute transport and chemical processes. These models are being developed from data and knowledge gained from in situ experiments such as the Redox Zone Experiment carried out at the underground laboratory of Äspö in Sweden. This experiment aimed at evaluating the effects of the construction of the access tunnel on the hydrogeological and hydrochemical conditions of a fracture zone intersected by the tunnel. Most chemical species showed dilution trends except for bicarbonate and sulphate which unexpectedly increased with time. Molinero and Samper [Molinero, J. and Samper, J. Groundwater flow and solute transport in fracture zones: an improved model for a large-scale field experiment at Äspö (Sweden). J. Hydraul. Res., 42, Extra Issue, 157–172] presented a two-dimensional water flow and solute transport finite element model which reproduced measured drawdowns and dilution curves of conservative species. Here we extend their model by using a reactive transport which accounts for aqueous complexation, acid–base, redox processes, dissolution–precipitation of calcite, quartz, hematite and pyrite, and cation exchange between Na⁺ and Ca²⁺. The model provides field-scale estimates of cation exchange capacity of the fracture zone and redox potential of groundwater recharge. It serves also to identify the mineral phases controlling the solubility of iron. In addition, the model is useful to test the relevance of several geochemical processes. Model results rule out calcite dissolution as the process causing the increase in bicarbonate concentration and reject the following possible sources of sulphate: (1) pyrite dissolution, (2) leaching of alkaline sulphate-rich waters from a nearby rock landfill and (3) dissolution of iron monosulphides contained in Baltic seafloor sediments. Based on these results, microbially mediated processes are postulated as the most likely hypothesis to explain the measured increase of dissolved bicarbonates and sulphates after tunnel construction.     

Analytical model of solute transport by unsteady unsaturated gravitational infiltration

Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils.     

Numerical analysis of water and solute transport in variably-saturated fractured clayey till

This study numerically investigates the influence of initial water content and rain intensities on the preferential migration of two fluorescent tracers, Acid Yellow 7 (AY7) and Sulforhodamine B (SB), through variably-saturated fractured clayey till. The simulations are based on the numerical model HydroGeoSphere, which solves 3D variably-saturated flow and solute transport in discretely-fractured porous media. Using detailed knowledge of the matrix, fracture, and biopore properties, the numerical model is calibrated and validated against experimental high-resolution tracer images/data collected under dry and wet soil conditions and for three different rain events. The model could reproduce reasonably well the observed preferential migration of AY7 and SB through the fractured till, although it did not capture the exact depth of migration and the negligible impact of the dead-end biopores in a near-saturated matrix. A sensitivity analysis suggests fast flow mechanisms and dynamic surface coating in the biopores, and the presence of a plough pan in the till.     

Kinematic wave approximation to solute transport along preferred flow paths in soils

A routing procedure is introduced which accounts for the loss of a conservative solute tracer from preferred paths during macropore flow. Water flow is treated as a series of kinematic waves from which the tracer is lost due to mixing previously stored soil water, and an expression for solute loss is added to a previously developed model. The model parameters are estimated through experiments at three different input rates applied to a column of a macroporous forest soil.The results of seven experimental runs indicate that solute losses are consistently highest at the early stages of infiltration and drainage flow. An empirical relationship is proposed which links the frequency distribution of the flow parameter with that for solute loss from the preferred path during transient water flow and solute transport.     

A two-region nonequilibrium model for solute transport in solution conduits in karstic aquifers

A two-region nonequilibrium model was used to calibrate initial solute-transport parameter estimates generated from tracer-breakthrough curves (TBCs) developed from tracer tests conducted in uni-axial solution conduits in karstic aquifers. Two-region nonequilibrium models account for partitioning of solute into mobile- and immobile-fluid regions to produce a more representative model fit to the strong tails associated with TBCs than do equilibrium models. The nonequilibrium model resulted in an increase in average flow velocities and a decrease in longitudinal dispersion coefficients over comparable estimates using an equilibrium model. Increases in velocity and decreases in dispersion were obtained at the expense of including parameters that describe solute partitioning and mass transfer rate for the mobile- and immobile-fluid regions. In addition, nonidentifiable sorption and mass transfer parameters for the immobile-fluid regions could only be described in terms of upper and lower bounds using readily determined identifiable ratios representing solute partitioning and system constraints based on known physical properties. The identifiable ratios and system constraints serve to minimize model nonuniqueness and renders the nonidentification problem trivial.     

非饱和土壤渗透系数空间不确定性对溶质运移的影响

包气带渗透系数的不确定性是影响非饱和带溶质运移的主要因素。应用贝叶斯方法对非饱和土壤渗透系数进行前处理,使用Monte-Carlo方法模拟其空间不确定性,并通过HYDRUS-1D模型对溶质运移进行数值模拟,研究包气带渗透系数的空间不确定性对溶质运移的影响。结果表明,由于包气带渗透性的不确定性使得溶质浓度分布呈现明显的不确定性,包气带内不同点的浓度值相差很大。与忽略包气带土性参数空间不确定性的模拟结果相对比,考虑包气带渗透系数不确定性的模拟结果与实际情况更加接近,更具合理性和科学性。同时,根据模拟结果,对实际工作中进行地下水数值模拟时溶质初始浓度输入值的确定提出相应建议。     

A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richards', Darcy flux, and advection-dispersion equations. The mixed form of Richards' equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head-water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov-Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian-Lagrangian method. A multi-step, fourth-order Runge-Kutta, reverse particle tracking technique and a quadratic-linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.