Semi-analytical solution of two-dimensional sharp interface LNAPL transport models

In this paper, we present semi-analytical solutions for two-dimensional equations governing transport of Light Non-Aqueous Phase Liquids (LNAPL) in unconfined aquifers. The proposed model is based on sharp interface displacement and steady groundwater flow assumptions, where both the water–LNAPL interface and the LNAPL–air interface are represented as sharp interfaces. In the case of steady groundwater flow, these equations can be reduced to a two-dimensional nonlinear solute transport equation, with the LNAPL thickness in the free product lens being the primary unknown variable. The linearized form of this solute transport equation falls into the category of two-dimensional transport equation with time-dependent dispersion coefficients. This equation can be solved analytically for an infinite domain region. In this paper, the general form of the analytical solution for the transport equation, as well as the solutions for some specific cases are presented. To demonstrate the utility of the proposed solution, numerical results obtained for two example problems are discussed and presented comparatively with a finite-element solution and other more restrictive solutions available in the literature. Although the solutions discussed in this paper have some simplifying assumptions, such as sharp-interfaces between fluid phases, steady groundwater flow and homogeneous aquifer properties, the semi-analytical solutions presented in this study may be used effectively as bench mark solutions in evaluating LNAPL migration in the subsurface. These solutions are simple and cost effective to implement and may be used in the calibration of other more complex numerical solutions that can be found in the literature.     

Analytical solutions for reactive transport under an infiltration-redistribution cycle

Transport of reactive solute in unsaturated soils under an infiltration-redistribution cycle is investigated. The study is based on the model of vertical flow and transport in the unsaturated zone proposed by Indelman et al. [J. Contam. Hydrol. 32 (1998) 77], and generalizes it by accounting for linear nonequilibrium kinetics. An exact analytical solution is derived for an irreversible desorption reaction. The transport of solute obeying linear kinetics is modeled by assuming equilibrium during the redistribution stage. The model which accounts for nonequilibrium during the infiltration and assumes equilibrium at the redistribution stage is termed partial equilibrium infiltration-redistribution model (PEIRM). It allows to derive approximate closed form solutions for transport in one-dimensional homogeneous soils. These solutions are further applied to computing the field-scale concentration by adopting the Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979) 461] column model. The effect of soil heterogeneity on the solute spread is investigated by modeling the hydraulic saturated conductivity as a random function of horizontal coordinates. The quality of the PEIRM is illustrated by calculating the critical values of the Damk?hler number which provide the achievable accuracy in estimating the solute mass in the mobile phase. The distinguishing feature of transport during the infiltration-redistribution cycle as compared to that of infiltration only is the finite depth of solute penetration. For irreversible desorption, the maximum solute penetration W/theta(r) is determined by the amount of applied water W and the residual water content theta(r). For sorption-desorption kinetics, the maximum depth of penetration z(r)(e, infinity ) also depends on the ratio between the rate of application and the column-saturated conductivity. It is shown that z(r)(e, infinity ) is bounded between the depths W/(theta(r)+K(d)) and W/theta(r) corresponding to the maximum solute penetration for equilibrium transport and for irreversible desorption, respectively. This feature of solute penetration explains the unusual phenomena of plume contraction after an initial period of spreading [Lessoff, S.C., Indelman, P., Dagan, G., 2002. Solute transport in infiltration-redistribution cycles in heterogeneous soils. In Raats, P.A.C., Smiles, D.,Warrick, A.W. (Eds), Environmental Mechanics: Water, Mass and Energy Transport in the Biosphere. American Geophysical Union, pp. 133-144]. Unlike transport under equilibrium conditions, when the solute is completely concentrated at the front, the solute under nonequilibrium conditions is spread out behind the front. Heterogeneity leads to additional spreading of the plume.     

Travel time and trajectory moments of conservative solutes in two-dimensional convergent flows

We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in sigmaY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999-3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019-3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139-193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit-Forchheimer assumption holds.     

Laboratory analog and numerical study of groundwater flow and solute transport in a karst aquifer with conduit and matrix domains

New mathematical and laboratory methods have been developed for simulating groundwater flow and solute transport in karst aquifers having conduits imbedded in a porous medium, such as limestone. The Stokes equations are used to model the flow in the conduits and the Darcy equation is used for the flow in the matrix. The Beavers–Joseph interface boundary conditions are adopted to describe the flow exchange at the interface boundary between the two domains. A laboratory analog is used to simulate the conduit and matrix domains of a karst aquifer. The conduit domain is located at the bottom of the transparent plexiglas laboratory analog and glass beads occupy the remaining space to represent the matrix domain. Water flows into and out of the two domains separately and each has its own supply and outflow reservoirs. Water and solute are exchanged through an interface between the two domains. Pressure transducers located within the matrix and conduit domains of the analog provide data that is processed and stored in digital format. Dye tracing experiments are recorded using time-lapse imaging. The data and images produced are analyzed by a spatial analysis program. The experiments provide not only hydraulic head distribution but also capture solute front images and mass exchange measurements between the conduit and matrix domains. In the experiment, we measure and record pressures, and quantify flow rates and solute transport. The results present a plausible argument that laboratory analogs can characterize groundwater water flow, solute transport, and mass exchange between the conduit and matrix domains in a karst aquifer. The analog validates the predictions of a numerical model and demonstrates the need of laboratory analogs to provide verification of proposed theories and the calibration of mathematical models.     

Simulation and analysis of solute transport in 2D fracture/pipe networks: the SOLFRAC program

The Time Domain Random Walk (TDRW) method has been recently developed by Delay and Bodin [Delay, F. and Bodin, J., 2001. Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks. Geophys. Res. Lett., 28(21): 4051-4054.] and Bodin et al. [Bodin, J., Porel, G. and Delay, F., 2003c. Simulation of solute transport in discrete fracture networks using the time domain random walk method. Earth Planet. Sci. Lett., 6566: 1-8.] for simulating solute transport in discrete fracture networks. It is assumed that the fracture network can reasonably be represented by a network of interconnected one-dimensional pipes (i.e. flow channels). Processes accounted for are: (1) advection and hydrodynamic dispersion in the channels, (2) matrix diffusion, (3) diffusion into stagnant zones within the fracture planes, (4) sorption reactions onto the fracture walls and in the matrix, (5) linear decay, and (6) mass sharing at fracture intersections. The TDRW method is handy and very efficient in terms of computation costs since it allows for the one-step calculation of the particle residence time in each bond of the network. This method has been programmed in C++, and efforts have been made to develop an efficient and user-friendly software, called SOLFRAC. This program is freely downloadable at the URL (labo.univ-poitiers.fr/hydrasa/intranet/telechargement.htm). It calculates solute transport into 2D pipe networks, while considering different types of injections and different concepts of local dispersion within each flow channel. Post-simulation analyses are also available, such as the mean velocity or the macroscopic dispersion at the scale of the entire network. The program may be used to evaluate how a given transport mechanism influences the macroscopic transport behaviour of fracture networks. It may also be used, as is the case, e.g., with analytical solutions, to interpret laboratory or field tracer test experiments performed in single fractures.     

Sorption of hydrophobic organic pollutants in saturated soil systems

Sorption equilibria and rates were characterized for a matrix of four aquifer sands and two slightly to moderately hydrophobic organic solutes (nitrobenzene and lindane), and the effects of sorption on the behavior of these solutes in saturated systems of the soils were determined. Experimental data were used to test and evaluate a variety of mathematical models for predicting contaminant fate and transport in groundwater systems.Observed equilibrium relationships between soil and solution phase solute concentrations were found to be described best by the nonlinear Freundlich isotherm model. It was further determined that the sorption process in the systems tested is rate controlled, requiring several days to approach equilibrium in completely mixed batch reactors. Subsequent modeling of solute transport in continuous flow soil column reactors was found to be most successful when rate-controlled models were used, the best results were obtained with a dual-resistance model incorporating the coupled mass transport steps of boundary-layer and intraparticle diffusion.     

Application of Unknown Groundwater Pollution Source Release History Estimation Methodology to Distributed Sources Incorporating Surface-Groundwater Interactions

Sources of contamination of groundwater are often difficult to characterize. However, it is essential for effective remediation of polluted groundwater resources. This study demonstrates an application of the linked simulation-optimization based methodology to estimate the release history from spatially distributed sources of pollution at an illustrative abandoned mine-site. In linked simulation-optimization approaches a numerical groundwater flow and transport simulation model is linked to the optimization model. In this study, topographic and geologic characteristics of the abandoned mine-site were simulated using a three-dimensional (3D) numerical groundwater flow model. Transport of contaminant in the groundwater was simulated using a 3D transient advective-dispersive contaminant transport model. Adsorption or chemical reaction of the contaminant was not considered in the contaminant transport model. Adaptive simulated annealing (ASA) was employed for solving the optimization problem. An optimization algorithm generates the candidate solutions corresponding to various unknown groundwater source characteristics. The candidate solutions are used as input in the numerical groundwater transport simulation model to generate the concentration of pollutant in the study area. This information is used to calculate the objective function value, which is utilized by the optimization algorithm to improve the candidate solution. This process continues until an optimal solution is obtained. Optimal solutions obtained in this study show that the linked simulation-optimization based methodology is potentially applicable for the characterization of spatially distributed pollutant sources, typically present at abandoned mine-sites.     

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.     

A proposed model to include a residual NAPL saturation in a hysteretic capillary pressure-saturation relationship

A residual non-aqueous phase liquid (NAPL) present in the vadose zone can act as a contaminant source for many years as the compounds of concern partition to infiltrating groundwater and air contained in the soil voids. Current pressure-saturation-relative permeability relationships do not include a residual NAPL saturation term in their formulation. This paper presents the results of series of two- and three-phase pressure cell experiments conducted to evaluate the residual NAPL saturation and its impact on the pressure-saturation relationship. A model was proposed to incorporate a residual NAPL saturation term into an existing hysteretic three-phase parametric model developed by Parker and Lenhard [Water Resour. Res. 23(12) (1987) 2187], Lenhard and Parker [Water Resour. Res. 23(12) (1987) 2197] and Lenhard [J. Contam. Hydrol. 9 (1992) 243]. The experimental results indicated that the magnitude of the residual NAPL saturation was a function of the maximum total liquid saturation reached and the water saturation. The proposed model to incorporate a residual NAPL saturation term is similar in form to the entrapment model proposed by Parker and Lenhard, which was based on an expression presented by Land [Soc. Pet. Eng. J. (June 1968) 149].     

Prediction and minimization of vertical migration of DNAPLS using surfactant enhanced aquifer remediation at neutral buoyancy

Surfactant enhanced aquifer remediation (SEAR) had previously been thought to require a capillary barrier below the contaminated zone to prevent the vertical migration of a microemulsion containing solubilized DNAPL. This paper shows the vertical migration of the dense microemulsion is described and predicted by the value of three dimensionless scaling groups. Embedded within these scaling groups are four design parameters. The value of these parameters can be manipulated in order to reduce the amount of vertical migration anticipated for a given remediation design. Plots have been constructed that illustrate the relationship between vertical migration and the value of the scaling groups; such plots can be used to predict vertical migration and to determine appropriate screen intervals of extraction wells to ensure full capture of the contaminants. This predictive capability has been verified in laboratory experiments. Predicted migration of the microemulsion agreed within about 2% of that observed. Development of the scaling groups is presented, remediation design implications are discussed, and laboratory verification is shown. Additional discussion of the laboratory work is given in a companion paper [Kostarelos, K., Pope, G.A., Rouse, B.A., Shook, G.M., 1998. A new concept: the use of neutrally-buoyant microemulsions for DNAPL remediation, J. Contam. Hydro., this edition].     

Determination of Henry's law constant for methyl tert-butyl ether (MTBE) at groundwater temperatures

The dimensionless Henry's law constant was determined for methyl tert-butyl ether (MTBE) at six temperatures (3, 5, 10, 15, 20 and 25 degrees C) by using a thermostatted flask (430 ml) containing an aqueous MTBE solution. The ratio between the gas phase and the water phase in the flask was approximately 1.7:1. The aim of this study was to acquire data needed to model the behaviour of MTBE at groundwater conditions. The dimensionless Henry's law constant at 10 degrees C is approximately 0.01 but is 0.03 at 25 degrees C. This is important for modelling MTBE because the variation of vaporization cannot be disregarded at groundwater temperatures. In a second experiment the water solubility of MTBE was determined to be 62.1 g/l at 5 degrees C and 35.5 g/l at 20 degrees C). The high solubility at low temperatures could cause MTBE plumes from spills (fuel accidents etc.) to spread rapidly.     

Solubilization of nitrotoluenes in micellar nonionic surfactant solutions

A key factor in selecting surfactants to enhance chemical or biological transformation or physical removal of an organic pollutant from contaminated soil is knowledge of the pollutant's solubility behavior in the surfactant solution. This study investigated the influence of nonionic surfactant structure on the solubility of 4-nitrotoluene (NT), 2,3-dinitrotoluene, 2,4-dinitrotoluene, 2,6-dinitrotoluene, and 2,4,6-trinitrotoluene (TNT) at room temperature. For a series of alkyl phenol ethoxylates (Tergitol NP-8 to NP-40), decreasing the ethoxylate chain length increased the solubility of these nitrotoluenes by a factor of two or less in 10 g l(-1) surfactant solutions, but did not significantly change their molar solubilization ratios (MSR, e.g. 0.02 for TNT) or their micelle-water partition coefficients (K(m), e.g. 3.4 for TNT). For Tergitol NP-8 solutions ranging from 1.0 to 12.4 g l(-1), no enhancement in NT solubility was found, suggesting that the cloud point was reached. The MSRs for Tween 80 were higher than those of Tween 20 and the MSRs of Brij-58 were higher than those for Brij-35. When comparing solutes, NT had the highest solubility and MSR (0.28-0.41), while TNT had the lowest solubility and MSR (0.02-0.03). A linear relationship between K(m) values and octanol-water partition coefficients based on Triton X-100 predicted the logK(m) values within 0.5 of their measured values. A linear solvation free energy correlation for K(m) suggested the importance of solute volume and effective hydrogen bond basicity in the partitioning process while implying that the nitrotoluenes are solubilized in a polar portion of the micelle.     

Application of continuous time random walk theory to nonequilibrium transport in soil

Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (υ) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (υ, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.     

Probability density function of non-reactive solute concentration in heterogeneous porous formations

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.     

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.     

Determination of Henry's law constant for elemental mercury

The assessment of the global mercury cycle involves estimations of the evasion of mercury form oceanic waters. In such estimations Henry's law constant is often used. In this study the Henry's law constant for elemental mercury has been re-determined in MQ water and artificial sea water. Moreover, for the first time it has been determined for 1.5M sodium chloride (NaCl) solution which is of relevance for modeling of atmospheric waters at coastal locations. For all solutions, experiments has been conducted at five different temperatures between 278 and 308K, using a novel technique, for mercury, based on direct measurements of the portioning of mercury between the aqueous and gaseous phase. Elemental mercury was extracted from the water column and the logarithm of the mass of extracted mercury was plotted against time. A dimensionless Henry's law constant, defined as: [Formula: see text] was obtained from the slope of the curve. Almost no difference was observed in the values comparing the Milli-Q water and artificial sea water, however for the 1.5M NaCl solution a salting-out effect was seen, i.e. the solubility of mercury in the water phase decreased. The decreased solubility will generate an increase in the value of Henry's law constant.     

Applied tracer tests in fractured rock: Can we predict natural gradient solute transport more accurately than fracture and matrix parameters?

Applied tracer tests provide a means to estimate aquifer parameters in fractured rock. The traditional approach to analysing these tests has been using a single fracture model to find the parameter values that generate the best fit to the measured breakthrough curve. In many cases, the ultimate aim is to predict solute transport under the natural gradient. Usually, no confidence limits are placed on parameter values and the impact of parameter errors on predictions of solute transport is not discussed. The assumption inherent in this approach is that the parameters determined under forced conditions will enable prediction of solute transport under the natural gradient. This paper considers the parameter and prediction uncertainty that might arise from analysis of breakthrough curves obtained from forced gradient applied tracer tests. By adding noise to an exact solution for transport in a single fracture in a porous matrix we create multiple realisations of an initial breakthrough curve. A least squares fitting routine is used to obtain a fit to each realisation, yielding a range of parameter values rather than a single set of absolute values. The suite of parameters is then used to make predictions of solute transport under lower hydraulic gradients and the uncertainty of estimated parameters and subsequent predictions of solute transport is compared. The results of this study show that predictions of breakthrough curve characteristics (first inflection point time, peak arrival time and peak concentration) for groundwater flow speeds with orders of magnitude smaller than that at which a test is conducted can sometimes be determined even more accurately than the fracture and matrix parameters.     

Modelling the solute transport under nonequilibrium conditions on the basis of mass transfer equations

A solute transport model that describes nonequilibrium adsorption in soil/groundwater systems by mass transfer equations for film and intraparticle diffusion is presented. The model is useful in cases where breakthrough curve spreading cannot be explained by dispersion only. To evaluate its validity, the model was applied to several data sets from column experiments. The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion. Furthermore, a sensitivity analysis was performed to illustrate the influence of different process and sorption parameters (pore water velocity, intraparticle mass transfer coefficient, isotherm nonlinearity) on the shape of the calculated breakthrough curves. The application of the proposed model is discussed in comparison to the widely used dispersed flow/local equilibrium model, and a relationship between both models, which is based on a lumped parameter approach, is shown.     

Pulsed pumping process optimization using a potential flow model

A computational model is applied to the optimization of pulsed pumping systems for efficient in situ remediation of groundwater contaminants. In the pulsed pumping mode of operation, periodic rather than continuous pumping is used. During the pump-off or trapping phase, natural gradient flow transports contaminated groundwater into a treatment zone surrounding a line of injection and extraction wells that transect the contaminant plume. Prior to breakthrough of the contaminated water from the treatment zone, the wells are activated and the pump-on or treatment phase ensues, wherein extracted water is augmented to stimulate pollutant degradation and recirculated for a sufficient period of time to achieve mandated levels of contaminant removal. An important design consideration in pulsed pumping groundwater remediation systems is the pumping schedule adopted to best minimize operational costs for the well grid while still satisfying treatment requirements. Using an analytic two-dimensional potential flow model, optimal pumping frequencies and pumping event durations have been investigated for a set of model aquifer-well systems with different well spacings and well-line lengths, and varying aquifer physical properties. The results for homogeneous systems with greater than five wells and moderate to high pumping rates are reduced to a single, dimensionless correlation. Results for heterogeneous systems are presented graphically in terms of dimensionless parameters to serve as an efficient tool for initial design and selection of the pumping regimen best suited for pulsed pumping operation for a particular well configuration and extraction rate. In the absence of significant retardation or degradation during the pump-off phase, average pumping rates for pulsed operation were found to be greater than the continuous pumping rate required to prevent contaminant breakthrough.