The New Potential for Understanding Groundwater Contaminant Transport

The groundwater remediation field has been changing constantly since it first emerged in the 1970s. The remediation field has evolved from a dissolved‐phase centric conceptual model to a DNAPL‐dominated one, which is now being questioned due to a renewed appreciation of matrix diffusion effects on remediation. Detailed observations about contaminant transport have emerged from the remediation field, and challenge the validity of one of the mainstays of the groundwater solute transport modeling world: the concept of mechanical dispersion (Payne et al. 2008). We review and discuss how a new conceptual model of contaminant transport based on diffusion (the usurper) may topple the well‐established position of mechanical dispersion (the status quo) that is commonly used in almost every groundwater contaminant transport model, and evaluate the status of existing models and modeling studies that were conducted using advection‐dispersion models.     

Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.     

Analytical models of steady-state plumes undergoing sequential first-order degradation

An exact, closed‐form analytical solution is derived for one‐dimensional (1D), coupled, steady‐state advection‐dispersion equations with sequential first‐order degradation of three dissolved species in groundwater. Dimensionless and mathematical analyses are used to examine the sensitivity of longitudinal dispersivity in the parent and daughter analytical solutions. The results indicate that the relative error decreases to less than 15% for the 1D advection‐dominated and advection‐dispersion analytical solutions of the parent and daughter when the Damköhler number of the parent decreases to less than 1 (slow degradation rate) and the Peclet number increases to greater than 6 (advection‐dominated). To estimate first‐order daughter product rate constants in advection‐dominated zones, 1D, two‐dimensional (2D), and three‐dimensional (3D) steady‐state analytical solutions with zero longitudinal dispersivity are also derived for three first‐order sequentially degrading compounds. The closed form of these exact analytical solutions has the advantage of having (1) no numerical integration or evaluation of complex‐valued error function arguments, (2) computational efficiency compared to problems with long times to reach steady state, and (3) minimal effort for incorporation into spreadsheets. These multispecies analytical solutions indicate that BIOCHLOR produces accurate results for 1D steady‐state, applications with longitudinal dispersion. Although BIOCHLOR is inaccurate in multidimensional applications with longitudinal dispersion, these multidimensional multispecies analytical solutions indicate that BIOCHLOR produces accurate steady‐state results when the longitudinal dispersion is zero. As an application, the 1D advection‐dominated analytical solution is applied to estimate field‐scale rate constants of 0.81, 0.74, and 0.69/year for trichloroethene, cis‐1,2‐dichloroethene, and vinyl chloride, respectively, at the Harris Palm Bay, FL, CERCLA site.     

Semi-analytical solutions for solute transport in fractured porous media using a strip source of finite width

Transient and steady-state analytical solutions are derived to investigate solute transport in a fractured porous medium consisting of evenly spaced, parallel discrete fractures. The solutions incorporate a finite width strip source, longitudinal and transverse dispersion in the fractures, source decay, aqueous phase decay, one-dimensional diffusion into the matrix, sorption to fracture walls, and sorption within the matrix. The solutions are derived using Laplace and Fourier transforms, and inverted by interchanging the order of integration and utilizing a numerical Laplace inversion algorithm. The solutions are verified for simplified cases by comparison to solutions derived by Batu [Batu V. A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type condition at the source. Wat Resour Res 1989;25(6):1125] and Sudicky and Frind [Sudicky EA, Frind EO. Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Wat Resour Res 1982;18(6):1634]. The application of the solutions to a fractured sandstone demonstrates that narrower source widths and larger values of transverse dispersivity both lead to lower downstream concentrations in the fractures and shorter steady-state plumes. The incorporation of aqueous phase decay and source concentration decay both lead to lower concentrations and shorter plumes, with even moderate amounts of decay significantly shortening the persistence of contamination.     

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin,France)

A groundwater flow model has been developed in order to study the chalk aquifer of Paris Basin, based on most of the geological and hydrological available data. The numerical processes are intended to modelling the groundwater flow in the Senonian (Late Cretaceous) formations and to visualize the tracer movement in groundwater resources in the experimental site of LaSalle Beauvais (northern part Paris Basin). Both objectives were achieved as follows: (i) the comprehension of the spatial distribution of the hydraulic conductivity in the chalk aquifer taking into account the characteristics of the hydrogeological system and (ii) the use of the analytical solution for describing one‐dimensional to two‐dimensional solute transport in a unidirectional steady‐state flow tracer with scale‐dependent dispersion. Advection and diffusion mechanisms are taken into account. Comparison between the breakthrough curves of the analytical and the numerical solutions provided an excellent agreement for various ranges of scale‐related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at each observation point. Thus, the derived new solutions are widely applicable and are very useful for the validation of numerical transport. The numerical approach is carried out by MT3DMS, a Modular 3‐D Multi‐Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, and based on total variation‐diminishing method using the ULTIMATE algorithm. The estimation of the infected surface could constitute an approach in water management and allows to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2016 John Wiley & Sons, Ltd.     

Saltwater intrusion modeling in heterogeneous confined aquifers using two-relaxation-time lattice Boltzmann method

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (LTRT) to solve saltwater intrusion problems. A directional-speed-of-sound (DSS) technique is introduced to take into account the hydraulic conductivity heterogeneity and discontinuity, as well as the velocity-dependent dispersion coefficient. The forcing terms in the LTRT model are customized in order to recover the density-dependent groundwater flow and mass transport equations. Using the LTRT with the squared DSS achieves at least second-order accuracy. The LTRT results are verified with Henry’s analytical solution as well as compared with several numerical examples and modified Henry problems that consider heterogeneous hydraulic conductivity and velocity-dependent dispersion. The numerical results show good agreement with the Henry analytical solution and with the numerical solutions obtained by other numerical methods.     

Analytical Solutions for Water Flow and Solute Transport in the Unsaturated Zone

Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant.     

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Many studies indicate that small‐scale heterogeneity and/or mobile–immobile mass exchange produce transient non‐Fickian plume behavior that is not well captured by the use of the standard, deterministic advection‐dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non‐Fickian transport coupled with simultaneous sequential first‐order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed‐form, steady‐state, multi‐species analytical solutions are also derived for non‐Fickian transport in highly heterogeneous aquifers with linear sorption–desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi‐species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over‐estimate cleanup rates and under‐predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.     

Assessing the validity of a lower-dimensional representation of fractures for numerical and analytical investigations

Due to their high aspect ratio fractures are often conceptualized as lower-dimensional structures embedded into the surrounding host matrix. This simplification is typically made within the context of numerical simulation, for the inverse estimation of the matrix-diffusion coefficient from break-through curves or for the derivation of analytical solutions describing flow and transport in a fracture–matrix system. It is generally justified by the so called Lauwerier assumption stating that the transversal dispersion inside the fracture is infinitely fast therefore hampering the formation of gradients across the width of the fracture. In this study we want to verify the applicability of such lower-dimensional modeling. To that end we investigate the occurrence of fracture-scale gradients in a simplified fracture–matrix model by virtue of analytical as well as numerical investigations. The relevant processes modeled are advection, dispersion, matrix diffusion and linear decay. In addition, we also investigate the impact on the inverse estimation of matrix-diffusion coefficients through analytical solutions, which assume a lower-dimensional fracture. Results show that a lower-dimensional modeling of fractures will only lead to errors for early periods of the time-dependent solution. Such errors may however, extent to the steady state if fast radioactive decay is considered. The estimation of the matrix-diffusion coefficient too is affected by the assumption of a lower-dimensional fracture. We see errors as big as 20% for the estimation procedure, the value of which depends on the ratio of the matrix-diffusion vs. the transversal dispersion coefficient. Our analysis suggest that a lower-dimensional representation of fractures is justified for many typical conditions and that special attention must only be paid in a confined number of cases.     

Two-dimensional power series solution for non-axisymmetrical transport in a radially convergent tracer test with scale-dependent dispersion

It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The power series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical solution to the two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the power series solution and the numerical solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at any observation point.     

Analytical model for fully three‐dimensional radial dispersion in a finite‐thickness aquifer

Analytical solutions for contaminant transport in a non‐uniform flow filed are very difficult and relatively rare in subsurface hydrology. The difficulty is because of the fact that velocity vector in the non‐uniform flow field is space‐dependent rather than constant. In this study, an analytical model is presented for describing the three‐dimensional contaminant transport from an area source in a radial flow field which is a simplest case of the non‐uniform flow. The development of the analytical model is achieved by coupling the power series technique, the Laplace transform and the two finite Fourier cosine transform. The developed analytical model is examined by comparing with the Laplace transform finite difference (LTFD) solution. Excellent agreements between the developed analytical model and the numerical model certificate the accuracy of the developed model. The developed model can evaluate solution for Peclet number up to 100. Moreover, the mathematical behaviours of the developed solution are also studied. More specifically, a hypothetical convergent flow tracer test is considered as an illustrative example to demonstrate the three‐dimensional concentration distribution in a radial flow field. The developed model can serve as benchmark to check the more comprehensive three‐dimensional numerical solutions describing non‐uniform flow contaminant transport. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of the thickness of a fresh water lens and of the transition zone between this lens and upwelling saline water

In regions with saline groundwater, fresh water lenses may develop due to rainwater infiltration. The amount of fresh water that is available for e.g. agricultural crops depends on the thickness of the lens and the extent of mixing between fresh and saline water. In this paper, we consider the mixing of fresh water and upward moving saline ground water in low-lying deltaic areas. The parameters that dominate the flow and transport problem are investigated using dimensionless groups and scaled sensitivities. We characterize the numerically simulated thicknesses of the lens and of the mixing zone by spatial moments. Rayleigh number and mass flux ratio, which is the ratio of the salt water seepage and the precipitation, determine the thickness of the fresh water lens. The local thickness of the mixing zone is mainly influenced by the dispersive/diffusive groups and the mass flux ratio. In addition, convergence of streamlines towards an outflow boundary affects the thickness, particularly in the vicinity of this boundary.Analytical and numerical steady state solutions for lens thickness are compared, taking into account upward seepage, for the two cases with and without a density difference between lens and underlying groundwater. Agreement between the numerical and analytical solutions for the lens thickness is good except when the mass flux ratio becomes small. For zero mass flux ratio, it is implicitly assumed in the analytical solution that salt water is stagnant, and that is unrealistic. Relative contributions of longitudinal and transversal hydrodynamic dispersion and diffusion to the thickness of the mixing zone are quantified numerically for different phases of lens formation. Longitudinal dispersion dominates in the early stages of lens formation, while diffusion and transversal dispersion dominate at steady state.     

Prediction of Remediation of a Heterogeneous Aquifer: A Case Study

Contaminant plumes whose characteristic length is smaller than the horizontal integral scale of the hydraulic conductivity, K, are abundant in shallow, phreatic aquifers. In such cases, the aquifer can be regarded as layered, with K being only a function of the vertical coordinate. The heterogeneity of K has a critical role upon the efficiency of remediation of such sites, for example, by Pump and Treat schemes. The expected efficiency is a random variable, with uncertainty. Quantifying this uncertainty can be of great importance to decision making. In this study, we focus on a case study in the coastal aquifer of Israel and compare two different approaches for constructing realizations of K: continuous and indicator. We observe a significant difference between the constructed realizations, which results in a considerable difference in the predicted remediation efficiency and its uncertainty. Furthermore, we study the effect of conditioning the realizations by a rather limited number of K data points. We find that the conditioning results in a major reduction of the uncertainty. In addition, we compare the results of the transport model to a simplified semi‐analytical solution that is based on assuming radial flow. We find a good agreement with the three‐dimensional numerical model. This result illustrates that the simplified solution can be used for prediction of the remediation efficiency when the flow at the plume vicinity can be regarded as radial.     

Evaluation of Mass Flux to and from Ground Water Using a Vertical Flux Model (VFLUX): Application to the Soil Vacuum Extraction Closure Problem

Site closure for soil vacuum extraction (SVE) application typically requires attainment or specified soil concentration standards based on the premise that mass flux from the vadose zone to ground water not result in levels exceeding maximum contaminant levels (MCLs). Unfortunately, realization of MCLs in ground water may not be attainable at many sites. This results in soil remediation efforts that may be in excess of what is necessary for future protection of ground water and soil remediation goals which often cannot be achieved within a reasonable time period. Soil venting practitioners have attempted to circumvent these problems by basing closure on some predefined percent total mass removal, or an approach to a vapor concentration asymptote. These approaches, however, are subjective and influenced by venting design. We propose an alternative strategy based on evaluation of five components: (1) site characterization, (2) design. (3) performance monitoring, (4) rule-limited vapor transport, and (5) mass flux to and from ground water. Demonstration of closure is dependent on satisfactory assessment of all five components. The focus of this paper is to support mass flux evaluation. We present a plan based on monitoring of three subsurface zones and develop an analytical one-dimensional vertical flux model we term VFLUX. VFLUX is a significant improvement over the well-known numerical one-dimensional model. VLEACH, which is often used for estimation of mass flux to ground water, because it allows for the presence of nonaqueous phase liquids (NAPLs) in soil, degradation, and a lime-dependent boundary condition at the water table inter-face. The time-dependent boundary condition is the center-piece of our mass flux approach because it dynamically links performance of ground water remediation lo SVE closure. Progress or lack of progress in ground water remediation results in either increasingly or decreasingly stringent closure requirements, respectively.     

1,4‐Dioxane Soil Remediation Using Enhanced Soil Vapor Extraction: I. Field Demonstration

1,4‐Dioxane is totally miscible in water, sequestering in vadose pore water that can serve as a source of long‐term groundwater contamination. Although some 1,4‐dioxane is removed by conventional soil vapor extraction (SVE), remediation is typically inefficient. SVE efficiency is hindered by low Henry’s Law constants at ambient temperature and redistribution to vadose pore water if SVE wells pull 1,4‐dioxane vapors across previously clean soil. It was hypothesized that heated air injection and more focused SVE extraction (“Enhanced SVE” or XSVE) could increase the efficiency of 1,4‐dioxane vadose treatment, and this new process was tested at former McClellan Air Force Base, CA. The XSVE system had four peripheral heated air injection wells surrounding a 6.1 m × 6.1 m × 9.1 m deep treatment zone with a central vapor extraction well. After 14 months of operation, soil temperatures reached as high as ~90 °C near the injection wells and the treatment zone was flushed with ~20,000 pore volumes of injected air. Post‐treatment sampling results showed reductions of ~94% in 1,4‐dioxane and ~45% in soil moisture. Given the simplicity of the remediation system components and the promising demonstration test results, XSVE has the potential to be a cost‐effective remediation option for vadose zone soil containing 1,4‐dioxane.     

Estimating the Impact of Vadose Zone Sources on Groundwater to Support Performance Assessment of Soil Vapor Extraction

Soil vapor extraction (SVE) is a prevalent remediation remedy for volatile organic compound (VOC) contaminants in the vadose zone. To support selection of an appropriate condition at which SVE may be terminated for site closure or for transition to another remedy, an evaluation is needed to determine whether vadose zone VOC contamination has been diminished sufficiently to keep groundwater concentrations below threshold values. A conceptual model for this evaluation was developed for VOC fate and transport from a vadose zone source to groundwater when vapor‐phase diffusive transport is the dominant transport process. A numerical analysis showed that, for these conditions, the groundwater concentration is controlled by a limited set of parameters, including site‐specific dimensions, vadose zone properties, and source characteristics. On the basis of these findings, a procedure was then developed for estimating groundwater concentrations using results from the three‐dimensional multiphase transport simulations for a matrix of parameter value combinations and covering a range of potential site conditions. Interpolation and scaling processes are applied to estimate groundwater concentrations at compliance (monitoring) wells for specific site conditions of interest using the data from the simulation results. The interpolation and scaling methodology using these simulation results provides a far less computationally intensive alternative to site‐specific three‐dimensional multiphase site modeling, while still allowing for parameter sensitivity and uncertainty analyses. With iterative application, the approach can be used to consider the effect of a diminishing vadose zone source over time on future groundwater concentrations. This novel approach and related simulation results have been incorporated into a user‐friendly Microsoft® Excel®‐based spreadsheet tool entitled SVEET (Soil Vapor Extraction Endstate Tool), which has been made available to the public.     

A finite element method for the diffusion-convection equation with constant coefficients

Existing numerical methods for the solution of the diffusion-convection equation are unsatisfactory for convection dominated flow problems. A new finite element method incorporating the method of characteristics for the solution of the diffusion-convection equation with constant coefficients in one spatial dimensions is derived. This method is capable of solving diffusion-convection equation without any of the difficulties encountered in the existing numerical methods for the whole spectrum of dispersion from pure diffusion, through mixed dispersion, to pure convection. Several examples for the one-dimensional case are solved and results are compared with the exact solutions. The generalization of the method to variable coefficients and to the diffusion-convection equation in two space dimensions are discussed.     

Influence of Soil Air Permeability Change on Soil Vapour Extraction Systems Design

Soil air permeability plays a decisive role in the effectiveness of soil vapour extraction (SVE) for the removal of volatile organic contaminants (VOCs) from soil. The objective of this work is to study the change of the soil air permeability during continuous venting and removal of contaminant from a polluted soil. SVE pilot experiments were conducted to investigate the interaction of soil air permeability with total liquids saturation. Oppositely to previous studies, air permeability was measured by fitting pressure data measured in a 3D laboratory venting pilot to an analytical airflow solution. The experimental correlation was compared with two different correlations published previously. A difference was observed between measured and calculated air relative air permeabilities especially for low water saturation degrees. The importance of the correct estimate of relative permeability was then illustrated by comparing vacuums and streamlines calculated using measured permeability and permeability values estimated with the two correlations tested here. Results show that an inappropriate assessment of relative permeability may engender significant errors in designing an SVE system. The second part of this work reports on the influence of air permeability change on the prediction capability of an SVE mathematical model. A significant difference between simulated breakthrough curves, estimated using firstly the relationship established experimentally and secondly the two other correlations, was observed. These results lead us to say that inadequate characterization of the air permeability change may generate significant errors in removal rate and closure time estimates.     

Analytical solutions for transport of decaying solutes in rivers with transient storage

Analytical solutions are presented for solute transport in rivers including the effects of transient storage and first order decay. The solute transport model considers an advection–dispersion equation for transport in the main channel linked to a first order mass exchange between the main channel and the transient storage zones. In case of a conservative tracer, it is shown that different analytical solutions presented in the literature are mathematically identical. For non-conservative solutes, first order decay reactions are considered with different reaction rate coefficients in the main river channel and in the dead zones. New analytical solutions are presented for different boundary conditions, i.e. instantaneous injection in an infinite river reach, and variable concentration time series input in a semi-infinite river reach. The correctness and accuracy of the analytical solutions is verified by comparison with the OTIS numerical model. The results of analytical and numerical approaches compare favourably and small differences can be attributed to the influence of boundary conditions. It is concluded that the presented analytical solutions for solute transport in rivers with transient storage and solute decay are accurate and correct, and can be usefully applied for analyses of tracer experiments and transport characteristics in rivers with mass exchange in dead zones.     

Efficient flow and transport simulations in reconstructed 3D pore geometries

Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element–finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection–diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion D_m of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated.