Effects of compound-specific dilution on transient transport and solute breakthrough: A pore-scale analysis

This pore-scale modeling study in saturated porous media shows that compound-specific effects are important not only at steady-state and for the lateral displacement of solutes with different diffusivities but also for transient transport and solute breakthrough. We performed flow and transport simulations in two-dimensional pore-scale domains with different arrangement of the solid grains leading to distinct characteristics of flow variability and connectivity, representing mildly and highly heterogeneous porous media, respectively. The results obtained for a range of average velocities representative of groundwater flow (0.1–10 m/day), show significant effects of aqueous diffusion on solute breakthrough curves. However, the magnitude of such effects can be masked by the flux-averaging approach used to measure solute breakthrough and can hinder the correct interpretation of the true dilution of different solutes. We propose, as a metric of mixing, a transient flux-related dilution index that allows quantifying the evolution of solute dilution at a given position along the main flow direction. For the different solute transport scenarios we obtained dilution breakthrough curves that complement and add important information to traditional solute breakthrough curves. Such dilution breakthrough curves allow capturing the compound-specific mixing of the different solutes and provide useful insights on the interplay between advective and diffusive processes, mass transfer limitations, and incomplete mixing in the heterogeneous pore-scale domains. The quantification of dilution for conservative solutes is in good agreement with the outcomes of mixing-controlled reactive transport simulations, in which the mass and concentration breakthrough curves of the product of an instantaneous transformation of two initially segregated reactants were used as measures of reactive mixing.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Analytical solutions of the advection‐dispersion equation for transient groundwater flow. A numerical validation

An analytical transport‐model was developed to simulate the propagation of a contaminant in one‐ and two‐dimensional transient flow in groundwater. It is proved that the distribution of concentration at a given time and for a given discharge is identical to that obtained for a different discharge if the volumetric flux of water is the same in the two cases. The results of simulations have been compared with results obtained using the MT3DMS numerical model. There is good agreement when the calculated concentrations are flux‐weighted concentrations. On the other hand, there is a notable divergence when the resident mode is considered. Resident mode concentrations express the mass per unit volume whereas flux mode concentrations express the ratio of mass flux to fluid flux. The solutions presented in this paper can thus be a useful alternative to code MT3DMS when the objective is to simulate concentrations in transient flow according to a resident mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling interaction of fluid and salt in an aquifer/lagoon system

To simulate the dynamic interaction between a saline lagoon and a ground water system, a numerical model for two-dimensional, variable-density, saturated-unsaturated, and coupled flow and solute transport (saltwater intrusion by finite elements and characteristics [SIFEC]) was modified to allow the volume of water and mass of salt in the lagoon to vary with each time step. The modified SIFEC allows the stage of a lagoon to vary in accordance with a functional relation between the stage and water volume of the lagoon, and also allows the salt concentration of the lagoon to vary in accordance with the salt budget of the lagoon including chemical precipitation and dissolution of salt. The updated stage and salt concentration of the lagoon are in turn used as transient boundary conditions for the coupled flow and solute transport model. The utility of the modified model was demonstrated by applying it to the eastern Mediterranean coastal region of Turkey for assessing impacts of climate change on the subsurface environment under scenarios of sea level rise, increased evaporation, and decreased precipitation.     

Sustainable conjunctive use of groundwater for additional irrigation

The key to ‘sustainable conjunctive use of groundwater for additional irrigation’ is the salt balance of groundwater below an irrigated field. This paper aims to develop a mathematical tool to study the accumulation of salt in the groundwater below an irrigated field as caused by irrigation recirculation. This study derives a salt balance of groundwater to ensure that the additional irrigation from groundwater remains possible in the future. The water and salt budgets by themselves do neither provide information concerning farmers' options nor on the limits of the individual terms in the budget equations. It is presumed that farmers will intuitively aim for (1) an optimal value of the actual evapotranspiration, and (2) a return flow as a feasible low fraction of the available water. We, therefore, derive the irrigation from groundwater Q as a consequence of the predefined farmers' aims to achieve a high actual evapotranspiration in combination with a given optimally used irrigation system. Our model concludes that the required amount of drainage is only dependent on the ratio of the salinity in the surface irrigation water and the acceptable salinity of the groundwater. The final salinity in the saturated zone only depends on salt‐carrying inflows and outflows. From the aforesaid model, it is further concluded that sustainable conjunctive use of groundwater for additional irrigation requires long‐term salt management, which should be founded on the essential controlling factors as derived in this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Understanding salt mobilization from an irrigated catchment in south‐eastern Australia

Groundwater discharge from the Riverine Plains of the southern Murray‐Darling Basin is a major process contributing salt to the Murray River in Australia. In this study, data from an irrigated 60 000 ha catchment in the Riverine Plains were analysed to understand groundwater discharge into deeply incised drains, the process dominating salt mobilization from the catchment. We applied three integrated methodologies: classification and regression trees (CART), conceptual modelling and artificial neural networks (ANNs) to a comprehensive, spatially lumped, monthly data set from July 1975 to December 2004. Using CART analysis, it was shown that rainfall was the most important variable consistently explaining the salt load patterns at the catchment outlet. Using the conceptual model representing spatially lumped groundwater discharge into deeply incised drains, we demonstrated that salt mobilization from the study catchment can be well represented by a rainfall contribution, influenced by the hydraulic head in the deep regional aquifer and potential evapotranspiration. Using ANNs, it was confirmed that rainfall had a much higher impact on salt loads at the catchment outlet than irrigation water use. All these results demonstrate that under conditions similar to those experienced from 1975 to 2004, it is rainfall rather than irrigation water use that governs salt mobilization from the study catchment. Management of salt mobilization from irrigated catchments has traditionally focussed on the improvement of irrigation practices but it could be equally important to further understand the scope for management to control groundwater discharge in these irrigation areas. Copyright © 2010 John Wiley & Sons, Ltd.     

Innovative Contaminant Mass Flux Monitoring in an Aquifer Subject to Tidal Effects

Exposure from groundwater contamination to aquatic receptors residing in receiving surface water is dependent upon the rate of contaminated groundwater discharge. Characterization of groundwater fluxes is challenging, especially in coastal environments where tidal fluctuations result in transient groundwater flows towards these receptors. This can also be further complicated by the high spatial heterogeneity of subsurface deposits enhanced by anthropogenic influences such as the mixing of natural sediments and backfill materials, the presence of subsurface built structures such as sheet pile walls or even occurrence of other sources of contaminant discharge. In this study, the finite volume point dilution method (FVPDM) was successfully used to characterize highly transient groundwater flows and contaminant mass fluxes within a coastal groundwater flow system influenced by marked tides. FVPDM tests were undertaken continuously for more than 48 h at six groundwater monitoring wells, in order to evaluate groundwater flow dynamics during several tide cycles. Contaminant concentrations were measured simultaneously which allowed calculating contaminant mass fluxes. The study highlighted the importance of the aquifer heterogeneity, with groundwater fluxes ranging from 10⁻⁷ to 10⁻³ m/s. Groundwater flux monitoring enabled a significant refinement of the conceptual site model, including the fact that inversion of groundwater fluxes was not observed at high tide. Results indicated that contaminant mass fluxes were particularly higher at a specific monitoring well, by more than three orders of magnitude, than at other wells of the investigated aquifer. This study provided crucial information for optimizing further field investigations and risk mitigation measures.     

Integrated water resource management in a major canal command in eastern India

The present rice‐dominated cropping system in the Hirakud canal command (eastern India) is under severe threat due to imbalance between irrigation water supply and demand. The canal water supply, which is the only source of irrigation, only meets 54% of the demand at 90% probability of exceedance (PE). In order to mitigate the irrigation water deficit from canal water, groundwater is considered as a supplemental source. Quasi‐three‐dimensional groundwater flow simulation modelling was, therefore, carried out by using Visual MODFLOW to detect the change in hydraulic head due to transient pumping stresses. The simulation model was calibrated and validated satisfactorily. Sensitivity analysis of the model parameters shows that groundwater recharge is most sensitive followed by aquifer hydraulic conductivity at almost all the sites of the command area, whereas the model is comparatively less sensitive to specific storage and specific yield. Enhanced pumping scenarios showed that groundwater extraction can be increased up to 50 times of the existing pumping without causing any adverse effect to the aquifer but the aquifer does not permit to exploit water in order to fulfill the irrigation water demand even at 10% PE. Hence, it is imperative to develop an optimal land and water resources management plan of the command area. Copyright © 2011 John Wiley & Sons, Ltd.     

An interactive multi-objective optimization framework for groundwater inverse modeling

The groundwater inverse problem of estimating heterogeneous groundwater model parameters (hydraulic conductivity in this case) given measurements of aquifer response (such as hydraulic heads) is known to be an ill-posed problem, with multiple parameter values giving similar fits to the aquifer response measurements. This problem is further exacerbated due to the lack of extensive data, typical of most real-world problems. In such cases, it is desirable to incorporate expert knowledge in the estimation process to generate more reasonable estimates. This work presents a novel interactive framework, called the ‘Interactive Multi-Objective Genetic Algorithm’ (IMOGA), to solve the groundwater inverse problem considering different sources of quantitative data as well as qualitative expert knowledge about the site. The IMOGA is unique in that it looks at groundwater model calibration as a multi-objective problem consisting of quantitative objectives – calibration error and regularization – and a ‘qualitative’ objective based on the preference of the geological expert for different spatial characteristics of the conductivity field. All these objectives are then included within a multi-objective genetic algorithm to find multiple solutions that represent the best combination of all quantitative and qualitative objectives. A hypothetical aquifer case-study (based on the test case presented by Freyberg [Freyberg DL. An exercise in ground-water model calibration and prediction. Ground Water 1988;26(3)], for which the ‘true’ parameter values are known, is used as a test case to demonstrate the applicability of this method. It is shown that using automated calibration techniques without using expert interaction leads to parameter values that are not consistent with site-knowledge. Adding expert interaction is shown to not only improve the plausibility of the estimated conductivity fields but also the predictive accuracy of the calibrated model.     

A coupled model for simulating surface water and groundwater interactions in coastal wetlands

Coastal wetlands are characterized by strong, dynamic interactions between surface water and groundwater. This paper presents a coupled model that simulates interacting surface water and groundwater flow and solute transport processes in these wetlands. The coupled model is based on two existing (sub) models for surface water and groundwater, respectively: ELCIRC (a three‐dimensional (3‐D) finite‐volume/finite‐difference model for simulating shallow water flow and solute transport in rivers, estuaries and coastal seas) and SUTRA (a 3‐D finite‐element/finite‐difference model for simulating variably saturated, variable‐density fluid flow and solute transport in porous media). Both submodels, using compatible unstructured meshes, are coupled spatially at the common interface between the surface water and groundwater bodies. The surface water level and solute concentrations computed by the ELCIRC model are used to determine the boundary conditions of the SUTRA‐based groundwater model at the interface. In turn, the groundwater model provides water and solute fluxes as inputs for the continuity equations of surface water flow and solute transport to account for the mass exchange across the interface. Additionally, flux from the seepage face was routed instantaneously to the nearest surface water cell according to the local sediment surface slope. With an external coupling approach, these two submodels run in parallel using time steps of different sizes. The time step (Δt_g) for the groundwater model is set to be larger than that (Δt_s) used by the surface water model for computational efficiency: Δt_g = M × Δt_s where M is an integer greater than 1. Data exchange takes place between the two submodels through a common database at synchronized times (e.g. end of each Δt_g). The coupled model was validated against two previously reported experiments on surface water and groundwater interactions in coastal lagoons. The results suggest that the model represents well the interacting surface water and groundwater flow and solute transport processes in the lagoons. Copyright © 2011 John Wiley & Sons, Ltd.     

Single-Well Injection-Drift Test to Estimate Groundwater Velocity

A simple algebraic equation is presented here to estimate the magnitude of groundwater velocity based on data from a single-well injection-drift test thereby eliminating the time-consuming and costly extraction phase. A volume of tracer-amended water was injected by forced-gradient into a single well followed by monitoring of the conservative solute tracers under natural-gradient conditions as their upgradient portions drifted back through the well. The breakthrough curve data from the single well during the drift phase was analyzed to determine the mean travel times of the tracers. The estimated mean upgradient travel distance back through the single well and the mean travel times of the tracers were used in a simple algebraic equation to estimate groundwater velocity. The groundwater velocity based on the single-well injection-drift test was estimated to be approximately 0.64 ft per day. Two transects of observation wells were used to monitor the natural-gradient tracer transport downgradient of the injection well. The one-dimensional, or dual-well, transport of the tracer from the injection well to the nearest downgradient observation well indicated that the groundwater velocity was 0.55 ft per day. The two-dimensional, or multi-well, transport of the center of mass of the tracers indicated that the groundwater velocity was 0.60 ft per day; the dual- and multi-well results were in excellent agreement with those from the single-well and validated the simple algebraic equation. The new single-well method presented here is relatively simple, rapid, and does not require an extraction phase.     

Hydraulic displacement of dense nonaqueous phase liquids for source zone stabilization

Hydraulic displacement is a mass removal technology suitable for stabilization of a dense, nonaqueous phase liquid (DNAPL) source zone, where stabilization is defined as reducing DNAPL saturations and reducing the risk of future pool mobilization. High resolution three-dimensional multiphase flow simulations incorporating a spatially correlated, heterogeneous porous medium illustrate that hydraulic displacement results in an increase in the amount of residual DNAPL present, which in turn results in increased solute concentrations in groundwater, an increase in the rate of DNAPL dissolution, and an increase in the solute mass flux. A higher percentage of DNAPL recovery is associated with higher initial DNAPL release volumes, lower density DNAPLs, more heterogeneous porous media, and increased drawdown of groundwater at extraction wells. The fact that higher rates of recovery are associated with more heterogeneous porous media stems from the fact that larger contrasts in permeability provide for a higher proportion of capillary barriers upon which DNAPL pooling and lateral migration can occur. Across all scenarios evaluated in this study, the ganglia-to-pool (GTP) ratio generally increased from approximately 0.1 to between approximately 0.3 and 0.7 depending on the type of DNAPL, the degree of heterogeneity, and the imposed hydraulic gradient. The volume of DNAPL recovered as a result of implementing hydraulic displacement ranged from between 9.4% and 45.2% of the initial release volume, with the largest percentage recovery associated with 1,1,1 trichloroethane, the least dense of the three DNAPLs considered.     

Implementation of Solute Transport in the Vadose Zone into the “HYDRUS Package for MODFLOW”

The “HYDRUS package for MODFLOW” is an existing MODFLOW package that allows MODFLOW to simultaneously evaluate transient water flow in both unsaturated and saturated zones. The package is based on incorporating parts of the HYDRUS-1D model (to simulate unsaturated water flow in the vadose zone) into MODFLOW (to simulate saturated groundwater flow). The coupled model is effective in addressing spatially variable saturated-unsaturated hydrological processes at the regional scale. However, one of the major limitations of this coupled model is that it does not have the capability to simulate solute transport along with water flow and therefore, the model cannot be employed for evaluating groundwater contamination. In this work, a modified unsaturated flow and transport package (modified HYDRUS package for MODFLOW and MT3DMS) has been developed and linked to the three-dimensional (3D) groundwater flow model MODFLOW and the 3D groundwater solute transport model MT3DMS. The new package can simulate, in addition to water flow in the vadose zone, also solute transport involving many biogeochemical processes and reactions, including first-order degradation, volatilization, linear or nonlinear sorption, one-site kinetic sorption, two-site sorption, and two-kinetic sites sorption. Due to complex interactions at the groundwater table, certain modifications of the pressure head (compared to the original coupling) and solute concentration profiles were incorporated into the modified HYDRUS package. The performance of the newly developed model is evaluated using HYDRUS (2D/3D), and the results indicate that the new model is effective in simulating the movement of water and contaminants in the saturated-unsaturated flow domains.     

Total variation diminishing schemes for pollutant transport in porous media

A bidimensional numerical model has been used in order to simulate the contaminant transport in the coastal groundwater area (Atlantic margin of the Rharb basin, Morocco). This groundwater is materialized by means of the salt contamination derived from several factors: evapotranspiration, lithological series formations, marine intrusion, and processes of interaction between water and rocks. In order to reduce the numerical diffusion and limit the numerical dispersion, we use the Superbee flux limiter as a total variation diminishing scheme to discretize the convective operator. This kind of discretization was applied to the coastal groundwater of the Rharb basin (Morocco). The results show that the Superbee flux limiter is efficient at drawing the path of the contaminant front with high accuracy. Consequently, this scheme could constitute an approach in water management and allows one to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2007 John Wiley & Sons, Ltd.     

Response of deep groundwater to land use change in desert basins of the Trans‐Pecos region,Texas, USA: Effects on infiltration,recharge, and nitrogen fluxes

Quantifying the effects of anthropogenic processes on groundwater in arid regions can be complicated by thick unsaturated zones with long transit times. Human activities can alter water and nutrient fluxes, but their impact on groundwater is not always clear. This study of basins in the Trans‐Pecos region of Texas links anthropogenic land use and vegetation change with alterations to unsaturated zone fluxes and regional increases in basin groundwater NO₃^? concentrations. Median increases in groundwater NO₃^? (by 0.7–0.9 mg‐N/l over periods ranging from 10 to 50+ years) occurred despite low precipitation (220–360 mm/year), high potential evapotranspiration (~1570 mm/year), and thick unsaturated zones (10–150+ m). Recent model simulations indicate net infiltration and groundwater recharge can occur beneath Trans‐Pecos basin floors, and may have increased due to irrigation and vegetation change. These processes were investigated further with chemical and isotopic data from groundwater and unsaturated zone cores. Some unsaturated zone solute profiles indicate flushing of natural salt accumulations has occurred. Results are consistent with human‐influenced flushing of naturally accumulated unsaturated zone nitrogen as an important source of NO₃^? to the groundwater. Regional mass balance calculations indicate the mass of natural unsaturated zone NO₃^? (122–910 kg‐N/ha) was sufficient to cause the observed groundwater NO₃^? increases, especially if augmented locally with the addition of fertilizer N. Groundwater NO₃^? trends can be explained by small volumes of high NO₃^? modern recharge mixed with larger volumes of older groundwater in wells. This study illustrates the importance of combining long‐term monitoring and targeted process studies to improve understanding of human impacts on recharge and nutrient cycling in arid regions, which are vulnerable to the effects of climate change and increasing human reliance on dryland ecosystems.     

Analytical solutions to the transient,unsaturated transport of water and contaminants through horizontal porous media

We present a range of analytical solutions to the combined transient water and solute transport for horizontal flow. We adopt the concept of a scale and time dependent dispersivity used for contaminant transport in aquifers and apply it to transient, unsaturated horizontal flow to develop similarity solutions for both constant solute concentration and solute flux boundary conditions. Through the use of a specific form of the water profile as used by Brutsaert [Water Resour Res 1968:4;785], the solute profiles can be reduced to a simple quadrature. We also derive a solution for the instantaneous injection of water and solute into a horizontal media for an arbitrary dispersivity. It is found that the solute concentration remains constant in both space and time as the water redistributes, suggesting that the solute does not disperse relative to the water.     

Containment of Sources of Groundwater Contamination: Analysis of Mass Fluxes

Cutoff walls and liners are used frequently as barriers to isolate contaminants at both controlled and uncontrolled hazardous waste sites. Neville and Andrews (2006) presented a containment criterion for contaminant isolation by a barrier. The analysis of Neville and Andrews (2006) yields the inward Darcy flux that balances the diffusive mass flux from the source so that the net mass flux is zero. A requirement of zero net mass flux may not be achievable in all situations. The analysis developed by Neville and Andrews (2006) is extended to develop straightforward expressions for the long-term mass fluxes across a barrier for any conditions. In cases where it may not be possible to satisfy a criterion of zero net mass flux, the results from an exact solution for transient solute transport are used to show how the mass fluxes evolve to their long-term values.     

Analytical Solution of Advective Mixing in a Conduit

The permeable conduit wall in a karst aquifer allows for water and solute to be exchanged between conduits and the limestone matrix. Contaminant sequestered in the limestone matrix is flushed into conduits following flood events. The contaminant released from the permeable wall will then mix with conduit water and will be transported downgradient in the conduit. A one-dimensional advection-dispersion equation is presented to describe this mixing-transport incorporating water flow and solute flux through the conduit wall. An analytical solution ignoring conduit dispersion is derived using the method of characteristics. Scale analysis is performed to provide a general guideline to estimate when conduit dispersion can be neglected. The solution also can be used to compute the distribution of solute in the matrix before flushing.     

Assessment of uncertainty associated with the estimation of well catchments by moment equations

Non-local stochastic moment equations are used successfully to analyze groundwater flow in randomly heterogeneous media. Here we present a moment equations-based approach to quantify the uncertainty associated with the estimation of well catchments. Our approach is based on the development of a complete second order formalism which allows obtaining the first statistical moments of the trajectories of conservative solute particles advected in a generally non-uniform groundwater flow. Approximate equations of moments of particles’ trajectories are then derived on the basis of a second order expansion in terms of the standard deviation of the aquifer log hydraulic conductivity. Analytical expressions are then obtained for the predictors of locations of mean stagnation points, together with their associated uncertainties. We implement our approach on heterogeneous media in bounded two-dimensional domains, with and without including the effect of conditioning on hydraulic conductivity information. The impact of domain size, boundary conditions, heterogeneity and non-stationarity of hydraulic conductivity on the prediction of a well catchment is explored. The results are compared against Monte Carlo simulations and semi-analytical solutions available in the literature. The methodology is applicable to both infinite and bounded domains and is free of distributional assumptions (and so applies to both Gaussian and non-Gaussian log hydraulic conductivity fields) and formally includes the effect of conditioning on available information.     

Comparison of Ensemble Kalman Filter groundwater-data assimilation methods based on stochastic moment equations and Monte Carlo simulation

Traditional Ensemble Kalman Filter (EnKF) data assimilation requires computationally intensive Monte Carlo (MC) sampling, which suffers from filter inbreeding unless the number of simulations is large. Recently we proposed an alternative EnKF groundwater-data assimilation method that obviates the need for sampling and is free of inbreeding issues. In our new approach, theoretical ensemble moments are approximated directly by solving a system of corresponding stochastic groundwater flow equations. Like MC-based EnKF, our moment equations (ME) approach allows Bayesian updating of system states and parameters in real-time as new data become available. Here we compare the performances and accuracies of the two approaches on two-dimensional transient groundwater flow toward a well pumping water in a synthetic, randomly heterogeneous confined aquifer subject to prescribed head and flux boundary conditions.