Search

When addressing the question of variable saturation and density groundwater flow in coastal zones, the highly nonlinear system of coupled water-salt equations may deserve more attention. The classical Picard scheme is associated with slow calculation speeds and low precision, which hardly meet the actual needs of users. Here, we developed a new numerical solution for coastal groundwater flow issues based on the Newton scheme and compared the advantages and disadvantages of different numerical methods by analyzing the cases of seawater intrusion. The simulation results indicated that the variable-density effect significantly extends the computation time of the model, but the Newton scheme still has the advantages of computational speed and better convergence compared with the Picard scheme, especially in conditions involving high-frequency and large-amplitude tidal fluctuations, steep aquifer slopes, and a coarse grid. Furthermore, the Newton-Picard method, based on the Newton and Picard schemes, improves the robustness of the Newton solution and optimizes the convergence of the Picard solution. This study has revealed the computational characteristics of the Newton scheme in addressing the issues of coastal variable saturation and density groundwater flow, providing new ideas and insights for numerical solutions to coastal groundwater flow problems.

Sea water intrusion is an important environmental issue that plagues the economic and social development in coastal areas. The implementation of quantitative simulation, prediction and visual management of sea water intrusion is a cost-effective means for monitoring and mechanism analysis of sea water intrusion, which can provide important theoretical and technical supports for the formulation of sea water intrusion control measures. VFT3D was proposed to model the sea water intrusion processes and predict the impacts on groundwater, which can comprehensively consider the effects of surface water and groundwater, simulate variable-density groundwater flow, and solve complex reactive migration problems. This article provides an introduction to the VFT3D model and presents an application of VFT3D to modeling seawater intrusion process. The simulated results are compared with those of the SEAWAT. The results show that the simulated water heads with VFT3D are close to the SEAWAT simulation results. The SEAWAT is unable to simulate complex chemical reactions during the sea water intrusion. The results indicate that geochemical processes (cation adsorption and exchange) have a significant effect on the movement of cations (Na+, K+, Mg2+ and Ca2+). Geochemical process leads to the concentration change in the transition zone, whose influence on the process of sea water intrusion can not be ignored. Therefore, the variable density and complex reaction process should be involved to more accurately describe the sea water intrusion, which can benefit the implementation of the underground saltwater remediation and management.

We investigate a fully nonlinear degenerate parabolic system describing variable-density flows of a two-component mixture through porous media. Using the Rothe method of semidiscretization in time we prove the global-in-time existence of weak solutions to the associated initial–boundary value problem under physically reasonable hypotheses on the data, the exponential constitutive equation and the mixed boundary conditions. [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology & Engineering Geology / Shuiwendizhi Gongchengdizhi is the property of Hydrogeology & Engineering Geology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this study is to develop an accurate and reliable numerical model of the coastal Talar aquifer threatened by seawater intrusion by developing an ensemble meta-model (MM). In comparison with previous methodologies, the developed model has the following superiority: (1) Its performance is enhanced by developing ensemble MMs using four different meta-modelling frameworks, i.e., artificial neural network, support vector regression, radial basis function, genetic programing and evolutionary polynomial regression; (2) The accuracy of different MMs based on 16 integration of four meta-modeling frameworks is compared; and (3) the effect of aquifer heterogeneity on the MM. The performance of the proposed MM was assessed using an illustrative case aquifer subject to seawater intrusion. The obtained results indicate that the ensemble MM that combines all four meta-modeling frameworks outperformed the GP and ANN models, with a correlation coefficient of 0.98. Moreover, the proposed MM using nonlinear-learning ensemble of SVR-EPR achieves a better and robust forecasting performance. Therefore, it can be considered as an accurate and robust simulator to predict salinity levels under different abstraction patterns in variable density flow. The result of uncertainty analyses reveals that robustness value and pumping rate are inversely proportional and scenarios with a robustness measure of about 12% are more reliable.

Study region: The study site is located in the south-western part of the Ukraine, in the area of the historical rock-salt mining town Solotvyno. The former mining area is situated in close vicinity to the River Tisza, the main tributary of the Danube River, the largest river in Europe. Study focus: After uncontrolled flooding of several salt mines, a one month advisory mission was launched by the European Commission to estimate the impact of the abandoned salt mines (containing large quantities of salt water) on the environment. As a consequence of the flooding, dozens of sinkholes formed and sinkhole forming processes are ongoing, with sinkhole diameters reaching 250 m. As river contamination by the release of large quantities of saltwater would lead to an international disaster, hydrogeological measurements were taken on-site to study the system. New hydrological insights of the region: At the study site, saturated (hyper-saline) water as well as fresh surface and groundwater were encountered in close vicinity to each other. Electrical conductivity, as a proxy for salinity, and temperature were measured on-site and water samples taken from surface-, ground- and mine waters were analyzed for chemistry and stable isotopes, providing new insights into groundwater flow dynamics. A conceptual model shows the salt dome, and potential flow paths from the mining area to the Tisza River, in the context of the mines and associated sinkholes potentially impacting the river water quality.

Variable density flow (VDF) modeling is a valuable tool for assessing the potential impacts of global climate change and sea level rise on coastal aquifers. When using any of these modeling tools, a quantitative relationship is needed to compute the fluid density from salt concentration. A full understanding of the relationship between fluid density and solute concentration and the correct implementation of the equation of state are critical for variable density modeling. The works of Baxter and his colleagues in the early 20th century showed that fluid density could be linearly correlated to salt concentrations. A constant density slope of 0.7 is often assumed and applied. The assumption is reasonable when the salinity is less than 100‰. The density slope can also be defined from chloride concentration data with the assumption of a constant ratio (55%) between chloride and total dissolved solids (TDS). Field data from central Florida indicate that the chloride/TDS ratio can be as low as 5%. Therefore, TDS is the preferred water quality data for fluid density determination in variable density modeling. Other issues with density slope are also discussed, and some commonly used values of density slope are provided in this technical note.

The southern coast of Laizhou Bay is one of the most serious geological disaster areas with sea-salted water intrusion in China. In order to study the process of sea-salted water intrusion, optimize the reasonable schemes for preventing seawater intrusion, the sea-salted water intrusion process was simulated by the variable density simulation method with 3D in northern coastal area of Weifang City, and the model was verified by the measured water level and TDS (Total Dissolved Solids)concentration. Furthermore, the numerical simulation was used to analyze the effect of different schemes in the next 50 years, and determine the optimal prevention schemes. The results showed that the natural groundwater flow field had gradually transformed into artificial field, and the influence of human activities on the flow field increased in the study area. It also demonstrated that there were two fresh water depression cones, and one brine depression cone, which were divided by watershed, and direction of groundwater flow was convergence to the funnel center. In next 50 years, the flow characteristics will not change fundamentally in the four kinds of prevention schemes, and the line of intrusion will rebound northward with the distance ranging from 500 to 8000m. Through the comparison of the four prevention schemes, it proved that the retraction distance caused by reducing exploitation of fresh water was the largest, which was the best prevention scheme. [ABSTRACT FROM AUTHOR]

Parameter estimation in variable‐density groundwater flow systems is confronted with challenges of strong nonlinearity and heavy computational burden. Relying on a variant of the Henry problem, we evaluate the performance of a domain localization scheme of the iterative ensemble Kalman filter in the framework of data assimilation settings for variable‐density groundwater flows in a seawater intrusion scenario. The performance of the approach is compared against (a) the corresponding domain localization scheme of the ensemble Kalman filter in its standard formulation as well as (b) a covariance localization scheme of the latter. The equivalent freshwater head, hf, and salinity, Sa, are set as the target state variables. The randomly heterogeneous field of equivalent freshwater hydraulic conductivity, Kf, is considered as the system parameter field. Density‐independent and density‐driven flow settings are considered to evaluate the assimilation results using various methods and data. When only hf data are assimilated, all tested approaches perform generally well and a localization scheme embedded in the iterative ensemble Kalman filter appears to consistently outperform the domain localized version of the standard ensemble Kalman filter (EnKF) in a density‐driven scenario; Dirichlet boundary conditions tend to show a more pronounced negative effect on estimating Kf for density‐independent than for density‐dependent flow conditions; hf data are more informative in a density‐dependent than in a density‐independent setting. The sole use of Sa information does not yield satisfactory updates of hf for the covariance localization scheme of the standard EnKF, while the sole use of hf does. The domain localization scheme leads to difficulties in the attainment of global filter convergence when only Sa data are used. A covariance localization scheme associated with a standard EnKF can significantly alleviate this issue. Key Points: We study localized forms of iterative ensemble Kalman filter for data assimilation in a density‐driven flowEquivalent freshwater head has higher data worth than salinity for estimating both equivalent freshwater head and salinityA local analysis scheme is not necessarily associated with a guaranteed filter convergence when only salinity data are used [ABSTRACT FROM AUTHOR]

Abstract: Brines are commonly found at depth in sedimentary basins. Many of these brines are known to be connate waters that have persisted since the early Paleozoic Era. Yet questions remain about their distribution and mechanisms for retention at depth in the Earth's crust. Here we demonstrate that there is insufficient topography to drive these dense fluids from the bottom of deep sedimentary basins. Our assessment based on driving force ratio indicates that sedimentary basins with driving force ratio > 1 contain connate waters and frequently host large evaporite deposits. These stagnant conditions appear to be relatively stable over geological time and insensitive to factors such as glaciations, erosion, compaction, and hydrocarbon generation. [ABSTRACT FROM AUTHOR]

The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of “baropycnal work”, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 1024 3 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates.

Seawater intrusion (SWI) is a complex process, where 3D modeling is often necessary in order to monitor and manage the affected aquifers. Here, we present a synthetic study to test a joint hydrogeophysical inversion approach aimed at solving the inverse problem of estimating initial and current saltwater distribution. First, we use a 3D groundwater model for variable density flow based on discretized flow and solute mass balance equations. In addition to the groundwater model, a 3D geophysical model was developed for direct current resistivity imaging and inversion. The objective function of the coupled problem consists of data misfit and regularization terms as well as a coupling term that relates groundwater and geophysical states. We present a novel approach to solve the inverse problem using an alternating direction method of multipliers (ADMM) to minimize this coupled objective function. ADMM enables to treat the groundwater and geophysical part separately and thus use the existing software with minor changes. To further reduce the computational cost, the sensitivities are derived analytically for the discretized system of equations, which allows us to efficiently compute the gradients in the minimization procedure. The method was tested on different synthetic scenarios with groundwater and geophysical data represented by solute mass fraction data and direct current resistivity data. With the ADMM approach, we were able to obtain better estimates for the solute distribution compared to just considering each data separately, solving the problem with a simple coupled approach or by a direct substitution of the coupling constraint. [ABSTRACT FROM AUTHOR]

Modeling variable density flow (VDF) in fractured porous media is computationally challenging. The challenges are mainly related to: (i) the high permeability contrast between the matrix and the fractures and, (ii) the nonlinearity induced by density variations. Due to their local mass conservation property, cell-centered methods, such as finite volumes (FV), mixed finite elements (MFE) or Discontinuous Galerkin (DG) methods are well suited for modeling mass transfer in highly heterogeneous domains. When applied for fractured media, these methods require small grid cells next to fractures because of the cross-flow equilibrium assumption (i.e. the pressure and concentration in the fracture and in the adjacent matrix grid-cells are assumed the same). To avoid this constraint, an efficient model is developed in this work using advanced cell-centered numerical methods for VDF in fractured porous media with cross-flow equilibrium assumed only across the fractures. The new model uses the hybrid MFE method for the flow discretization in the matrix and in the fracture continua. Mass transport in the matrix is modeled using a monotonic upwind MFE scheme. Advection-dominated transport in fractures is discretized with the DG method, which is well adapted for hyperbolic equations. The new model ensures continuity of pressure, concentration, fluid mass flux, advective and dispersive contaminant fluxes at matrix-fracture interfaces as well as at the intersection of several fractures. The time discretization is performed using high-order adaptive time integration techniques via the method of lines (MOL). The developed model is first validated by comparison against a 2D-2D model for a test problem dealing with linear flow and transport in a 2D domain involving a "+"-shaped barrier/fracture network. Then, the MFE-DG model is used for the simulation of the Henry saltwater intrusion problem and the results are validated by comparison against the semi-analytical solution in the case of unfractured and fractured aquifers. Finally, the simulation of a transport problem with variable viscosity in a fractured heterogeneous domain points out the superiority of the new model in terms of accuracy and efficiency when compared to a standard finite element model. • A new 2D-1D model is developed for Variable-density flow in fractured porous media. • Hybrid Mixed Finite Element (MFE) method is used for the flow discretization. • Upwind MFE method is used for the transport in the matrix. • DG method is used for the advection-dominated transport in fractures. • Numerical experiments highlight the efficiency of the new model. [ABSTRACT FROM AUTHOR]

Variable density flow in porous media has been studied primarily using numerical models because it is a semi-chaotic and transient process. Most of these studies have been 2D, owing to the computational restrictions on 3D simulations, and the ability to observe variable density flow in 2D experimentation. However, it is recognised that variable density flow is a three-dimensional process. A 3D system may cause weaker variable density flow than a 2D system due to stronger dispersion, but may also result in bigger fingers and hence stronger variable density flow because of more space for fingers to coalesce. This study aimed to determine the representativeness of 2D modelling to simulate 3D variable density flow. 3D homogeneous sand column experiments were conducted at three different water flow velocities with three different bromide tracer solutions mixed with methanol resulting in different density ratios. Both 2D axisymmetric and 3D numerical simulations were performed to reproduce experimental data. Experimental results showed that the magnitude of variable density flow increases with decreasing flow rates and decreasing density ratios. The shapes of the observed breakthrough curves differed significantly from those produced by 2D axisymmetric and 3D simulations. Compared to 2D simulations, the onset of instabilities was delayed but the growth was more pronounced in 3D simulations. Despite this difference, both 2D axisymmetric and 3D models successfully simulated mass recovery with high efficiency (between 77% and 99%). This study indicates that 2D simulations are sufficient to understand integrated features of variable density flow in homogeneous sand column experiments. [ABSTRACT FROM AUTHOR]

We consider a simple model describing the motion of a two-component mixture through a porous medium. We discuss well posedness of the associated initial-boundary value problem, in particular, with respect to the choice of boundary and far-field conditions. The existence of global-in-time solutions is proved in the ideal case when the fluid occupies the whole physical space. Finally, similar results are obtained also for the boundary value problems in the simplified 1-D geometry. [ABSTRACT FROM AUTHOR]

A two-dimensional variable-density groundwater flow and transport model was developed to provide a conceptual understanding of past and future conditions of nitrate (NO3) transport and estimate groundwater nitrate flux to the Gulf of Mexico. Simulation results show that contaminant discharge to the coast decreases as the extent of saltwater intrusion increases. Other natural and/or artificial surface waters such as navigation channels may serve as major sinks for contaminant loading and act to alter expected transport pathways discharging contaminants to other areas. Concentrations of NO3 in the saturated zone were estimated to range between 30 and 160 mg∙L−1 as NO3. Relatively high hydraulic vertical gradients and mixing likely play a significant role in the transport processes, enhancing dilution and contaminant migration to depth. Residence times of NO3 in the deeper aquifers vary from 100 (locally) to about 300 years through the investigated aquifer system. NO3 mass fluxes from the shallow aquifers (0 to 5.7 × 104 mg∙m−2∙day−1) were primarily directed towards the navigation channel, which intersects and captures a portion of the shallow groundwater flow/discharge. Direct NO3 discharge to the sea (i.e. Gulf of Mexico) from the shallow aquifer was very low (0 to 9.0 × 101 mg · m−2∙day−1) compared with discharge from the deeper aquifer system (0 to 8.2 × 103 mg∙m−2∙day−1). Both model-calibrated and radiocarbon tracer-determined contaminant flux estimates reveal similar discharge trends, validating the use of the model for density-dependent flow conditions. The modelling approach shows promise to evaluate contaminant and nutrient loading for similar coastal regions worldwide. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an autobiographical and biographical historical account of the genesis, evolution and resolution of the Elder Problem. It begins with John W. Elder and his autobiographical story leading to his groundbreaking work on natural convection at Cambridge in the 1960’s. His seminal work published in the Journal of Fluid Mechanics in 1967 became the basis for the modern benchmark of variable density flow simulators that we know today as “The Elder Problem”. There have been well known and major challenges with the Elder Problem model benchmark—notably the multiple solutions that were ultimately uncovered using different numerical models. Most recently, it has been shown that the multiple solutions are indeed physically realistic bifurcation solutions to the Elder Problem and not numerically spurious artefacts. The quandary of the Elder Problem has now been solved—a major scientific breakthrough for fluid mechanics and for numerical modelling. This paper—records, reflections, reminiscences, stories and anecdotes—is an historical autobiographical and biographical memoir. It is the personal story of the Elder Problem told by some of the key scientists who established and solved the Elder Problem. 2017 marks the 50 year anniversary of the classical work by John W. Elder published in Journal of Fluid Mechanics in 1967. This set the stage for this scientific story over some five decades. This paper is a celebration and commemoration of the life and times of John W. Elder, the problem named in his honour, and some of the key scientists who worked on, and ultimately solved, it.

A three dimensional model is presented for the simulation of seawater intrusion in coastal aquifers by considering the development of a transition zone and thus the variable density flow approach. The model is applied to a heterogeneous coastal aquifer to study the effects of the pumping rate, the salinity of freshwater inflow and the thickness of the aquifer, on the degradation of pumped water quality through wells in certain location. Even for an optimum pumping scheme solution based on a simple two-dimensional flow model, we simulate freshwater degradation in pumped water which depends on the salinity of freshwater inflow and aquifer thickness. [ABSTRACT FROM AUTHOR]

Summary This paper considers the impact of tidal forcing on regional groundwater flow in an unconfined coastal aquifer. Numerical models are used to quantify this impact for a wide range of hydrogeological conditions. Both a shallow and a deep aquifer are investigated with regard to three dimensionless parameter groups that determine the groundwater flow to a large extent. Analytical expressions are presented that allow for a quick estimate of the regional scale effect of tidal forcing under the same conditions as used in the numerical models. Quantitatively, the results in this paper are complementary to previous studies by taking into account variable density groundwater flow, dispersive salt transport and a seepage face in the intertidal area. Qualitatively, the results are in line with previous investigations. The time-averaged hydraulic head at the high tide mark increases upon a decrease of each of the three considered dimensionless parameter groups: R (including the ratio of the hydraulic conductivity and the precipitation excess), α (the slope of the intertidal area) and A L (the ratio of the width of the fresh water lens and the tidal amplitude). The relative change of the location and the hydraulic head of the groundwater divide, which together characterize regional groundwater flow, increase as α and A L decrease, but decrease as R decreases. The difference between the analytical solutions and numerical results is small. Therefore, the presented analytical solutions can be used to estimate the bias that is introduced in a numerical model if tidal forcing is neglected. The results should be used with caution in case of significant wave forcing, as this was not considered. [ABSTRACT FROM AUTHOR]

Highlights: [•] POD is applied to the coupled variable-density flow and solute transport system. [•] Detailed derivation is presented for the developed GFEM-POD reduced-order model. [•] Henry problem and Elder problem are tested to confirm the proposed procedure. [•] Accuracy is mainly influenced by the optimal selection and update of snapshots. [•] Reduced model can substitute full model with much less computational cost. [ABSTRACT FROM AUTHOR]

During the 1990s, groundwater overexploitation has resulted in seawater intrusion in the coastal aquifer of the Shenzhen city, China. Although water supply facilities have been improved and alleviated seawater intrusion in recent years, groundwater overexploitation is still of great concern in some local areas. In this work we present a three-dimensional density-dependent numerical model developed with the FEFLOW code, which is aimed at simulating the extent of seawater intrusion while including tidal effects and different groundwater pumping scenarios. Model calibration, using waterheads and reported chloride concentration, has been performed based on the data from 14 boreholes, which were monitored from May 2008 to December 2009. A fairly good fitness between the observed and computed values was obtained by a manual trial-and-error method. Model prediction has been carried out forward 3 years with the calibrated model taking into account high, medium and low tide levels and different groundwater exploitation schemes. The model results show that tide-induced seawater intrusion significantly affects the groundwater levels and concentrations near the estuarine of the Dasha river, which implies that an important hydraulic connection exists between this river and groundwater, even considering that some anti-seepage measures were taken in the river bed. Two pumping scenarios were considered in the calibrated model in order to predict the future changes in the water levels and chloride concentration. The numerical results reveal a decreased tendency of seawater intrusion if groundwater exploitation does not reach an upper bound of about 1.32 × 10 m/d. The model results provide also insights for controlling seawater intrusion in such coastal aquifer systems. [ABSTRACT FROM AUTHOR]

Abstract: Seawater intrusion (SI) is a global issue, exacerbated by increasing demands for freshwater in coastal zones and predisposed to the influences of rising sea levels and changing climates. This review presents the state of knowledge in SI research, compares classes of methods for assessing and managing SI, and suggests areas for future research. We subdivide SI research into categories relating to processes, measurement, prediction and management. Considerable research effort spanning more than 50years has provided an extensive array of field, laboratory and computer-based techniques for SI investigation. Despite this, knowledge gaps exist in SI process understanding, in particular associated with transient SI processes and timeframes, and the characterization and prediction of freshwater–saltwater interfaces over regional scales and in highly heterogeneous and dynamic settings. Multidisciplinary research is warranted to evaluate interactions between SI and submarine groundwater discharge, ecosystem health and unsaturated zone processes. Recent advances in numerical simulation, calibration and optimization techniques require rigorous field-scale application to contemporary issues of climate change, sea-level rise, and socioeconomic and ecological factors that are inseparable elements of SI management. The number of well-characterized examples of SI is small, and this has impeded understanding of field-scale processes, such as those controlling mixing zones, saltwater upconing, heterogeneity effects and other factors. Current SI process understanding is based mainly on numerical simulation and laboratory sand-tank experimentation to unravel the combined effects of tides, surface water–groundwater interaction, heterogeneity, pumping and density contrasts. The research effort would benefit from intensive measurement campaigns to delineate accurately interfaces and their movement in response to real-world coastal aquifer stresses, encompassing a range of geological and hydrological settings. [Copyright &y& Elsevier]

Abstract: This intermediate scale laboratory experimental study was designed to improve the conceptual understanding of aquifer flushing time associated with diffuse saltwater contamination of coastal aquifers due to a tsunami-like event. The motivation comes from field observations made after the tsunami in December, 2004 in South Asia. The focus is on the role and effects of heterogeneity on flushing effectiveness. A scheme that combines experimentation in a 4.8m long laboratory tank and numerical modeling was used. To demonstrate the effects of geologic heterogeneity, plume migration and flushing times were analyzed in both homogeneous and layered media and under different boundary conditions (ambient flow, saltwater infiltration rate, freshwater recharge). Saltwater and freshwater infiltrations imitate the results of the groundwater salinization from the tsunami and freshening from the monsoon rainfall. The saltwater plume behavior was monitored both through visual observations (digital photography) of the dyed salt water and using measurements taken from several electrical conductivity sensors installed through the tank walls. The variable-density, three dimensional code HST3D was used to simulate the tank experiments and understand the fate and movement of the saltwater plume under field conditions. The results from the tank experiments and modeling demonstrated that macro-scale heterogeneity significantly influenced the migration patterns and flushing times of diffuse saltwater contamination. Ambient flow had a direct influence on total flush-out time, and heterogeneity impacted flush-out times for the top part of the tank and total flush-out times. The presence of a continuous low-permeability layer caused a 40% increase in complete flush-out time due to the slower flow of salt water in the low-permeability layer. When a relatively small opening was introduced in the low-permeability layer, salt water migrated quickly into a higher-permeable layer below causing a reduction in flush-out time. Freshwater recharge caused an early dilution of salt water in the top part of the tank in the case of a layered media, but also pushed the saltwater plume into the low-permeability layer which led to increased total flush-out times. [Copyright &y& Elsevier]

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract: Konz, M., Ackerer, P., Younes, A., Huggenberger, P., Zechner, E., 2009a. 2D Stable Layered Laboratory-scale Experiments for Testing Density-coupled Flow Models. Water Resources Research, 45. doi:10.1029/2008WR007118., a series of laboratory-scale 2D tank experiments were conducted and accurately simulated for density driven flow problems on homogeneous porous media. In the present work, we extended the numerical and experimental studies to heterogeneous problems. The heterogeneous porous medium was constructed with a low permeability zone in the centre of the tank and had well-defined parameters and boundary conditions. Concentration distributions were measured in high resolution using a photometric method and an image analysis technique. The numerical model used for the simulations was based on efficient advanced approximations for both spatial and temporal discretizations. The Method Of Lines (MOL) was used to allow higher-order temporal discretization. Three different boundary conditions, corresponding to different localizations of the inflow and the outflow openings at the opposite edges of the tank, were applied to investigate different flow scenarios in the heterogeneous porous medium flow tank. Simulation results of all three density coupled experiments revealed a density-dependent behavior of dispersion. Thus, a reduction of dispersivites was required to obtain a good matching of the experimental data. The high quality of the experiments enabled a detailed testing of numerical variable-density flow codes under heterogeneous conditions. Therefore, the experiments were considered to be reliable benchmark tests. [Copyright &y& Elsevier]

Abstract: In this paper, we develop the discrete compatibility-constraint pressure-correction algorithm for transient simulations of variable density flows at low-Mach numbers. The constraint for the velocity field is constructed from a combination of the discrete equations of continuity and scalar (e.g. energy) transport, imposing that the newly predicted state must be compatible, in agreement with the equation of state. This way, mass and scalar conservation are guaranteed and the equation of state is exactly fulfilled at every time step. For comparison reasons, two other types of well-known pressure-correction algorithms are also used. The first class, denoted as continuity-constraint pressure-correction, is based on a constraint for the velocity field that is derived solely from the continuity equation. The second class, denoted as analytical compatibility-constraint pressure-correction, constructs the constraint from an analytical combination of the material derivative of the equation of state and the continuity and scalar equations. The algorithms are tested for three example fluid configurations: a single-fluid ideal gas, a two-fluid inert mixture and a two-fluid reacting mixture. The latter is special in the sense that the equation of state is non-linear and not everywhere differentiable. The continuity-constraint pressure-correction algorithm yields unstable solutions if density ratios are high. The analytical compatibility-constraint pressure-correction algorithm yields stable results, but the predicted states do not correspond to the equation of state. The discrete compatibility-constraint pressure-correction algorithm performs well on all test cases: the simulation results are stable and exactly match the equation of state. [Copyright &y& Elsevier]

Variable density flow (VDF) modeling is a valuable tool for assessing the potential impacts of global climate change and sea level rise on coastal aquifers. When using any of these modeling tools, a quantitative relationship is needed to compute the fluid density from salt concentration. A full understanding of the relationship between fluid density and solute concentration and the correct implementation of the equation of state are critical for variable density modeling. The works of Baxter and his colleagues in the early 20th century showed that fluid density could be linearly correlated to salt concentrations. A constant density slope of 0.7 is often assumed and applied. The assumption is reasonable when the salinity is less than 100‰. The density slope can also be defined from chloride concentration data with the assumption of a constant ratio (55%) between chloride and total dissolved solids (TDS). Field data from central Florida indicate that the chloride/TDS ratio can be as low as 5%. Therefore, TDS is the preferred water quality data for fluid density determination in variable density modeling. Other issues with density slope are also discussed, and some commonly used values of density slope are provided in this technical note. [ABSTRACT FROM AUTHOR]

Abundant data indicate significant fluid and solute fluxes across low-permeability shales in the Gulf of Mexico, the precise mechanisms of which are poorly understood. In this study, we analyze possible modes of intrafracture and interfracture free convection that may occur across fractured low-permeability layers, such as shales. Fracture spacing, fracture aperture, shale thickness, and the density gradient across the shale unit are shown to play key roles in the governing fluid and solute transport processes. All modes of free convection (parallel to the fracture plane, perpendicular to the fracture plane, and convection between fractures on the larger layer scale) are theoretically possible for reasonable hydrogeologic parameters. Free convection parallel to the fracture plane is shown to be the dominant (and most likely) mode of free convection, requiring only very modest salinity differences for onset to occur. Least likely is convection perpendicular to the fracture plane. The results presented here suggest that free convection may not be uncommon in thick shale sequences, such as in the Gulf of Mexico Basin. An important consequence of these findings is that analyses that do not consider both interfracture and intrafracture convection modes may significantly underestimate the likelihood of the occurrence of free convection. These findings have important implications for the study of free convection and solute transport processes in fractured low-permeability media and associated numerical modeling analyses. [ABSTRACT FROM AUTHOR]

Abstract: When the Navier–Stokes equations are solved on a colocated mesh, a spurious mode for the pressure can appear if no special attention is paid to the discretization of the pressure. This pressure mode can be suppressed by a pressure-weighted interpolation formula for the mass flux over a cell-face. In this paper, a similar cure is presented in the framework of pressure-correction methods in variable density flow. Special attention is given to the solvability condition for the resulting Poisson-like equation for the pressure. It consists of two remedies: a correction term for the cell-face velocity is introduced and the stencil for the discrete Laplacian is compacted. We finally show the applicability of the method on general curvilinear coordinate systems in three dimensions. [Copyright &y& Elsevier]

Abstract: The Henry formulation, which couples subsurface flow and salt transport via a variable-density flow formulation, can be used to evaluate the extent of sea water intrusion into coastal aquifers. The coupling gives rise to nontrivial flow patterns that are very different from those observed in inland aquifers. We investigate the influence of these flow patterns on the transport of conservative contaminants in a coastal aquifer. The flow is characterized by two dimensionless parameters: the Péclet number, which compares the relative effects of advective and dispersive transport mechanisms, and a coupling parameter, which describes the importance of the salt water boundary on the flow. We focus our attention on two regimes – low and intermediate Péclet number flows. Two transport scenarios are solved analytically by means of a perturbation analysis. The first, a natural attenuation scenario, describes the flushing of a contaminant from a coastal aquifer by clean fresh water, while the second, a contaminant spill scenario, considers an isolated point source. [Copyright &y& Elsevier]

Summary: Understanding the discharge behaviour of saline groundwater into fresh surface water can be critical for the effective management of water resources. While variable density flow has been studied intensely in a number of settings, the role it plays on the discharge behaviour of saline groundwater into freshwater streams is often neglected when calculating salt loads into a stream. The aim of this study was to determine what role variable-density flow behaviour plays in surface water/groundwater interaction in a stably-stratified fresh surface water/saline groundwater interface. The mixed convection ratio M, a measure of the ratio of density driven flow to advective driven flow, was defined for a matrix of one-dimensional numerical simulations that employed both varying hydraulic and density gradients. Vertical salt breakthrough into the surface water only occurred in the advection dominated cases (M <1) and the salt flux into the surface water increased with increasing groundwater concentration until M reached a value of 1. Beyond this, when the flow was driven by the density difference between the two fluids (M >1) vertical discharge of salt into surface water did not occur and the saltwater/freshwater interface migrated downwards with increasing density differences between the two fluids. This study therefore shows that there is a critical concentration difference that maximises salt loads to a surface water body and that a density-invariant approach to estimate the salt flux into the surface water (as the product of flow velocity determined through a potentiometric analysis and groundwater concentration) may be inadequate, especially where large density differences exist between the fresher surface water body and the underlying saline groundwater. The study is a purely theoretical approach and conclusions were drawn from simplified 1D simulations. Hence, further laboratory and modelling work is needed to confirm and test the plausibility of these findings for more realistic 2D and 3D cases. [Copyright &y& Elsevier]

A benchmark problem involving the rotating movement of three immiscible fluids is proposed for verifying the density-dependent flow component of groundwater flow codes. The problem consists of a two-dimensional strip in the vertical plane filled with three fluids of different densities separated by interfaces. Initially, the interfaces between the fluids make a 45° angle with the horizontal. Over time, the fluids rotate to the stable position whereby the interfaces are horizontal; all flow is caused by density differences. Two cases of the problem are presented, one resulting in a symmetric flow field and one resulting in an asymmetric flow field. An exact analytical solution for the initial flow field is presented by application of the vortex theory and complex variables. Numerical results are obtained using three variable-density groundwater flow codes (SWI, MOCDENS3D, and SEAWAT). Initial horizontal velocities of the interfaces, as simulated by the three codes, compare well with the exact solution. The three codes are used to simulate the positions of the interfaces at two times; the three codes produce nearly identical results. The agreement between the results is evidence that the specific rotational behavior predicted by the models is correct. It also shows that the proposed problem may be used to benchmark variable-density codes. It is concluded that the three models can be used to model accurately the movement of interfaces between immiscible fluids, and have little or no numerical dispersion. [Copyright &y& Elsevier]

This paper presents a technique to restore the balance between freshwater and saline water in coastal aquifers in order to mitigate seawater intrusion problems. Brackish water can be pumped from the dispersion zone and then used to develop green lands in the coastal areas or to irrigate certain types of crops. A two-dimensional finite element model (2D-FED), has been employed to verify this technique. The model is based on the dispersion zone approach with a variable density flow. Simulations were preformed in the vertical view and equiconcentration and equipotential lines were plotted for different locations of brackish water pumping. In all of the tested runs the width of dispersion zone has reduced significantly due to brackish water pumping. The quality of the pumped water differs according to the location of pumping. A study case on the Madras aquifer in India is presented. [ABSTRACT FROM AUTHOR]