Equivalent Freshwater Head Research Articles

Field and Numerical Investigations of Wave Effects on Groundwater Flow and Salt Transport in a Sandy Beach

AbstractCoastal dynamic forces, such as waves and tides, altogether drive groundwater circulation and salt transport in the intertidal zone. However, few numerical studies have ever considered the combined effects of waves and tides. In this study, the fluctuations of wave height are integrated with tidal level together using an iterative least squares fitting method, in which the wave height can be acquired from measured sea level in the surf zone, and this fitted wave height is further verified by wind speed. Groundwater flow and salt transport were then simulated using the MARUN code to evaluate the impacts after considering wave effect. The simulated equivalent freshwater head and salinity of the model with wave effect presented less difference with the measured data compared with the simulated results of the model without wave effect. After incorporating the wave effect in a model, submarine groundwater discharge (SGD) was increased, among which recirculated SGD grew more rapidly than the fresh, leading to the proportion of the fresh SGD accounting for a small proportion (1.1%). The water influx and efflux rates increased greatly especially during the period of high wave height. Most of the influx occurred in the intertidal zone, while a considerable amount of efflux occurred in the subtidal zone. The iterative algorithm to separate the wave height from the mixed field data can be employed to identify and quantify the respective effects of tides and the combined effects of waves and tides on the density‐dependent beach groundwater flow.

Hydraulic-Head Formulation for Density-Dependent Flow and Transport.

Density-dependent flow and transport solutions for coastal saltwater intrusion investigations, analyses of fluid injection into deep brines, and studies of convective fingering and instabilities of denser fluids moving through less dense fluids typically formulate the groundwater flow equation in terms of pressure or equivalent freshwater head. A formulation of the flow equation in terms of hydraulic head is presented here as an alternative. The hydraulic-head formulation can facilitate adaptation of existing constant-density groundwater flow codes to include density-driven flow by avoiding the need to convert between freshwater head and hydraulic head within the code and by incorporating density-dependent terms as a compartmentalized "correction" to constant-density calculations already performed by the code. The hydraulic-head formulation also accommodates complexities such as unconfined groundwater flow and Newton-Raphson solution schemes more readily than the freshwater-head formulation. Simulation results are presented for four example problems solved using an implementation of the hydraulic-head formulation in MODFLOW.

Rebuttal to \u201cThe case of the Biscayne Bay and aquifer near Miami, Florida: density-driven flow of seawater or gravitationally driven discharge of deep saline groundwater?\u201d by Weyer (Environ Earth Sci 2018, 77:1\u201316)

A recent paper by Weyer (Environ Earth Sci 2018, 77:1–16) challenges the widely accepted interpretation of groundwater heads and salinities in the coastal Biscayne aquifer near Miami, Florida, USA. Weyer (2018) suggests that the body of saltwater that underlies fresh groundwater just inland of the coast is not a recirculating wedge of seawater, but results instead from upward migration of deep saline groundwater driven by regional flow. Perhaps more significantly, Weyer (2018) also asserts that established hydrologic theory is fundamentally incorrect with respect to buoyancy. Instead of acting along the direction of gravity (that is, vertically), Weyer (2018) claims, buoyancy acts instead along the direction of the pressure gradient. As a result, Weyer (2018) considers currently available density-dependent groundwater flow and transport modeling codes, and the analyses based on them, to be in error. In this rebuttal, we clarify the inaccuracies in the main points of Weyer’s (2018) paper. First, we explain that Weyer (2018) has misinterpreted observed equivalent freshwater heads in the Biscayne aquifer and that his alternative hypothesis concerning the source of the saltwater does not explain the observed salinities. Then, we review the established theory of buoyancy to identify the problem with Weyer’s (2018) alternative theory. Finally, we present theory and cite successful benchmark simulations to affirm the suitability of currently available codes for modeling density-dependent groundwater flow and transport.

Data Assimilation in Density‐Dependent Subsurface Flows via Localized Iterative Ensemble Kalman Filter

AbstractParameter 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.

Numerical simulation of seawater intrusion to coastal aquifers and brine water/freshwater interaction in south coast of Laizhou Bay, China

Seawater intrusion and brine water/freshwater interaction have significantly affected agriculture, industry and public water supply at Laizhou Bay, Shandong Province, China. In this study, a two-dimensional SEAWAT model is developed to simulate the seawater intrusion to coastal aquifers and brine water/fresh water interaction in the south of Laizhou Bay. This model is applied to predict the seawater intrusion and brine water/freshwater interface development in the coming years. The model profile is perpendicular to the coastal line with two interfaces, freshwater-saline water interface near the shore and inland brine water-saline water-seawater interface. The hydrogeological parameters in the SEAWAT-2000 model are calibrated by the head and salinity measurements. The precipitation infiltration coefficient, boundary conditions and thicknesses of aquifers are studied in a sensitivity analysis. The predicted results indicate that equivalent freshwater head in shallow freshwater-saline water area will decline 2.0 m by the end of the forecasting period, caused by groundwater over-pumping for farmland irrigation. The groundwater head in the brine-saline water area will also decrease about 1.8 m by the end of forecasting period, caused by excessive brine mining. Salinity finally decreases below 105 g/L in the brine area, but increases in other areas and contaminates fresh groundwater resources.

Modeling Seawater Intrusion to Coastal Aquifers in South Coast of Laizhou Bay, China

In this study, a two-dimensional SEAWAT 2000 model is developed to simulate the seawater intrusion to coastal aquifers and brine water/fresh water interaction in the south of Laizhou Bay, Shandong Province, China and forecast the seawater intrusion and brine water/freshwater interface development in the coming years. The model profile is perpendicular to the coastal line, about 40 km long and 110 m in depth, and consists of two interfaces, freshwater-saline water interface and brine water-saline water-seawater interface. The parameters of aquifers in the SEAWAT-2000 model are calibrated by trial-error method repeatedly to fit the head and salinity measurements. Based on the historical groundwater and brine water exploration and natural precipitation condition, the prediction results indicate that equivalent freshwater head in shallow freshwater-saline water area will decrease year by year and decline 2.0 m in the forecasting period, caused by groundwater over-pumping for irrigating farmlands. The groundwater head in the brine-saline water area will also decrease about 1.8 m in forecasting period. A larger depression cone appears in the brine area, with smaller funnels in other areas. The salinity in the brine area finally drops below 105g/l. In the meanwhile, the salinity increases in other areas, damage fresh groundwater resources.

Impacts of inland boundary conditions on modeling seawater intrusion in coastal aquifers due to sea-level rise

Inland boundary conditions have significant impacts on seawater intrusion (SWI) due to sea-level rise (SLR). This study investigated the impacts of three inland boundary conditions (flux-controlled (FC), head-controlled (HC) and general-head boundary (GHB)) on modeling SWI due to SLR in coastal aquifers. First, we used the TOUGH2/EOS7 software program to solve the standard Henry’s problem and compared the results with those from the literatures. Numerical simulations were performed to investigate the impacts of the three inland boundary conditions on SWI induced by SLR in confined coastal aquifers (standard Henry’s problem) and unconfined coastal aquifers (Henry’s problem extended to unconfined domains). The simulation results show that HC systems in both confined and unconfined coastal aquifers are remarkably vulnerable to the effects of SLR owing to the resulting decreased head difference, while FC systems are relatively insensitive to SLR because the equivalent freshwater head at the inland boundary can increase by a similar magnitude to the SLR. The GHB boundary is more realistic than the other two boundary conditions: the recharge decreases because of SLR depending on the aquifer properties and the head difference between the reference head and the equivalent freshwater head at the seaside boundary.

Impact of climate variability on the salinization of the coastal wetland-aquifer system of the Po Delta, Italy

Deltaic coastal areas are constituted by a patchwork of brackish lagoons and freshwater bodies; these coastal wetland-aquifer systems are fragile ecosystems that usually respond quickly to climate changes. To understand the hydrological processes occurring within the lagoons and the groundwater system of the Po River Delta (Italy), the contribution of both evaporation and anthropogenic factors on groundwater salinization was assessed. A time series (2002–2015) of monthly average climatic data and a temperature-salinity dataset were used in three adjacent saline-brackish lagoons with the aim to identify the actual evaporation patterns and predict future trends using artificial neural networks (ANN). Moreover, the use of groundwater and surface water equivalent freshwater heads, along with the geological architecture, allowed linking the fluctuation of lagoon salinities with the degree of hydraulic connection between wetland and aquifer system. Results show that the less a lagoon is hydraulically connected with the aquifer, the higher is the salinity peak that could be reached at the end of the summer period. ANN forecasts highlight that in the near future this behaviour would be the rule rather than the exception. The increase in salinity of surface waters could be of serious concern, especially for aquaculture, sensitive to sharp salinity increases.

Numerical study of groundwater flow cycling controlled by seawater/freshwater interaction in a coastal karst aquifer through conduit network using CFPv2

In this study, a groundwater flow cycling in a karst springshed and an interaction between two springs, Spring Creek Springs and Wakulla Springs, through a subground conduit network are numerically simulated using CFPv2, the latest research version of MODFLOW-CFP (Conduit Flow Process). The Spring Creek Springs and Wakulla Springs, located in a marine estuary and 11 miles inland, respectively, are two major groundwater discharge spots in the Woodville Karst Plain (WKP), North Florida, USA. A three-phase conceptual model of groundwater flow cycling between the two springs and surface water recharge from a major surface creek (Lost Creek) was proposed in various rainfall conditions. A high permeable subground karst conduit network connecting the two springs was found by tracer tests and cave diving. Flow rate of discharge, salinity, sea level and tide height at Spring Creek Springs could significantly affect groundwater discharge and water stage at Wakulla Springs simultaneously.Based on the conceptual model, a numerical hybrid discrete-continuum groundwater flow model is developed using CFPv2 and calibrated by field measurements. Non-laminar flows in conduits and flow exchange between conduits and porous medium are implemented in the hybrid coupling numerical model. Time-variable salinity and equivalent freshwater head boundary conditions at the submarine spring as well as changing recharges have significant impacts on seawater/freshwater interaction and springs’ discharges. The developed numerical model is used to simulate the dynamic hydrological process and quantitatively represent the three-phase conceptual model from June 2007 to June 2010. Simulated results of two springs’ discharges match reasonably well to measurements with correlation coefficients 0.891 and 0.866 at Spring Creeks Springs and Wakulla Springs, respectively. The impacts of sea level rise on regional groundwater flow field and relationship between the inland springs and submarine springs are evaluated as well in this study.

Performance of different assessment methods to evaluate contaminant sources and fate in a coastal aquifer.

The present study deals with the application of different monitoring techniques and numerical models to characterize coastal aquifers affected by multiple sources of contamination. Specifically, equivalent freshwater heads in 243 monitoring wells were used to reconstruct the piezometric map of the studied aquifer; flow meter tests were carried out to infer vertical groundwater fluxes at selected wells; deuterium and oxygen isotopes were used to identify the groundwater origin, and tritium was analyzed to estimate the residence time; compound-specific isotope analyses and microbial analyses were employed to track different sources of contamination and their degradation; numerical modelling was used to estimate and verify groundwater flow direction and magnitude throughout the aquifer. The comparison of the information level for each technique allowed determining which of the applied approaches showed the best results to locate the possible sources and better understanding of the fate of the contaminants. This study reports a detailed site characterization process and outcomes for a coastal industrial site, where a comprehensive conceptual model of pollution and seawater intrusion has been built using different assessment methods. Information and results from this study encourages combining different methods for the design and implementation of the monitoring activities in real-life coastal contaminated sites in order to develop an appropriate strategy for control and remediation of the contamination.

Assessment of Density‐Induced Tracer Movement in Groundwater Velocity Measurements with Point Velocity Probes (PVPs)

AbstractThe concept of equivalent freshwater head was adapted to predict the conditions under which density‐driven flow would adversely impact measured groundwater velocities using point velocity probes (PVPs). Theoretically, vertical flow will result from any density contrast between the PVP tracer and the groundwater. However, laboratory testing of tracers with salinities ranging from 0 to 2000 mg NaCl/L showed that horizontal velocities could be determined with good accuracy with up to 60% of the total flow being vertical due to density effects in a gravel medium. The available data suggest that density effects are less likely to be pronounced in sandy sediments. The relative amount of vertical flow due to tracer density can be estimated from vertical and horizontal velocities measured with PVPs, or from the ratio of vertical to horizontal hydraulic gradients. The equivalent freshwater gradient produced from a given tracer salinity at 10 °C (a typical groundwater temperature at moderate latitudes) can be estimated from 7.80 × 10−7 × (MNaCl), where MNaCl is the mass of NaCl added, in mg, to 1 L of site groundwater in the mixing of the tracer. Equations for other temperatures were also determined.

Experimental evidence for seismically initiated gas bubble nucleation and growth in groundwater as a mechanism for coseismic borehole water level rise and remotely triggered seismicity

AbstractChanges in borehole water levels and remotely triggered seismicity occur in response to near and distant earthquakes at locations around the globe, but the mechanisms for these phenomena are not well understood. Experiments were conducted to show that seismically initiated gas bubble growth in groundwater can trigger a sustained increase in pore fluid pressure consistent in magnitude with observed coseismic borehole water level rise, constituting a physically plausible mechanism for remote triggering of secondary earthquakes through the reduction of effective stress in critically loaded geologic faults. A portion of the CO2 degassing from the Earth's crust dissolves in groundwater where seismic Rayleigh and P waves cause dilational strain, which can reduce pore fluid pressure to or below the bubble pressure, triggering CO2 gas bubble growth in the saturated zone, indicated by a spontaneous buildup of pore fluid pressure. Excess pore fluid pressure was measured in response to the application of 0.1–1.0 MPa, 0.01–0.30 Hz confining stress oscillations to a Berea sandstone core flooded with initially subsaturated aqueous CO2, under conditions representative of a confined aquifer. Confining stress oscillations equivalent to the dynamic stress of the 28 June 1992 Mw 7.3 Landers, California, earthquake Rayleigh wave as it traveled through the Long Valley caldera, and Parkfield, California, increased the pore fluid pressure in the Berea core by an average of 36 ± 15 cm and 23 ± 15 cm of equivalent freshwater head, respectively, in agreement with 41.8 cm and 34 cm rises recorded in wells at those locations.

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant-density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant-density flow) if the coastal heads are corrected to ((α + 1)/α)hs - B/2α, in which hs is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value hs1+α/α. The accuracy of using these corrections is demonstrated by consistency between constant-density Darcy's solution and variable-density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant-density flow relative to variable-density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant-density groundwater flow models.

Modeling flow and reactive transport to explain mineral zoning in the Atacama salt flat aquifer, Chile

Geochemical processes are typically neglected when modeling groundwater flow in highly saline systems. In the Atacama salt flat, northern Chile, field data indicate that the main aquifer presents a mineralogical zoning consisting of carbonates, sulfates and halite, which is a result of precipitation and/or dissolution reactions. When precipitation and/or dissolution of minerals are active processes in the aquifer, physical properties that control groundwater flow, such as porosity and permeability, would also change. Until now, groundwater flow in the Atacama salt flat has been simulated with conventional constant- or variable-density flow models. This study, for the first time, investigated the importance of incorporating geochemical processes in modeling the Atacama salt flat aquifer. In particular, the impact of mineral precipitation/dissolution on aquifer’s physical properties and flow patterns was studied. To this end, the SHEMAT code was utilized to develop a two-dimensional numerical groundwater flow model in the eastern border of the Atacama salt flat. The SHEMAT code solves the classic groundwater flow equation coupled to the reactive transport of ions and mineral precipitation, with variable density, viscosity, porosity and permeability. When geochemical processes were included in the simulations, the model reproduced reasonably well the mineral zoning evidenced by field observations. Mineral precipitation was responsible of a strong permeability reduction in areas of the aquifer associated with halite and calcite formation. Permeability alterations were responsible of changes in the equivalent freshwater head that resulted in significant flow pattern variations compared to variable-density flow models. These results highlight the importance of considering geochemical processes that modify the aquifer’s physical properties when modeling groundwater flow in highly saline aquifers such as the Atacama salt flat aquifer.

Incorporating the concept of equivalent freshwater head in successive horizontal simulations of seawater intrusion in the Nile Delta aquifer, Egypt

Summary A new approach to study seawater intrusion problems in coastal aquifers is presented. The approach is demonstrated for the case of the Nile Delta aquifer in Egypt. FEFLOW, a 3D finite element variable density model, is employed, however, because of the lack of 3D data, and to demonstrate the proposed approach, the simulations are performed in 2D horizontal views. The concept of equivalent freshwater head (usually implemented in 2D vertical simulations) is adapted in the horizontal (areal) simulations. After calibration against field observations, the simulations are conducted at four horizontal sections located at different levels (100, 200, 300 and 400 m) below the mean seawater level. The depth of the horizontal section is identified through assigning an appropriate pressure “equivalent freshwater” head at the boundaries. The study domain is modified for the horizontal sections at 300 and 400 m, respectively, to account for the aquifer geometry at these depths. The effect of freshwater recharge from the Nile River on the seawater intrusion is observed in the upper layer around its two main branches. The results of the horizontal simulations clearly demonstrate the variation of water concentration in the vertical direction. As the depth increases, the transition zone (in which the concentration varies from the seawater to the freshwater concentration) is shifted toward the landside and become more extensive. At the lower levels of the Nile Delta aquifer, the seawater migrates much further inland as compared to the shallower levels. The concept of horizontal simulations at different levels is further developed to produce meaningful concentration distributions in the vertical sections. This approach allows for a better realization of seawater intrusion in coastal aquifers.

Assessing the Effect of Saltwater Intrusion on Petroleum Hydrocarbons Plumes Via Numerical Modelling

A contamination by petroleum hydrocarbons was detected in a sandy aquifer below a petrochemical plant in Southern Italy. The site is located near the coastline and bordered by canals which, together with pumping wells, control submarine groundwater discharge toward the sea and seawater intrusion (SWI) inland. In this study, a three-dimensional flow and transport model was developed using SEAWAT-4.0 to simulate the density-dependent groundwater flow system. Equivalent freshwater heads from 246 piezometers were employed to calibrate the flow simulation, while salinity in 193 piezometers was used to calibrate the conservative transport. A second dissolved species, total petroleum hydrocarbons (TPH), was included in the numerical model to simulate the plumes originating from light non-aqueous-phase liquid. A detailed field investigation was performed in order to determine the fate of dissolved hydrocarbons. Fifteen depth profiles obtained from multilevel samplers (MLS) were used to improve the conceptual model, originally built using a standard monitoring technique with integrated depth sampling (IDS) of salinity and TPH concentrations. The calibrated simulation emphasises that density-dependent flow has a great influence on the migration pattern of the hydrocarbons plume. This study confirms that calibration of density-dependent models in sites affected by SWI can be successfully reached only with MLS data, while standard IDS data can lead to misleading results. Thus, it is recommended to include MLS in the characterization protocols of contaminated sites affected by SWI, in order to properly manage environmental pollution problems of coastal zones.

Representing the Coastal Boundary Condition in Regional Groundwater Flow Models

Numerical experiments were performed to investigate how the coastal boundary condition could be approximated in a groundwater flow model to yield accurate values for hydraulic heads and fluxes in the freshwater part of a coastal aquifer. These experiments consisted of obtaining steady-state solutions for hydraulic heads in a vertical cross section using the groundwater flow code MODFLOW and comparing the results to a steady-state solution in a similar cross section for equivalent freshwater heads obtained using the variable-density flow and transport code SEAWAT, which was considered to be the accurate solution to the problem. Six different boundary conditions that have been used to approximate the coastal boundary in groundwater flow models were tested, and simulations were run for both specified-flux and specified-head boundary conditions at the upstream freshwater boundary. For both upstream boundary conditions, the MODFLOW solution that best matched the SEAWAT solution for hydraulic heads and fluxes in the freshwater part of the aquifer was the solution in which equivalent freshwater heads were specified over the full thickness of the aquifer at the coastal boundary.

Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia

Seawater intrusion in coastal agricultural areas due to groundwater abstraction is a major environmental problem along the northeastern coast of Australia. Management options are being explored using numerical modelling, however, questions remain concerning the appropriate level of sophistication in models, choice of seaward boundary conditions, and how to accommodate heterogeneity and data uncertainty. The choice of seaward boundary condition is important since it affects the amount of salt transported into the aquifers and forms the focus of the present study. The impact of this boundary condition is illustrated for the seawater-intrusion problem in the Gooburrum aquifers, which occur within Tertiary sedimentary strata. A two-dimensional variable-density groundwater and solute-transport model was constructed using the computer code 2DFEMFAT (Cheng et al. 1998). The code was tested against an experiment for a steady-state freshwater-saltwater interface and against the Elder (Elder 1967) free-convection problem. Numerical simulations show that the imposition of the commonly-used equivalent hydrostatic freshwater heads, combined with a constant salt concentration at the seaward boundary, results in overestimated seawater intrusion in the lower Gooburrum aquifer. Since the imposition of this boundary condition allows water flow across the boundary, which subsequently takes salt into the aquifer, a careful check is essential to estimate whether too much mass of salt is introduced.

Mathematical modelling of groundwater flow at Sellafield, UK

Sellafield in West Cumbria was a potential site for the location of the UK's first underground repository for radioactive, intermediate level waste (ILW). The repository was to lie around 650 m beneath the ground surface within rocks of the Borrowdale volcanic group (BVG), a thick suite of SW dipping, fractured, folded and metamorphosed Ordovician meta-andesites and ignimbrites. These are overlain by an onlapping sequence of Carboniferous and Permo-Triassic sediments. In situ borehole measurements showed that upward trending fluid pressure gradients exist in the area of the potential repository site, and that there are three distinct fluid types in the subsurface; fresh, saline and brine (at depth, to the west of the site). Simulations of fluid flow in the Sellafield region were undertaken with a 2D, steady-state, coupled fluid and heat flow simulation code (OILGEN). In both simplified and geologically complex models, topographically driven flow dominated the regional hydrogeology. Fluids trended persistently upwards through the potential repository site. The dense brine to the west of the site promoted upward deflection of topographically driven groundwaters. The inclusion in hydrogeological models of faults and variably saline sub-surface fluids was essential to the accurate reproduction of regional hydraulic head variations. Sensitivity analyses of geological variables showed that the rate of groundwater flow through the potential repository site was dependent upon the hydraulic conductivity of the BVG, and was unaffected by the hydraulic conductivity of other hydrostratigraphic units. Calibration of the model was achieved by matching simulated subsurface pressures to those measured in situ. Simulations performed with BVG hydraulic conductivity 100 times the base case median value provided the “best-fit” comparison between the calculated equivalent freshwater head and that measured in situ, regardless of the hydraulic conductivity of other hydrostratigraphic units. Transient mass transport simulations utilising the hydraulic conductivities of this “best fit” simulation showed that fluids passing through the potential repository site could reach the surface in 15 000 years. Simple safety case implications drawn from the results of the study showed that the measured BVG hydraulic conductivity must be less than 0.03 m year −1 to be simply declared safe. Recent BVG hydraulic conductivity measurements showed that the maximum BVG hydraulic conductivity is around 1000 times this safety limit.

Solution and scaling of one‐dimensional groundwater‐solute flow with large density variations

A scaling analysis and solution of one‐dimensional groundwater‐solute flow is presented for the steady state case when density is strongly dependent on the concentration. The solution is applicable to one‐dimensional vertical or sloping flow with constant head and solute concentrations at the inlet and outlet. The dependent dimensionless variables (density, concentration, equivalent freshwater head, and fluid velocity) are shown to be a function of four dimensionless groups: a Peclet number of diffusion, a Peclet number of dispersion, a buoyancy number, and a density number. In practice, however, the dependent variables are shown to be independent of the density number and only a function of the remaining three dimensionless groups. The results show that the velocity decreases quickly by several orders of magnitude as the Peclet and buoyancy numbers increase. The rapid decrease in velocity occurs when the buoyancy number (defined as the ratio of the buoyancy force to equivalent freshwater driving force) is greater than unity. We further show that aquifers can have substantial velocity reductions even when density variations are not large, whereas aquitards will exhibit relative small velocity reductions independent of density variations. Implications of the velocity reduction to hydrogeologic investigations of nuclear waste disposal sites are discussed.