Henry Problem Research Articles

Assessing salinity hazards in coastal aquifers: implications of temperature boundary conditions on aquifer–ocean interaction

Investigating the repercussions of climate change and irrigation timing on groundwater contamination necessitates thorough examination of the fluctuations in seawater and groundwater recharge temperature. This study introduces an innovative numerical approach to analyze groundwater salinity and temperature dynamics across three distinct scenarios using the SEAWAT code based on Henry's problem. The first scenario delves into the impact of seawater temperature, the second focuses on the consequences of aquifer freshwater recharge temperature, and the third amalgamates the effects of both scenarios. Remarkably, the study reveals that saltwater intrusion (SWI) experiences a decline attributable to the aquifer's heightened seawater temperature and the diminished inland freshwater temperature. Furthermore, combining these two scenarios has a more pronounced effect on aquifer pollution; the temperature-induced changes in SWI for this third scanrio reach + 8.10%, + 12.70%, + 16.20%, + 24.90%, + 28.30%, and + 31.80% compared to the case without considering the temperature effect. Notably, our results propose a potential strategy to mitigate SWI by introducing cold freshwater recharge into aquifers, such as irrigation at night time when water temperature is low. This innovative approach underscores the interconnectedness of various environmental factors. It provides a practical avenue for proactive intervention in safeguarding groundwater quality against the adverse impacts of climate change and irrigation practices.

Groundwater salinization risk in coastal regions triggered by earthquake-induced saltwater intrusion

Anthropogenic factors such as over-pumping and natural events such as earthquakes impact coastal aquifers by reducing freshwater recharge, aquifer water budgets, and increasing saltwater intrusion (SWI). This study investigates the impact of hydrodynamic forces induced by earthquakes on SWI in one hypothetical case, namely, the Henry problem, and a real case of the Biscayne aquifer located in Florida, USA. The analysis was carried out using the analytical solution of estimating the earthquake’s induced hydrodynamic pressure and applying the SEAWAT code to investigate the SWI for the base case and three scenarios, namely for the horizontal acceleration (αh) by 0.10 g, 0.20 g, and 0.30 g. The results show that earthquakes might considerably increase the SWI in coastal aquifers. Moreover, the rise in salinity across expansive land areas significantly threatens agricultural productivity and jeopardizes food security. Namely, in the case of Biscayne aquifer, salinity was increased by 12.10%, 21.90%, and 45.70% for the horizontal seismic acceleration of 0.1 g, 0.20 g, and 0.30 g, respectively. Hence, the conclusions drawn from this study underscore the need for carefull consideration of earthquake impacts in future planning and water management strategies for coastal regions. This proactive approach is crucial to preemptively address and mitigate the groundwater salinization hazard associated with SWI fluctuations due to earthquakes.

Shoreline subsurface dams to protect coastal aquifers from sea level rise and saltwater intrusion

Fresh groundwater in arid and highly populated regions is limited. In coastal aquifers, the deterioration of fresh groundwater is accelerated by saltwater intrusion, primarily occurring through lateral encroachment and vertical movements in the proximity of discharging wells. Coastal regions have high salinity due to saline intrusion, where many abstraction wells are turned off by this high salinity, which leads to increased freshwater supply costs. This study investigates the performance of new approach using the shoreline subsurface dams (SSDs) for mitigating the saline water wedge in coastal aquifers, where the dams are installed at the shoreline (distance from shoreline = 0). Specifically, the current study's novelty is testing the effectiveness of SSDs by different relative heights ranging from 0.05 to 0.50 in the test case (Henry problem) and from 0.09 to 0.53 relative to the aquifer thickness in the field scale aquifer (Biscayne aquifer, Florida, USA). The results showed an exponential increase in salt repulsion for increasing SSDs height, reaching a maximum of + 0.70%, + 1.80%, + 3.25%, + 5.80%, + 10.45%, and + 18.40% for the dam height to aquifer thickness ratios of 0.09, 0.18, 0.26, 0.35, 0.44 and 0.53, respectively, in the field scale case. The SSDs increase the freshwater storage at the coastal zones where the low salinity occurs and reduces the freshwater supply cost. Despite the positive impact of height on repulsion, important factors such as economics, construction aspects, geographical suitability, and environmental impacts must be considered for real applications. This is crucial to develop feasible solutions applicable globally under the growing pressure of sea level rise.

Uncertainty quantification in the Henry problem using the multilevel Monte Carlo method

We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain Henry saltwater intrusion problem. Unknown porosity, permeability and recharge parameters are modelled by using random fields. The classical deterministic Henry problem is non-linear and time-dependent, and can easily take several hours of computing time. Uncertain settings require the solution of multiple realisations of the deterministic problem, and the total computational cost increases drastically. Instead of computing of hundreds random realisations, typically the mean value and the variance are computed. The standard methods such as the Monte Carlo or surrogate-based methods are a good choice, but they compute all stochastic realisations on the same, often, very fine mesh. They also do not balance the stochastic and discretisation errors. These facts motivated us to apply the MLMC method. We demonstrate that by solving the Henry problem on multi-level spatial and temporal meshes, the MLMC method reduces the overall computational and storage costs. To reduce the computing cost further, parallelization is performed in both physical and stochastic spaces. To solve each deterministic scenario, we run the parallel multigrid solver ug4 in a black-box fashion.

Optimization of pumping and injection regimes for mitigation of seawater intrusion

Seawater intrusion (SWI) stands as a significant challenge impacting coastal aquifers worldwide. The emergence of SWI is a natural phenomenon owing to the density difference between seawater and freshwater. Even without any pumping, the seawater naturally advances inland until a hydrostatic equilibrium between the two water sources is reached. However, human interventions, such as excessive groundwater extraction, coastal developments, and land use as well as climate change intensify the SWI predicament. Efficient solutions to counteract the SWI problem involve the implementation of hydraulic barriers. By employing the Henry problem as a benchmark, the Finite Element Simulator (FEFLOW), which is a numerical modeling software, was used for simulating the flow and transport processes. An integrated FEFLOW-Python code was developed to optimize hydraulic barriers for mitigating SWI. The methodology aims to achieve the maximum possible reduction in SWI by iteratively adjusting the locations and rates of pumping and injection wells. Unlike other investigations, this study explores the utilization of negative SWI barriers to extract brackish water from the dispersion zone and potentially offer a cost-effective alternative water source for desalination plants’ intakes. For the Henry Problem, to maximize the reduction in of SWI, brackish water extraction wells should be situated near the center-bottom of the intrusion zone, with a pumping rate of 2.5 m3/day. For injection wells, the optimal location varies depending on the injection rate (I). Achieving the highest retardation (61%) occurs when the injection rate is 1 m3/day, positioned at the aquifer’s bottom and close to the coastal boundary. However, for injection rates below 0.7 m3/day, the injection well’s optimal location shifts towards the seawater intrusion toe. This study presents a novel approach by establishing explicit correlations for optimizing hydraulic barriers to effectively manage and mitigate SWI.

Uncertainty quantification in coastal aquifers using the multilevel Monte Carlo method

AbstractWe are solving a problem of salinisation of coastal aquifers. As a test case example, we consider the Henry saltwater intrusion problem. Since porosity, permeability and recharge are unknown or only known at a few points, we model them using random fields and random variables. The Henry problem describes a two‐phase flow and is non‐linear and time‐dependent. The solution to be found is the expectation of the salt mass fraction, which is uncertain and time‐dependent. To estimate this expectation, we use the well‐known multilevel Monte Carlo (MLMC) method. The MLMC method takes just a few samples on computationally expensive (fine) meshes and more samples on cheap (coarse) meshes. Then, by building a telescoping sum, the MLMC method estimates the expected value at a much lower computational cost than the classical Monte Carlo method. The deterministic solver used here is the well‐known parallel and scalable ug4 solver.

Freshwater cooling injection to mitigate saltwater intrusion and support sustainable groundwater management

This study examined the influence of thermal forcing on saltwater intrusion into nearshore aquifers (SWI) in the context of sea level rise due to climate change and continued groundwater withdrawal due to increasing demand. The study used the SEAWAT code to test two case studies: the Henry problem as a benchmark and the Biscayne Aquifer, Florida, USA, as a real case. Simulations were performed for the base case, sea level rise (SLR), and inland groundwater recharge reductions. A new management method was proposed for mitigating SWI in nearshore aquifers using the Abstraction of saline water, Desalination, Cooling the desalinated water, and Injection into the aquifer (ADCI) strategy. The method was tested with different freshwater temperatures of 25, 20, 15, 10, and 5 °C. The results showed that freshwater recharge in coastal regions is sensitive to the thermal regime, resulting in the attenuation of SWI. The results of this study are important for the sustainable management of groundwater resources in coastal areas to meet increasing water demands. The Biscayne salt repulsion reached +9.80 %, +10 %, +10.20 %, +10.30 %, and + 10.50 % for changing the injection recharge by 25, 20, 15, 10, and 5 °C. Future planning, design, and development of SWI mitigation measures should consider thermal regime effects. In addition, a cost–benefit analysis for this method using 3D models is needed to determine the feasibility and economic aspect of cooling water supply compared to current techniques.

Sustainable management of two‐directional lateral and upconing saltwater intrusion in coastline aquifers to alleviate water scarcity

AbstractLateral saltwater intrusion (LSWI) and vertical saltwater intrusion (VSWI) are the major problems in coastal aquifers. Coastal aquifers are subjected to natural and artificial changes, including sea‐level rise, decreasing inland recharge, and overexploitation of production wells' water resources. Therefore, this study investigates the influence of changing the coastal aquifers boundary conditions considering climate changes' effect. Parameters describing the upward saline well parameters based on the abstraction conditions, also, the top layer properties were studied based on the erosion and sediments, irrigation, and drainage conditions. For this purpose, the SEAWAT model was employed to simulate lateral SWI based on Henry's problem principle. The sensitivity analysis of the mentioned parameters was accomplished considering as a case study the Biscayne aquifer in the Cutler Ridge area near Deering Estate, Florida, USA, where the LSWI and VSWI were also investigated. The results indicate that the boundary conditions, abstraction well parameters, and top layer cost significantly impact aquifer LSWI and water upconing. The simulation results of the Biscayne aquifer for a saline water head of 84.86 cm for 2060 indicate a decrease in freshwater recharge by 30% and increasing the saltwater concentration by 14.30%. At the same time, the LSWI increased by 3.30%, 22.80%, and 8.70%, while the relative upconing heights reached 0.63, 0.60, and 0.47 compared with 0.42 for the current situation. Increasing the upward saline abstraction well discharge rates by 50% increases the LSWI by 9.40%. In contrast, increasing the depth by 10%; decreases the distance by 30%, the screen length by 30%, the LSWI decreased by 1.80%, 25.10%, and 1.30%, respectively. At the same time, the relative VSWI height reached 0.60, 0.39, 0.48, and 0.40, respectively. Moreover, decreasing the top layer hydraulic conductivity by 25% and increasing the aquitards layer depths by 200% decreased the LSWI by 4.90% and 7.80%, respectively. At the same time, the relative VSWI height reached 0.34 and 0.30, respectively. In addition, the saline water heads, a freshwater recharge should be controlled to manage SWI; the upward well should be utilized at a low abstraction rate, far from the seaside, and with minimum screen length. The agriculture activity for decreasing the soil permeability for the top layer must be extended for better management of the SWI. The solution‐oriented findings resulting from this study might be useful for decision‐makers and engineers to develop effective management measures to tackle the SWI issue in coastal aquifers.

Effect of Flow‐Direction‐Dependent Dispersivity on Seawater Intrusion in Coastal Aquifers

AbstractFlow‐direction‐dependent (FDD) dispersivity in coastal aquifers (CAs) may strongly affect the inland extend of seawater intrusion (SWI) and the accompanying vertical salinity distribution. FDD dispersivity may predict greater inland intrusion of the saltwater wedge, but less vertical spreading of salinity than does the classical flow‐direction‐independent (FDI) dispersivity, the standard currently employed in most numerical CA models. Dispersion processes play a key role in the SWI process and directly affect CA pumped water quality. Constant FDI dispersivities may be inappropriate in representing mixing processes due to large differences between depth and horizontal salinity transport scales, and due to typical structured heterogeneities in aquifer fabrics. Comparison of FDI and FDD model forecasts for the classical Henry problem (HP) steady‐state SWI, based on a new HP semianalytical solution with FDD and on a numerical FDI model modified to additionally represent FDD, highlights the theoretical types of differences implied by these alternative dispersivity assumptions and exactly how each parameter affects the solution. Large differences between FDI and FDD dispersivity forecasts of time‐dependent SWI in large scale heterogeneous aquifers occur in a typical CA (Akkar CA, Lebanon). The FDD model forecasts that future salinities in pumping wells will exceed the potable water limit, whereas the FDI model greatly underestimates the historic inland intrusion of the saltwater wedge and forecasts no impact on future Akkar CA potable water supply. These results indicate the importance of employing the appropriate dispersion process representation when creating model‐based SWI forecasts, especially for developing effective CA management strategies.

Cost-effective management measures for coastal aquifers affected by saltwater intrusion and climate change.

Sustainable management of natural water resources and food security in the face of changing climate conditions is critical to the livelihood of coastal communities. Increasing inundation and saltwater intrusion (SWI) will likely adversely affect agricultural production and the associated beach access for tourism. This study uses an integrated surface-ground water model to introduce a new approach for retardation of SWI that consists of placing aquifer fill materials along the existing shoreline using Coastal Land Reclamation (CLR). The modeling results suggest that the artificial aquifer materials could be designed to decrease SWI by increasing the infiltration area of coastal precipitation, collecting runoffs from the catchment area, and applying treated wastewater or desalinated brackish water-using coastal wave energy to reduce water treatment costs. The SEAWAT model was applied to verify that it correctly addressed Henry's problem and then applied to the Biscayne aquifer, Florida, USA. In this study, to better inform Coastal Aquifer Management (CAM), we developed four modeling scenarios, namely, Physical Surface Barriers (PSB), including the artificial aquifer widths, permeability, and side slopes and recharge. In the base case scenario without artificial aquifer placement, results show that seawater levels would increase aquifer salinity and displace large amounts of presently available fresh groundwater. More specifically, for the Biscayne aquifer, approximately 0.50% of available fresh groundwater will be lost (that is, 41,192 m3) per km of the width of the aquifer considering the increasing seawater level. Furthermore, the results suggest that placing the PSB aquifer with a smaller permeability of <100 m per day at a width of approximately 615 m increases the available fresh groundwater by approximately 45.20 and 43.90% per km of shoreline, respectively. Similarly, decreasing the slope on the aquifer-ocean side and increasing the aquifer recharge will increase freshwater availability by about 43.90 and 44.50% per km of the aquifer. Finally, placing an aquifer fill along the shallow shoreline increases net revenues to the coastal community through increased agricultural production and possibly tourism that offset fill placement and water treatment costs. This study is useful for integrated management of coastal zones by delaying aquifer salinity, protecting fresh groundwater bodies, increasing agricultural lands, supporting surface water supplies by harvesting rainfall and flash flooding, and desalinating saline water using wave energy. Also, the feasibility of freshwater storage and costs for CAM is achieved in this study.

Simulating the effects of model parameters on stagnation points position during seawater intrusion.

Several works have been performed in order to understand seawater intrusion by simulating the Henry problem. Investigations were implemented by simulating the effect of many parameters (fractured aquifer, dispersion and diffusion, geochemical reactions, heterogeneity, anisotropy, boundary conditions) on the flow and transport. This paper focus on the concept of the "stagnation point," and this concept plays an important role in modeling, management and characterization of coastal aquifer. A total of forty-eight simulations, including the base case, were made to explore the effect of molecular diffusion coefficient, dispersivity, and seawater density on the position of the stagnation point. It was found that the increase of the molecular diffusion coefficient or the dispersivity leads to a downward displacement of the stagnation to the aquifer bottom and the lowest point position is reached for a Pe value of 0.35. For the seawater density effect, numerical results predict a nonlinear behavior of the stagnation point position, where the downward displacement is detected only for a ρs ranging from 1025 to 1045kg/m3.

Modeling of the Saltwater Intrusion Using the Level Set Method. Application to Henry’s Problem

The salt intrusion phenomenon is caused by overexploitation of aquifers in coastal areas. This physical phenomenon has been the subject of numerous studies and numerous methods have been proposed, with the aim of protecting the quality of the water in these aquifers. This work proposes a two-dimensional saline intrusion model using the sharp interface approach and the level set method. It consists of a parabolic equation modeling the underground flow and a hyperbolic Equation (the level set equation) which makes it possible to track the evolution of the interface. High-order numerical schemes such as the space scheme WENO5 and the third-order time scheme TVD-RK were used for the numerical resolution of the hyperbolic equation. To limit the tightening of the contour curves of the level set function, the redistanciation or reinitialization algorithm proposed by Sussma et al. (1994) was used. To ensure the effectiveness and reliability of the proposed method, two tests relating to the standard Henry problem and the modified Henry problem were performed. Recall that Henry’s problem uses the variable density modeling approach in a confined and homogeneous aquifer. By comparing the results obtained by the level set method with reinitialization (LSMR) and those obtained by Henry (1964), and by Simpson and Clement (2004), we see in the two test cases that the level set method reproduces well the toe, the tip and the behaviour of the interface. These results correspond to the results obtained by Abarca for Henry’s problem with constant dispersion coefficients. The results obtained with LSMR, reproduced the interface with a slight spacing compared to those obtained by Henry. According to Abarca (2006), this spacing is due to the absence of the longitudinal and transversal dispersion coefficients in the model.

A New Normalized Groundwater Age-Based Index for Quantitative Evaluation of the Vulnerability to Seawater Intrusion in Coastal Aquifers: Implications for Management and Risk Assessments

The vulnerability of coastal aquifers to seawater intrusion has been largely relying on data-driven indexing approaches despite their shortcomings to depict the complex processes of groundwater flow and mass transport under variable velocity conditions. This paper introduces a modelling-based alternative technique relying on a normalized saltwater age vulnerability index post-processed from results of a variable density flow simulation. This distributed index is obtained from the steady-state distribution of the salinity and a restriction of the mean groundwater age to a mean saltwater age distribution. This approach provides a novel way to shift from the concentration space into a vulnerability assessment space to evaluate the threats to coastal aquifers. The method requires only a sequential numerical solution of two steady state sets of equations. Several variants of the hypothetical Henry problem and a case study in Lebanon are selected for demonstration. Results highlight this approach ability to rank, compare, and validate different scenarios for coastal water resources management. A novel concept of zero-vulnerability line/surface delineating the coastal area threatened by seawater intrusion has shown to be relevant for optimal management of coastal aquifers and risk assessments. Hence, this work provides a new tool to sustainably manage and protect coastal groundwater resources.

Sustainable saltwater intrusion management in coastal aquifers under climatic changes for humid and hyper-arid regions

Saltwater Intrusion (SWI) in many coastal areas is accelerated by freshwater boundary changes due to over-pumping and decreasing aquifer recharge and sea-level rise. This study aims to control SWI due to the rise in sea levels in three climate regions: (i) humid and wet regions using storage dams at different heads and recharge ponds, (ii) hyper-arid and arid regions using physical barriers and wastewater treatment aquifer, brackish water abstraction, and desalination (TRAD) method, and (iii) semi-arid and semi-humid regions using a combination of flooding water recharge well-field and cut-off wall. The study was developed using the world benchmark problem of Henry's problem and Biscayne aquifer in the Cutler Ridge area near Deering Estate, Florida, USA. The finite-difference code SEAWAT was used in numerical simulations. The numerical results indicated that increasing the artificial recharge lake capacity minimizes the SWI in humid and wet regions with a high level of flooding. Moreover, the intrusion is mitigated using physical barriers and the TRAD method for hyper-arid and arid regions. Combining physical barriers during dry seasons and recharge wells for wet seasons resulted in suitable measures to managed the SWI in semi-arid and semi-humid regions. Finally, the best strategy to mitigate the SWI and minimize the desalination costs depends on the precipitation rates. Therefore, the methodology applied to this study represents a valuable tool in order to select the best method based on the climate conditions and particularly the precipitation intensity to increase the water budget in freshwater aquifers.

A fully interior penalty discontinuous Galerkin method for variable density groundwater flow problems

Discontinuous Galerkin (DG) methods due to their robustness properties, e.g. local conservation, low numerical dispersion, and well-capturing strong shocks and physical discontinuities, are well-suited for the simulation of Variable Density Flow (VDF) in porous media. This paper aims at introducing, in a unified format, the general class of Interior Penalty DG (IPDG) methods to solve the VDF equations. A combination of symmetric, non-symmetric and incomplete IPDG methods is used to discretize both head and concentration variables. Compatibility analysis is performed to prevent the loss of accuracy of the IPDG methods in simulations of coupled flow and transport equations. An accurate technique is used for time integration, based on a non-iterative procedure and adaptive time stepping with embedded error control. Several benchmarks are investigated to validate the proposed DG scheme and to examine its performance in simulating VDF problems. The new DG scheme reproduces better the experimental data than the conventional SEAWAT model. Its results are in excellent agreement with a recent semi-analytical solution of the Henry problem, dealing with seawater intrusion under convection-dominating conditions. The performance of the DG scheme is examined by simulating the challenging problem of natural convection in porous enclosure. The method is compared against a finite element solution obtained with COMSOL multi-physics. The numerical experiments indicate clearly that high-order DG method is much more appropriate than standard conforming Galerkin method in simulating VDF problems while at the same time, guaranteeing a better precision and high-fidelity solutions. The proposed numerical method can be extended to 3D problems.

Thermal Effects on Flow and Salinity Distributions in Coastal Confined Aquifers

AbstractCoastal aquifers provide an important hydrologic connection between terrestrial freshwater and oceanic seawater. Understanding the water flow and salinity distributions in those aquifers is essential to manage seawater intrusion and regional groundwater resources. For the last 50 yr, these processes have been extensively examined; however, previous studies typically assumed isothermal conditions and overlooked groundwater‐seawater temperature contrasts, as commonly found along the global coastline. Here, we validated a solute and heat transport model against laboratory experiments and then revisited the classical Henry problem for coastal confined aquifers. We found that as the seawater temperature increases or freshwater temperature decreases, the freshwater‐seawater interface retreats seaward and thus the freshwater storage increases. This occurs as a result of temperature‐induced changes to the fluid density and aquifer hydraulic conductivity. Furthermore, double diffusion of salt and heat can induce two circulation cells in opposing directions in the saltwater wedge once the seawater temperature exceeds that of groundwater by a certain extent. Consequently, the circulating seawater flux and associated travel time change dramatically compared with isotheral conditions. Overall, the effect of thermal forcing can be significant, as demonstrated by a sensitivity analysis considering a large range of groundwater‐seawater temperature contrasts. These results highlight the impact of changing thermal regimes on the flow and salinity distributions in coastal confined aquifers and provide guidance for better assessment of water resources in coastal zones.

Mitigation of seawater intrusion in coastal aquifers using coastal earth fill considering future sea level rise

Saltwater intrusion (SWI) is a physical problem that threatens many coastal aquifers all over the world. Saltwater intrusion is increasing with abstraction and rise in sea level. Coastal aquifer protection is essential to protect groundwater resources in these areas. A number of methods have been developed to protect coastal aquifers from SWI. This paper presents the impact of sea level rise on SWI in coastal aquifers and application of coastal earth fill as a new technique to control SWI. Different future sea level rise scenarios were studied and different coastal earth fill with an appropriate soil to extend the coastline towards the sea in order to control SWI was studied using SEAWAT model. The proposed control measure is numerically assessed by Henry's problem and then applied to a real case study of Biscayne aquifer, Florida, USA. For each aquifer, the corresponding relation was developed between the intrusion length of saltwater wedge and the width of fill. The results showed that increasing the fill width resulted in decreasing the intrusion length. In the case of Biscayne aquifer, increasing the fill width by 10, 20, 30, and 40% of the aquifer length resulted in retarding the intrusion to 329, 192, 42, and - 48m respectively. Using 150- and 300-m fill widths retards the intrusion length by 32.3% and 60.5%. In addition, increasing the fill width to 465m can retard SWI by 91.3%. This approach is capable to control the future risks of SWI and sea level rise.

Effects of Aquifer Bed Slope and Sea Level on Saltwater Intrusion in Coastal Aquifers

The quality of groundwater resources in coastal aquifers is affected by saltwater intrusion. Over-abstraction of groundwater and seawater level rise due to climate change accelerate the intrusion process. This paper investigates the effects of aquifer bed slope and seaside slope on saltwater intrusion. The possible impacts of increasing seawater head due to sea level rise and decreasing groundwater level due to over-pumping and reduction in recharge are also investigated. A numerical model (SEAWAT) is applied to well-known Henry problem to assess the movement of the dispersion zone under different settings of bed and seaside slopes. The results showed that increasing seaside slope increased the intrusion of saltwater by 53.2% and 117% for slopes of 1:1 and 2:1, respectively. Increasing the bed slope toward the land decreased the intrusion length by 2% and 4.8%, respectively. On the other hand, increasing the bed slope toward the seaside increased the intrusion length by 3.6% and 6.4% for bed slopes of 20:1 and 10:1, respectively. The impacts of reducing the groundwater level at the land side and increasing the seawater level at the shoreline by 5% and 10% considering different slopes are studied. The intrusion length increased under both conditions. Unlike Henry problem, the current investigation considers inclined beds and sea boundaries and, hence, provides a better representation of the field conditions.

Uncertainty analysis for seawater intrusion in fractured coastal aquifers: Effects of fracture location, aperture, density and hydrodynamic parameters

In this study we use polynomial chaos expansion (PCE) to perform uncertainty analysis for seawater intrusion (SWI) in fractured coastal aquifers (FCAs) which is simulated using the coupled discrete fracture network (DFN) and variable-density flow (VDF) models. The DFN-VDF model requires detailed discontinuous analysis of the fractures. In real field applications, these characteristics are usually uncertain which may have a major effect on the predictive capability of the model. Thus, we perform global sensitivity analysis (GSA) to provide a preliminary assessment on how these uncertainties can affect the model outputs. As our conceptual model, we consider fractured configurations of the Henry Problem which is widely used to understand SWI processes. A finite element DFN-VDF model is developed in the framework of COMSOL Multiphysics®. We examine the uncertainty of several SWI metrics and salinity distribution due to the incomplete knowledge of fracture characteristics. PCE is used as a surrogate model to reduce the computational burden. A new sparse PCE technique is used to allow for high polynomial orders at low computational cost. The Sobol’ indices (SIs) are used as sensitivity measures to identify the key variables driving the model outputs uncertainties. The proposed GSA methodology based on PCE and SIs is useful for identifying the source of uncertainties on the model outputs with an affordable computational cost and an acceptable accuracy. It shows that fracture hydraulic conductivity is the first source of uncertainty on the salinity distribution. The imperfect knowledge of fracture location and density affects mainly the toe position and the total flux of saltwater entering the aquifer. Marginal effects based on the PCE are used to understand the effects of fracture characteristics on SWI. The findings provide a technical support for monitoring, controlling and preventing SWI in FCAs.

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.