3D Variable-density Research Articles

Island hydrogeology in the tropics: Constraining a 3D variable-density groundwater flow and solute transport model with geophysics

Saltwater intrusion is the greatest risk to coastal community water supplies where they are dependent on fresh groundwater as the main source of supply. For small, fractured bedrock island aquifers, the fresh groundwater lens dynamics and transition zone geometry are complex. This study investigated the impacts of projected increases in groundwater pumping on a fresh groundwater lens to evaluate changes to the lens geometry and localized up-coning from the deeper, more saline aquifers beneath a small bedrock island in the tropics. A combination of traditional hydrogeological datasets and an airborne electromagnetic survey were used to develop a three-dimensional density-dependent groundwater flow and solute transport model using the SEAWAT code. This investigation represents one of very few studies that have taken such an approach. The model was calibrated using observed groundwater hydraulic heads and chloride concentration data, and calculated chloride values based on bulk conductivity measurements determined from inverted geophysical data. A staged calibration approach was adopted, firstly assessing the time-average lens extent and geometry, and secondly considering the seasonal groundwater level response. In the calibration, the geophysical data helped constrain the lens geometry in the absence of hydraulic head and chloride data. The calibrated model was used to test scenarios where groundwater pumping rates were increased above the current demand of 452 m3 d−1, showing that the lens is likely to be stable, i.e., its available storage is not expected to contract excessively, for extraction rates of up to 3,000 m3 d−1. The combined use of geophysical data and a numerical modeling approach was advantageous in investigating the lens characteristics. It also demonstrated how these techniques can be used together to evaluate coastal water resources and to manage water supply risks for coastal communities. The study demonstrated that the freshwater lens can likely support the freshwater demands of the remote community, and is a preferred option compared with high-cost and more complicated options such as seawater desalination and managed aquifer recharge.

Generalized Gauss-FFT 3D forward gravity modeling for irregular topographic mass having any 3D variable density contrast

A fully numerical forward model for estimating gravity anomalies in the Fourier domain is presented for irregular topographic mass distributions. Modified Parker’s formula using the Gauss-FFT method is utilized for getting better accuracy than the standard FFT algorithm. Existing frequency domain forward modeling for topographic surfaces uses common analytically derivable density functions for evaluating gravity anomalies. But in the real scenario, subsurface mass distributions can take any functional form of depth. Our presented algorithm provides a generalized approach for evaluating forward gravity anomalies due to any horizontal and vertical variation of density distributions. The computational cost depends on the irregularities of the topographic surfaces and the complexity of the functional form of density distributions. The presented algorithm is compared with analytical solutions and space domain prismatic model approximation. A complex, analytically non-integrable density distribution was also considered and compared with the space domain model. The presented algorithm accurately estimates gravity anomalies in all cases, and the results are close to the space domain prismatic model. Finally, an observed gravity anomaly of the real sedimentary basin and its corresponding inverted basement depth for parabolic density variation is considered to evaluate forward anomalies using our presented algorithm. The estimated gravity anomalies provide close approximations to observed gravity anomalies, revealing the proposed algorithm’s reliability for any 3D topographic forward modeling.

Joint estimation of groundwater salinity and hydrogeological parameters using variable-density groundwater flow, salt transport modelling and airborne electromagnetic surveys

Freshwater aquifers in low elevation coastal zones are known to be threatened by saltwater intrusion (SWI). As these areas host a significant share of the world's population, an excellent understanding of this phenomenon is required to effectively manage the availability of freshwater. SWI is a dynamic process, therefore saline groundwater distributions can change quickly over time – particularly in stressed areas with anthropogenic drivers. To model these changes, regional 3D variable-density groundwater (3D-VDG) flow and coupled salt transport models are often used to estimate the current (and future distributions) of saline groundwater. Unfortunately, parameterising 3D-VDG models is a challenging task with many uncertainties. Generally, uncertainty is reduced through the addition of observational data – such as Airborne Electromagnetic (AEM) surveys or ground-based information – that offer information about parameters such as salinity and hydraulic head. Recent research has shown the ability of AEM surveys to provide accurate 3D groundwater salinity models across regional scales, as well as highlighting the potential for good survey repeatability. To this end we investigated the novel approach of using repeat AEM surveys (flown over the same area at different points in time) and 3D-VDG models to jointly improve the parameterisation of 3D-VDG models - while simultaneously providing a detailed 3D map of groundwater salinity distributions. Using detailed 3D synthetic models, the results of this study quantitatively highlight the usefulness of this approach, while offering practical information on implementation and further research.

Impacts of Sea Level Rise and Groundwater Extraction Scenarios on Fresh Groundwater Resources in the Nile Delta Governorates, Egypt

As Egypt’s population increases, the demand for fresh groundwater extraction will intensify. Consequently, the groundwater quality will deteriorate, including an increase in salinization. On the other hand, salinization caused by saltwater intrusion in the coastal Nile Delta Aquifer (NDA) is also threatening the groundwater resources. The aim of this article is to assess the situation in 2010 (since this is when most data is sufficiently available) regarding the available fresh groundwater resources and to evaluate future salinization in the NDA using a 3D variable-density groundwater flow model coupled with salt transport that was developed with SEAWAT. This is achieved by examining six future scenarios that combine two driving forces: increased extraction and sea level rise (SLR). Given the prognosis of the intergovernmental panel on climate change (IPCC), the scenarios are used to assess the impact of groundwater extraction versus SLR on the seawater intrusion in the Delta and evaluate their contributions to increased groundwater salinization. The results show that groundwater extraction has a greater impact on salinization of the NDA than SLR, while the two factors combined cause the largest reduction of available fresh groundwater resources. The significant findings of this research are the determination of the groundwater volumes of fresh water, brackish, light brackish and saline water in the NDA as a whole and in each governorate and the identification of the governorates that are most vulnerable to salinization. It is highly recommended that the results of this analysis are considered in future mitigation and/or adaptation plans.

Accelerated 3D T2 mapping with dictionary-based matching for prostate imaging.

To develop a fast and accurate method for 3D T2 mapping of prostate cancer using undersampled acquisition and dictionary-based fitting. 3D high-resolution T2 -weighted images (0.9 × 0.9 × 3 mm3 ) were obtained with a multishot T2 -prepared balanced steady-state free precession (T2 -prep-bSSFP) acquisition sequence using a 3D variable density undersampled Cartesian trajectory. Each T2 -weighted image was reconstructed using total variation regularized sensitivity encoding. A flexible simulation framework based on extended phase graphs generated a dictionary of magnetization signals, which was customized to the proposed sequence. The dictionary was matched to the acquired T2 -weighted images to retrieve quantitative T2 values, which were then compared to gold-standard spin echo acquisition values using monoexponential fitting. The proposed approach was validated in simulations and a T1 /T2 phantom, and feasibility was tested in 8 healthy subjects. The simulation analysis showed that the proposed T2 mapping approach is robust to noise and typically observed T1 variations. T2 values obtained in the phantom with T2 prep-bSSFP and the acquisition-specific, dictionary-based matching were highly correlated with the gold-standard spin echo method (r = 0.99). Furthermore, no differences were observed with the accelerated acquisition compared to the fully sampled acquisition (r = 0.99). T2 values obtained in prostate peripheral zone, central gland, and muscle in healthy subjects (age, 26 ± 6 years) were 97 ± 14, 76 ± 7, and 36 ± 3 ms, respectively. 3D quantitative T2 mapping of the whole prostate can be achieved in 3 minutes.

Synergy of climate change and local pressures on saltwater intrusion in coastal urban areas: effective adaptation for policy planning

ABSTRACTThis article examines the relative impacts of anthropogenic interventions and global climate change on the dynamics of saltwater intrusion in highly urbanized coastal aquifers. For this purpose, simulations of the impacts of sea-level rise and abstraction scenarios for the near future were undertaken for a pilot aquifer using a multi-objective 3D variable-density flow and solute transport model. We find that sea-level rise associated with climate change has less influence on the encroachment of salinity than anthropogenic abstraction, which has a more appreciable impact on saltwater intrusion through greater sensitivity to water consumption and seasonality.

Representativeness of 2D models to simulate 3D unstable variable density flow in porous media

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.

Density-dependent numerical simulations of the impact of underground dams on groundwater storage on Samui island, Thailand

Samui island in southern Thailand has become an increasingly attractive tourist spot over the last decades. However, the enormous numbers of tourists has led to deficits of the available water resources, mainly surface water stored in a few reservoirs across the island during the dry season of the year, which is also the main tourist season. The Department of Groundwater Resources (DGR) has been aware of this problem and initialized a project of underground dam construction which is supposed to impede the natural groundwater outflow toward the sea and, hence, to increase the usable groundwater storage on Samui island during the dry season. The dam will be initially designed as two impermeable underground-walls amid the two rock-gorges that cut through the three layers of the aquifer system, reaching down to a maximum depth of about 50 m. A top of the 2 m wide dam which ends below the upper unconfined aquifer layer, a vertical layer of high permeability will be specified, so that a “spillway-like” over-flow of the groundwater with only minor impacts on the subsurface ecology downstream toward the sea will be generated. Based on this conceptual model, a 3D-variable density groundwater flow and transport model has been set up and calibrated in both steady and transient modes. In the subsequent modeling analysis the underground dam with the above spillway characteristics has been embedded into the model by specifying the corresponding vertical curtains of low and high conductivity, respectively. Finally, groundwater pumps upstream of the underground dams have been included into the model. Simulations without and with the hydraulic structures have been performed to ascertain the differences with respect to groundwater levels and storage and to evaluate the overall functionality of the underground dam. The results show that the underground dam is able to raise groundwater levels, that is, groundwater storage. The budget analysis of the simulation sets indicates that the underground dams serve well their purpose, particularly, for long dry spells, as more groundwater can be pumped out than would be possible without such a hydraulic structure. Finally, analyses of the seawater intrusion problem based on (1) the Ghyben-Herzberg formula, (2) analytical solutions of the sharp interface problem under Dupuit’s assumption, and (3) using the density-dependent SEAWAT – flow and solute transport modeling of the transition zone have been carried out. Differences in the landward extensions of the seawater intrusion fronts for the analytical and numerical solutions are found; however, the general predictions of the analytical theory are supported by the SEAWAT model in general, that is, a landward progression of the seawater intrusion front for pumping conditions and a partly retreat again in the presence of the two underground dams. In any case, seawater intrusion in the coastal zone of the study region does not extend deep enough inland to adversely impact the quality of the pumped groundwater there.

Assessment of Saltwater Intrusion and Discharges to a Wetland with a 3D Transient Variable Density Flow Model: The Coastal Plane Oropesa-Torreblanca Aquifer, Spain

The proper characterization of coastal aquifers requires modeling variable density flow effects. However, most models estimate processes as saline intrusion based on 2D models with constant density and are rarely calibrated to honor salinity measurements. These facts limit the model predictions reliability, affecting the estimated hydrodynamic parameters, external stresses, and other model outputs that can be critical for planning or management decisions. This paper describes the re-assessment of a coastal aquifer model (Oropesa-Torreblanca, eastern Spain) subjected to moderate-to-high saline intrusion with a transient 3D variable density flow model. Previous models were based on 2D low-resolution grids without variable density effects. The new model honors the observed trends of both piezometric and salinity data. Results show the importance of the variable density effects having on critical outputs as sea intrusion and the discharges to a local wetland of high environmental value. The widespread intrusion process and its current stabilization are confirmed but, compared to previous models, the annual average intrusion is 156% higher, discharge to the wetland increases 30%, and the inflows from neighboring formations increase 22%. The more accurate aquifer models, as well as the new discharges and intrusion estimations, are important contributions for future water and environmental planning decisions in the area.

3D Variable Density Flow Simulation to Evaluate Pumping Schemes in Coastal Aquifers

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.

Estándar de comparación tridimensional para la simulación de flujo de densidad variable y transporte: coincidencia de modo de estabilidad semianalítica para una convección estacionaria inestable en una caja porosa inclinada

This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.

3D vector gravity potential and line integrals for the gravity anomaly of a rectangular prism with 3D variable density contrast

Three-dimensional rectangular prisms are building blocks for calculating gravity anomalies from irregular 3D mass bodies with spatially variable density contrasts. A 3D vector gravity potential is defined for a 3D rectangular prism with density contrast varying in depth and horizontally. The vertical component of the gravity anomaly equals the flux of the 3D vector gravity potential through the enclosed surface of the prism. Thus, the 3D integral for the gravity anomaly is reduced to a 2D surface integral. In turn, a 2D vector gravity potential is defined. The vertical component of the gravity anomaly equals the net circulation of the 2D vector gravity potential along the enclosed contour bounding the surfaces of the prism. The 3D integral for the gravity anomaly is reduced to 1D line integrals. Further analytical or numerical solutions can then be obtained from the line integrals, depending on the forms of the density contrast functions. If an analytical solution cannot be obtained, the line-integral method is semianalytical, requiring numerical quadratures to be carried out at the final stages. Singularity and discontinuity exist in the algorithm and the method of exclusive infinitesimal sphere or circle is effective to remove them. Then the vector-potential line-integral method can calculate the gravity anomaly resulting from a rectangular prism with density contrast, varying simply in one direction and sophisticatedly in three directions. The advantage of the method is that the constraint to the form of the density contrast is greatly reduced and the numerical calculation for the gravity anomaly is fast.

Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures

Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes.