Density Slopes in Variable Density Flow Modeling

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

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.

Efficient Stochastic Simulation of Seawater Intrusion, With Mixing, in Confined Coastal Aquifers

We present a high-efficiency method for simulating seawater intrusion (SWI), with mixing, in confined coastal aquifers based on uncoupled equations in the through-flow region of the aquifer. The flow field is calculated analytically and the tracer transport numerically, via spatial splitting along the principal directions (PD) of transport. Advection-dispersion processes along streamlines are simulated with the very efficient matched artificial dispersivity (MAD) method of Syriopoulou and Koussis and the system of discretized transverse-dispersion equations is solved with the Thomas algorithm. These concepts are embedded in the 2D-MADPD-SWI model, yielding comparable solutions to those of the uncoupled SWI equations with the state-of-the-art FEFLOW code, but faster, while 2D-MADPD-SWI achieves an at least hundredfold faster solution than a variable-density flow model. We demonstrate the utility of the 2D-MADPD-SWI model in stochastic Monte Carlo simulations by assessing the uncertainty on the advance of the 1,500 ppm TDS line (limit of tolerable salinity for irrigation) due to randomly variable hydraulic conductivity and freshwater flow rate.

Investigating the impact of the Pleistocene sea-level lowstand on offshore fresh groundwater on the New Jersey shelf

<p>Offshore fresh groundwater reservoirs have been identified on continental shelves in several regions of the world. In many cases, sea-level change over geologic time-scales has been identified as a key factor in the emplacement of these freshwater systems. This numerical study analyzes a range of paleo-hydrogeological conditions on the New Jersey transect during the late Pleistocene, during which vast sections of the shelf were sub-aerially exposed. Coupled variable-density flow and heat transport simulations were conducted on a geologically representative 2D shelf model using SHEMAT-Suite. The model combines sequence stratigraphic interpretation of 2D depth migrated seismic lines and a stochastic facies distribution, with petrophysical properties derived from IODP Expedition 313 well data. The study considers a 60<sub></sub>000 year period of surface meteoric recharge, and the subsequent marine transgression from 12 000 years ago to present-day. A sensitivity analysis is conducted for key factors that influence offshore freshened groundwater emplacement during recharge phase: (1) topography-driven flow, and (2) permeability anisotropy. Systematically introducing anisotropy resulted in a 11 % – 31 % decrease in emplaced volume relative to the base-case. The results were analysed to determine whether the late Pleistocene sea-level lowstand drove enough freshwater emplacement that can explain the complex present-day observations. All of the simulated scenarios indicate that surface recharge lead to freshening of sediments across the entire transect during this period, even in case of high permeability anisotropy. The observations also suggest that the cyclical flushing and re-salinification of shelf sediments that takes place over glacial – interglacial cycles is an asymmetrical process, which favours storage of freshened pore fluid in the long run.</p>

Computational investigation of the cavitation vortex dynamics in flow over a three-dimensional hydrofoil by a new transport-based model

Cavitation is of significant practical interest due to its unsteady features which could induce destructive effects such as drastic drop in efficiency, noise, vibration, and corrosion for propulsion systems, rudders and other hydraulic machinery. A thorough understanding of the hydrodynamics in the cavitating flow past a three-dimensional hydrofoil makes indicators for an improved control performance of these hydraulic systems. Hence, a computational investigation of the cavitating flow over the Delft Twist-11 hydrofoil was performed with special emphasis on the cavitation vortex dynamics. A new transport-based cavitation model was proposed and compared with the conventional Schnerr–Sauer model through the predictions of cavitation characteristics, for which available experimental data were also provided. The results show that, as compared with the Schnerr–Sauer model, the proposed model can predict closer engineering parameters, including time-mean lift coefficient and vapor shedding frequency with the experiments. In addition, more reasonable structure and dynamics of the three-dimensional unsteady sheet/cloud cavitation patterns, including the cavity growth, break-off, and collapse downstream are captured by the proposed model. With the help of the vorticity transport equation in a variable density flow, further analysis of the flow field predicted by the proposed model reveals that cavitation promotes the production of vortex as well as the flow instabilities. Vorticity production in the cavitating flow is mainly induced by the terms of vortex stretching and vortex dilatation, while the baroclinic torque only contributes in the region of shedding and collapse of the cloud cavity and the contribution of the viscous diffusion term is negligible as compared with the other three terms. The main significance of this study is that it demonstrates the potential of a robust transport-based cavitation model to investigate the unsteady dynamics in the cavitating flow past a three-dimensional twisted hydrofoil and expected to make sense for other hydraulic machinery.

Prediction of seawater intrusion to coastal aquifers based on non-dimensional diagrams

<p>A numerical analysis of the groundwater flow and contaminant transport equations, based on the variable density flow approach, is used for the construction of non-dimensional diagrams to predict seawater intrusion to confined coastal aquifers. The classical Henry’s seawater intrusion problem is analysed by using a finite element model. The model’s equations are written in non-dimensional form and the numerical solutions depend solely on three non-dimensional parameters:</p><p>α=q΄/Κ<sup>0</sup>, β=(bΚ<sup>0</sup>)/(nD<sub>m</sub>), α΄=bS<sup>0</sup>/n                                                                                           (eq. 1 a,b,c)</p><p>where q’ is the freshwater recharge rate (m/d), K<sup>0</sup> the freshwater hydraulic conductivity (m/d), b the aquifer thickness, n the porosity (-), D<sub>m</sub> the molecular diffusion coefficient (m<sup>2</sup>/d) and S<sup>0</sup> the freshwater specific storage (1/m). Please note that hydraulic conductivity appears in two of the non-dimensional parameters, α and β.</p><p>The non-dimensional formulation has led to the construction of non-dimensional diagrams of salt distribution for a homogeneous and isotropic confined aquifer with horizontal base and constant thickness that is uniformly recharged with freshwater. These diagrams illustrate the influence of the key hydrological and hydraulic parameters, and furthermore, can be used to predict the evolution of seawater intrusion in real case studies.</p><p>The numerical simulations were carried out up to the equilibrium state for different values of the non-dimensional parameters of equation 1. By decreasing the value of parameter α=q΄/Κ<sup>0</sup>, seawater intrusion is advancing inland and the width of dispersion zone is increasing. By increasing the parameter β=(bΚ<sup>0</sup>)/(nD<sub>m</sub>), the seawater-freshwater transition zone is narrowing and shifted to the seaside at the upper part of the aquifer, while the intrusion of saltwater is advancing inland at the lower part of the aquifer. The distribution of the salts in the aquifer was found essentially identical for different values of the parameter α΄=bS<sup>0</sup>/n; hence this parameter exhibits very low sensitivity, which makes it of low importance, especially for real case studies.</p><p>Overall, the non-dimensional diagrams – constructed by following the variable density flow approach and under specific assumptions – can be used for a quick and direct prediction of seawater intrusion in real aquifers. These diagrams would be useful for an initial prediction at the case studies of the PRIMA MEDSAL project (www.medsal.net), namely the coastal aquifers in Rhodope (Greece), Samos island (Greece), Bouficha (Tunisia), Bouteldja (Algeria), Tarsus (Turkey) and under specific assumptions to the karstic aquifer in Salento (Italy).</p>