Variable Density Flow
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Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3292
Weixing Guo

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.

2021 ◽  
pp. 104077
Anis Younes ◽  
Behshad Koohbor ◽  
Benjamin Belfort ◽  
Philippe Ackerer ◽  
Joanna Doummar ◽  

2021 ◽  
Ariel Thomas ◽  
Sönke Reiche ◽  
Christoph Clauser

<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>

2020 ◽  
Charalampos Doulgeris ◽  
Evangelos Tziritis ◽  
Vassilios Pisinaras ◽  
Andreas Panagopoulos ◽  
Christoph Külls

<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 (, 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>

The comparison between incompressible and compressible flow for aerodynamic coefficients and flow characteristics has been made for NACA 2412 airfoil. The FEM is used to obtain results. The fluid domain of 10C has been constructed to initialize the boundary conditions of incompressible and compressible flow conditions. The structured mesh has been applied in order to achieve accurate results. The Spallart-Allmaras turbulence model has been used to solve both incompressible and compressible flow conditions. The method validation that has been conducted at incompressible flow has shown close agreement between numerical and experimental lift coefficient. From velocity magnitude and static pressure, contours, the compressible flow has the highest-pressure distribution compared to incompressible flow. Therefore, it has been proven that the coefficient of force at ninety degrees to the direction of the flow direction of the airfoil subjected to a variable density flow was much higher compared to incompressible flow.

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Vincent E. A. Post ◽  
Georg J. Houben ◽  
Leonard Stoeckl ◽  
Jürgen Sültenfuß

Tritium (3H) and its daughter product 3He have been widely used as tracers in hydrological studies, but quantitative analyses of their behaviour in freshwater lenses and the transition zone in coastal aquifers are presently lacking. In this paper, the fate of 3H and 3He in the freshwater lens and the transition zone as well as the saltwater wedge is studied using numerical variable-density flow and transport models of different degrees of complexity. The models are based on the conditions on the German island of Langeoog, which is uniquely suited for this purpose because of the high 3H concentration of the North Sea. It is found that most bomb-related tritiogenic 3He still resides in the freshwater lens, making it a useful tracer for young (<60 years) groundwater. Differences in dispersive transport between 3H and 3He can cause an apparent age bias on the order of 10 years. Under favourable conditions, 3H from seawater can penetrate deep into the offshore part of the aquifer and has potential to be used as a tracer to study saltwater circulation patterns. Our modelling suggests that the field-observed 3H in the transition zone does not originate from seawater but from freshwater affected by the bomb peak. Yet in models with a low (αL=0.5 m) dispersivity, no 3H was sequestered into the transition zone and the transition zone width was underestimated. Better results were obtained with αL=5 m, a value that is higher than in comparable modelling studies, which suggests that further work is needed to better understand the controls (tides, lithological heterogeneity, or transience of recharge and pumping) on transition zone mixing processes.

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