Solute transport and geochemical modeling of the coastal quaternary aquifer, Delta Dahab Basin, South Sinai, Egypt

The wadi dahab delta is in a dry, arid coastal zone within Egypt’s south Sinai Peninsula’s eastern portion. The primary water source is the Quaternary coastal alluvial aquifer. The groundwater salinity varies from 890to 8213 mg/L, with a mean value of 3417 mg/L. The dissolved major ions have been used to calculate the seawater mixing index(SWMI) using a linear equation that discriminates the groundwater mostly affected by water–rock interaction(SWMI 1>) and other samples mixed with Seawater(SWMI < 1). The isotopic composition of groundwater for specifically chosen groundwater samples ranges from-0.645‰ to +5.212‰ for δ^(18)O and from-9.582‰ to + 22.778‰ for δ^(2)H, where the seawater represented by a Red Sea water sample(δ^(18)O + 1.64‰-δ^(2)H + 9.80‰) and reject brine water are considerably enriched the isotopic groundwater values. The geochemical NETPATH model constrained by the dissolved significant ions, isotopes, and the rock aquifer forming minerals as phases indicate the mixing percent with the seawater ranges from 9% to 97% of seawater from 91% to 3% of original recharge water. According to the SEAWAT 3-D flow models, seawater has penetrated the Northeastern Dahab delta aquifer, with the intrusion zone extending1500 m inland. The salt dissolution, upwelling of saline water, recharge from the upstream mountain block, and seawater encroachment are the primary aspects contributing to the deterioration of groundwater quality. These findings may have significance for effective groundwater withdrawal management in arid locations worldwide with similar hydrogeological systems.

Numerical Modelling of Dissolving and Driving Exploitation of Potash Salt in the Qarhan Playa——A Coupled Model of Reactive Solute Transport and Chemical Equilibrium in a Multi-component Underground Brine System

Firstly, the macroscopic chemical equilibrium state of a series of chemical reactions between intercrystal brine and its media salt layer （salt deposit） in Qarhan Salt Lake was studied by using the Pitzer theory. The concept of macroscopic solubility product and its relation with accumulated ore dissolving ratio were presented, which are used in the numerical model of dissolving and driving exploitation of potassium salt in Qarhan Salt Lake. And secondly, with a model forming idea of transport model for reacting solutes in the multi-component fresh groundwater system in porous media being a reference, a two-dimensional transport model coupled with a series of chemical reactions in a multi-component brine porous system （salt deposits） was developed by using the Pitzer theory. Meanwhile, the model was applied to model potassium/magnesium transport in Qarhan Salt Lake in order to study the transfer law of solid and liquid phases in the dissolving and driving process and to design the optimal injection/abstraction strategy for dissolving and capturing maximum Potassium/ Magnesium in the mining of salt deposits in Qarhan Salt Lake.

A one-dimensional transport model for multi-component solute in saturated soil

A modified multi-component solute diffusion equation described with diffusion flux was derived in detail based on the classical MaxwellStefan diffusion theory. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. The chemical potential gradient is considered the driving force. A one-dimensional model for transport of multi-component solute in saturated soil was developed based on the modified diffusion equation and the modified competitive Langmuir adsorption equation. Numerical calculation of a case of two heavy metal ion species, which was chosen as an example, was carried out using the finite element software COMSOL Multiphysics. A comparative analysis was performed between the multi-component solute transport model developed in this study and the convection-diffusion transport model of single-component solute based on Fick's law. Simulation results show that the transport behavior of each species in a multi-component solute system is different from that in a single-component system, and the friction characteristics considered in the developed model contribute to obstructing the movement of each solute component. At the same time,the influence of modified competitive Langmuir adsorption on solute transport was investigated. These research results can provide strong theoretical support for the design of antifouling barriers in landfills and the maintenance of operation stability.

Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.

Modeling impact of culture facilities on hydrodynamics and solute transport in marine aquaculture waters of North Yellow Sea

An increasing number of marine aquaculture facilities have been placed in shallow bays and open sea,which might significantly affect hydrodynamic and solute transport processes in marine aquaculture waters.In this study,a coupled hydrodynamic and solute transport model was developed with high-resolution schemes in marine aquaculture waters based on depth-averaged shallow water equations.A new expression of drag force was incorporated into the momentum equations to express the resistance of suspended culture cages.The coupled model was used to simulate the effect of suspended structures on tidal currents and the movement of a contaminant cloud in the marine aquaculture of the North Yellow Sea,China.The simulation results showed a low-velocity area appearing inside the aquaculture cage area,with a maximum reduction rate of velocity close to 45%under high-density culture.The results also showed that tidal currents were sensitive to the density of suspended cages,the length of cages,and the drag coefficients of cages.The transport processes of pollutants inside aquaculture facilities were inhibited away from the vicinity of the culture cage area because of the diminished tidal currents.Therefore,the suspended cages significantly affected the transport processes of pollutants in the coastal aquaculture waters.Furthermore,the reduced horizontal velocity significantly decreased the food supply for the aquaculture areas from the surrounding sea.

An Efficient Approach for Transforming Unbalanced Transportation Problems into Balanced Problems in Order to Find Optimal Solutions

In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.

A Solute Pinning Approach to Solute Drag in Multi-Component Solid Solution Alloys

The Cahn, Lücke and Stüwe theory remains the backbone of more complex analysis dealing with solute drag, however, the mathematical treatment is rather involved. A new approach based on solute pinning the boundary has therefore recently been suggested, which has the main advantage of a simpler mathematical treatment. In the present paper this approach has been generalized to take into account the influence of different types of solute atoms in the high solute content/low driving force regime.

Impact of stress on solute transport in a fracture network: A comparison study

This paper compares numerical modeling of the effect of stress on solute transport （advection and matrix diffusion） in fractured rocks in which fracture apertures are correlated with fracture lengths. It is mainly motivated by the performance and safety assessments of underground radioactive waste repositories. Five research teams used different approaches to model stress/deformation, flow and transport pro- cesses, based on either discrete fracture network or equivalent continuum models. The simulation results derived by various teams generally demonstrated that rock stresses could significantly influence solute transport processes through stress-induced changes in fracture apertures and associated changes in per- meability. Reasonably good agreement was achieved regarding advection and matrix diffusion given the same fracture network, while some observed discrepancies could be explained by different mechanical or transport modeling approaches.

Simulation of solute transportation within porous particles during the bioleaching process

A mathematical model, accounting for the sulfuric acid and ferric ions diffusion and the copper sulfide mineral leaching process, was developed for an ore particle by considering its porous structure. It was simulated with the simulation tool COMSOL Multiphysics. The simulation results show that the highest acid and ferric concentrations near the particle surface are apparent, while the concentrations in the central particle increase slightly as the less-porous ore core with low permeability prevents the oxidation from penetrating. The extraction of the mineral near the particle surface is the maximum, mainly because of ample sulfuric acid, ferric ions, bacteria, and oxygen available for the leaching process. Because of low oxidation concentration in the central part of the particle, the reaction rate and copper sulphide conversion are small. The simulation shows good agreement with the experimental results.

Mathematical model for coupled reactive flow and solute transport during heap bioleaching of copper sulfide

Based on the momentum and mass conservation equations, a comprehensive model of heap bioleaching process is developed to investigate the interaction between chemical reactions, solution flow, gas flow, and solute transport within the leaching system. The governing equations are solved numerically using the COMSOL Multiphysics software for the coupled reactive flow and solute transport at micro-scale, meso-scale and macro-scale levels. At or near the surface of ore particle, the acid concentration is relatively higher than that in the central area, while the concentration gradient decreases after 72 d of leaching. The flow simulation between ore particles by combining X-ray CT technology shows that the highest velocity in narrow pore reaches 0.375 m/s. The air velocity within the dump shows that the velocity near the top and side surface is relatively high, which leads to the high oxygen concentration in that area. The coupled heat transfer and liquid flow process shows that the solution can act as an effective remover from the heap, dropping the highest temperature from 60 to 38 ℃. The reagent transfer coupled with solution flow is also analyzed. The results obtained allow us to obtain a better understanding of the fundamental physical phenomenon of the bioleaching process.

The solute carrier transporters and the brain:Physiological and pharmacological implications

Solute carriers(SLCs)are the largest family of transmembrane transporters that determine the exchange of various substances,including nutrients,ions,metabolites,and drugs across biological membranes.To date,the presence of about 287 SLC genes have been identified in the brain,among which mutations or the resultant dysfunctions of 71 SLC genes have been reported to be correlated with human brain disorders.Although increasing interest in SLCs have focused on drug development,SLCs are currently still under-explored as drug targets,especially in the brain.We summarize the main substrates and functions of SLCs that are expressed in the brain,with an emphasis on selected SLCs that are important physiologically,pathologically,and pharmacologically in the blood-brain barrier,astrocytes,and neurons.Evidence suggests that a fraction of SLCs are regulated along with the occurrences of brain disorders,among which epilepsy,neurodegenerative diseases,and autism are representative.Given the review of SLCs involved in the onset and procession of brain disorders,we hope these SLCs will be screened as promising drug targets to improve drug delivery to the brain.

Solute transport characteristics of a deep soil profile in the Loess Plateau,China

Understanding solute transport behaviors of deep soil profile in the Loess Plateau is helpful for ecological construction and agricultural production improvement. In this study, solute transport processes of a deep soil profile were measured by a conservative tracer experiment using 25 undisturbed soil cores （20 cm long and 7 cm diameter for each） continuously sampled from the surface downward to the depth of 500 cm in the Loess Plateau of China. The solute transport breakthrough curves （BTCs） were analyzed in terms of the convection-dispersion equation （CDE） and the mobile-immobile model （MIM）. Average pore-water velocity and dispersion coefficient （or effective dispersion coefficient） were calculated using the CDE and MIM. Basic soil properties and water infiltration parameters were also determined to explore their influence on the solute transport parameters. Both pore-water velocity and dispersion coefficient （or effective dispersion coefficient） generally decreased with increasing depth, and the dispersivity fluctuated along the soil profile. There was a good linear correlation between log-transformed pore-water velocity and dispersion coefficient, with a slope of about 1.0 and an average dispersivity of 0.25 for the entire soil profile. Generally speaking, the soil was more homogeneous along the soil profile. Our results also show that hydrodynamic dispersion is the dominant mechanism of solute transport of loess soils in the study area.

Impact of normal stress-induced closure on laboratory-scale solute transport in a natural rock fracture

The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study.The fracture is created from a measured surface of a granite rock sample.The Bandis model is used to calculate the fracture closure due to normal stress,and the fluid flow is simulated by solving the Reynold equation.The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture.The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures.It causes fracture closure and creates asperity contact areas,which significantly reduces the effective hydraulic aperture and enhances flow channeling.Consequently,the reduced aperture and enhanced channeling affect travel time distributions.In particular,the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport.The fracture normal stiffness correlates linearly with the 5th and 95th percentiles of the normalized travel time.The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.

Lattice Boltzmann simulation of solute transport in a single rough fracture

In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that (1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.

Unsaturated flow and solute transport in a porous column using spherical ore particles

This paper dealt with the development of a two-dimensional （2D） mathematical model for column leaching and confirmed the important simulation parameters through experiment. The unsaturated state of the variably saturated flow column and the solute transport of copper ions were studied during leaching. The fluid flow problem was handled using the Richards equation on the premise of an ambient pressure column air, where the van Genuchten formulas were applied to define the nonlinear relationships of pressure head with the retention and permeability properties. The ore column permeability test gave a varied hydraulic conductivity, which was analyzed in the model. In the solute transport problem, the copper ion concentration was solved using the advection-diffusion-reaction equation whose reaction term was determined by the joint analysis of experimental copper leaching rate and the shrinking core model. Particle-and column-scale leaching tests were carried out to illustrate the difference and connection of copper extraction in both processes. This fluid flow and solute transport cou-pled model was determined through the finite element method using the numerical simulation software, COMSOL Multiphysics.

Experimental Study of Preferential Solute Transportation During Dump Leaching

The production of dump leaching of the Dexing Copper Mine was affected by a preferential solution flow. Formative mechanism of the preferential solution flow was investigated by analyzing the relationship between both dump permeability and surface tension and ore diameter. The preferential solution flow occured in the fine ore area when the application rate was low. The preferential solution flow entered into the coarse ore area because the negative pore water pressure disappeared with an increase of the application rate. The preferential solute transportation experiment was conducted by selecting NaCl as mineral. Results of the experiment showed that the concentration of the outflow solution reduced over time. The concentration of the coarse ore area outflow solution was greater than that of the fine ore area. The process of NaCl leaching can be divided into two stages. NaCl was carried out directly by diffusion--convection during the first stage, so the leaching rate increased sharply. But in the second stage, only a small amount of NaCl dissolved in the immobile water. The leaching rate increased slowly because NaC1, dissolved in the immobile water, can only be leached by diffusion.

New Approach to Find Initial Basic Feasible Solution (IBFS) for Optimal Solution in Transportation Problem

Minimizing transportation time and getting optimal solutions are always considered as important factors while solving transportation problem. This paper shows a new approach for finding initial basic solution for transportation problem which reduces cost of transportation more than any transportation method such as LCM, northwest, Vogel’s approximation and so on. This method has been illustrated by taking an example;afterwards, it compares basic initial feasible solution with other methods IBF and optimal dictate solutions such as MODI and Steppingstone method.

A multiscale 3D finite element analysis of fluid/solute transport in mechanically loaded bone

The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system （LCS） is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching （FRAP） approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis （FEA） approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional （3D） linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform （FEBio） to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces （shear and drag forces） for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.

Determination of groundwater solute transport parameters in finite element modelling using tracer injection and withdrawal testing data

The groundwater tracer injection and withdrawal tests are often carried out for the determination of aquifer solute transport parameters.However,the parameter analyses encounter a great difficulty due to the radial flow nature and the variability of the temporal boundary conditions.An adaptive methodology for the determination of groundwater solute transport parameters using tracer injection and withdrawal test data had been developed and illustrated through an actual case.The methodology includes the treatment of the tracer boundary condition at the tracer injection well,the normalization of tracer concentration,the groundwater solute transport finite element modelling and the method of least squares to optimize the parameters.An application of this methodology was carried out in a field test in the South of Hanoi city.The tested aquifer is Pleistocene aquifer,which is a main aquifer and has been providing domestic water supply to the city since the French time.Effective porosity of 0.31,longitudinal dispersivity of 2.2 m,and hydrodynamic dispersion coefficients from D=220 m^(2)/d right outside the pumping well screen to D=15.8 m^(2)/d right outside the tracer injection well screen have been obtained for the aquifer at the test site.The minimal sum of squares of the differences between the observed and model normalized tracer concentration is 0.00119,which is corresponding to the average absolute difference between observed and model normalized concentrations of 0.0355(while 1 is the worst and 0 is the best fit).