Model Of Ion Transport Research Articles

Investigation of the performance determinants in the treatment of arsenic-contaminated water by continuous electrodeionization

Abstract Arsenic is one of the most toxic elements which cause serious human health problems with even a little amount in water. This study investigated the pentavalent arsenic anion (HAsO42−) removal from water using continuous electrodeionization (CEDI). CEDI is a hybrid separation process of electrodialysis and ion exchange process that removes ionized species from liquids using electrical potential. The arsenics removal behavior with the change in the system condition was investigated under the programmed cell potential. Potentials from 0.8 to 5.2 V by 0.2 V step change were introduced with three-hour retention time to investigate the cell saturation level. At each potential step, conductivity, ion concentration, and pH of each compartment of CEDI stack were analyzed together to develop an ion transport and ion exchange model. Under the fixed feed condition, three major parameters, the resin saturation level, the cell voltage, and the age of a cell, affected the removal efficiency of the CEDI operation. The relationship among the factors are entangled, and they have a complex impact on ion removal efficiency. This study proposes ion drain rate (IDR) as an important indicator of the electroregeneration state. The system response to the voltage change was classified into five types by observing the IDR value in the concentrate stream and the conductivity in the diluate stream. While the system showed the highest ion removal efficiency under a high voltage, a low cell age, and a low saturation level condition, the three factors are complementary to one another.

Conductivity Modulation of Gold Thin Film at Room Temperature via All-Solid-State Electric-Double-Layer Gating Accelerated by Nonlinear Ionic Transport.

We demonstrated the field-effect conductivity modulation of a gold thin film by all-solid-state electric-double-layer (EDL) gating at room temperature using an epitaxially grown oxide fast lithium conductor, La2/3-xLi3xTiO3 (LLT), as a solid electrolyte. The linearly increasing gold conductivity with increasing gate bias demonstrates that the conductivity modulation is indeed due to carrier injection by EDL gating. The response time becomes exponentially faster with increasing gate bias, a result of the onset of nonlinear ionic transportation. This nonlinear dynamic response indicates that the ionic motion-driven device can be much faster than would be estimated from a linear ionic transport model.

Determination of Ion Channel and Pump Fluxes for Chinese Hamster Ovary Cells using Rubidium Uptake Measurement

Cells expend a significant portion of their energy and have considerable apparatus to control the flow ions across the cell membrane. Ions concentrations have also been demonstrated to be important to processes such as apoptosis and implicated in monitoring cells metabolism for biopharmaceutical production. Accurate quantitative modelling of ion transport is challenging since the densities of ion channels and pumps are known for relatively few cells. In this work the ion channels and pumps fluxes for CHO cells were estimated using Rubidium uptake measurements combined with Ouabain inhibition of pumps.Attached CHO cells were incubated in a buffer containing 5.4 mM Rb and in some cases Ouabain was also added to the buffer in different concentrations over a period of two hours to inhibit the Na+-K+ ATPase pump to study passive and active ion fluxes across the membrane.Using Inductively Coupled Plasma Optical Emission Spectrometry, the Rb content of the lysed cells after two hours of incubation was 10.6 mg/L, which is a result of Rb transfer through the channels and pumps. From this, the Rb flux through the active and passive pathways is estimated to be 8.5×10−12 mol.cm−2.s−1.The Rb entry through the diffusion pathway was estimated using Ouabain to inhibit the Na+-K+ ATPase activity. With 5 mM concentration of Ouabain the inhibition was maximized and the Rb uptake is reduced by 80% compared to the control. From this result the Rb flux through the channels is estimated to be 2.8×10−12 mol.cm−2.s−1.The obtained results were used in temporal ion concentration simulations using methodology of Hernandez 2000. These simulations are in agreement with the work where ion pumps were inhibited via ATP production inhibition in Mitochondria using Oligomycin (B. Saboktakin Rizi, Biomicrofluidics, 2014).

Effective Ion Diffusion in Charged Nanoporous Materials

Multiscale models of ion transport in porous media relate microscopic material properties (e.g., pore size distribution and pore connectivity) to their macroscopic counterparts (e.g., porosity, effective diffusion coefficient and effective electrical conductivity). We derive a macroscopic model of ion transport in electrically charged nanoporous materials, and the corresponding effective diffusion coefficient, electric conductivity and transference numbers, that explicitly account for dynamic changes in electrical double layer (EDL) and possible overlap of EDLs in nanopores. The general equations comprising this model reduce to a model of an electrical double layer capacitor (EDLC) used to interpret measurements of the EDLC voltage response to charging. While the original representation relies on empirical coefficients (e.g., Bruggeman’s relation), our effective coefficients are derived from the first principles and vary with a range of electrochemical conditions (e.g., initial concentration of ions in the electrolyte). The resulting model predictions of the EDLC voltage response match the experimental data better than the original model does.

Improving the Lithium Ion Transport in Polymer Electrolytes by Functionalized Ionic-Liquid Additives: Simulations and Modeling

We present a theoretical study combining molecular dynamics (MD) simulations with an analytical lithium ion transport model [Maitra and Heuer, Phys. Rev. Lett. 2007, 98, 227802] to highlight a novel strategy to increase the lithium mobility in polymer electrolytes based on poly(ethylene oxide) (PEO). This is achieved by using a pyrrolidinium-based ionic liquid (IL) where the cation has been chemically functionalized by a short oligoether side chain [von Zamory et al., Phys. Chem. Chem. Phys. 2016, 18(31), 21539] as an additive. Since the oligoether moieties at the pyrrolidinium cations form pronounced coordinations to the lithium ions for sufficiently long side chains, the ions can be detached from the PEO backbone. In this way, a fundamentally new lithium ion transport mechanism is established (shuttling mechanism), in which the lithium dynamics is decoupled from the polymer dynamics, the latter typically being slow under experimental conditions. Based on our simulations, we incorporate this novel mechanism into our existing model, which accurately reproduces the observed lithium dynamics. We demonstrate that the use of oligoether-functionalized IL additives significantly increases the lithium diffusivity. Finally, we show that for experimentally relevant electrolytes containing long polymer chains, an even stronger increase of the lithium mobility can be expected.

Ionic transport and barrier effect of anodic oxide layer in a solid-state Al2O3 capacitor under high electric field

Dry anodic oxidation as an effective electrical self-healing method in a solid-state Al2O3 capacitor was investigated in terms of ionic transport study. Sol-gel-derived amorphous aluminum oxide (AmAO) film as dielectric and aluminum (Al) film as top electrode of the capacitor were prepared on platinized silicon substrates. When a negative voltage was applied to the Al electrode pad, the ionic transport would induce the failure of the Al electrode. Nevertheless, such failure could be inhibited by the barrier effect of an anodic aluminum oxide (AAO) layer formed at the Al/AmAO interface when positive voltage was applied to the Al electrode pad previously. The barrier effect of the AAO layer was controlled by the maximum applied positive voltage. An ionic transport model was proposed to explore the dry anodic oxidation in the solid-state Al2O3 capacitor.

Computational modeling of epithelial fluid and ion transport in the parotid duct after transfection of human aquaporin-1.

Following transfection of aquaporin into the parotid ducts of minipigs with salivary hypofunction, the resulting increase in salivary flow rates contradicts current understanding of ductal fluid transport. We show that the change in saliva electrochemistry and flow rate can be explained by changes in expression of ion transporters in the ductal cell membranes, using a mathematical model replicating a single parotid duct.

Can the Transport Properties of Molten Salts and Ionic Liquids Be Used To Determine Ion Association?

There have long been arguments supporting the concept of ion association in molten salts and ionic liquids, largely based on differences between the conductivity and that predicted from self-diffusion coefficients by the Nernst-Einstein equation for noninteracting ions. It is known from molecular dynamics simulations that even simple models based on charged hard spheres show such a difference due to the (anti)-correlation of ion motions. Formally this is expressed as a difference between the velocity cross-correlation coefficient of the oppositely charged ions and the mean of those for the two like-charged ions. This article examines molten salt and ionic liquid transport property data, comparing simple and model associated salts (ZnCl2, PbCl2, and TlCl) including weakly dissociated molecular liquids (H2O, HCOOH, H2SO4). Analysis employing Laity resistance coefficients (rij) shows that the common ion-association rationalization is flawed, consistent with recent direct measurements of the degree of ionicity in ionic liquid chlorides and with theoretical studies. However, the protic ionic liquids [PyrOMe][BF4] and [DBUH][CH3SO3] have larger than usual NE deviation parameters (>0.5), and large negative like-ion rii, analogous to those of ZnCl2. Structural, spectroscopic, and theoretical studies are suggested to determine whether these are indeed genuine examples of association.

Ion transport in the zebrafish kidney from a human disease angle: possibilities, considerations, and future perspectives.

Unique experimental advantages, such as its embryonic/larval transparency, high-throughput nature, and ease of genetic modification, underpin the rapid emergence of the zebrafish (Danio rerio) as a preeminent model in biomedical research. Particularly in the field of nephrology, the zebrafish provides a promising model for studying the physiological implications of human solute transport processes along consecutive nephron segments. However, although the zebrafish might be considered a valuable model for numerous renal ion transport diseases and functional studies of many channels and transporters, not all human renal electrolyte transport mechanisms and human diseases can be modeled in the zebrafish. With this review, we explore the ontogeny of zebrafish renal ion transport, its nephron structure and function, and thereby demonstrate the clinical translational value of this model. By critical assessment of genomic and amino acid conservation of human proteins involved in renal ion handling (channels, transporters, and claudins), kidney and nephron segment conservation, and renal electrolyte transport physiology in the zebrafish, we provide researchers and nephrologists with an indication of the possibilities and considerations of the zebrafish as a model for human renal ion transport. Combined with advanced techniques envisioned for the future, implementation of the zebrafish might expand beyond unraveling pathophysiological mechanisms that underlie distinct genetic or environmentally, i.e., pharmacological and lifestyle, induced renal transport deficits. Specifically, the ease of drug administration and the exploitation of improved genetic approaches might argue for the adoption of the zebrafish as a model for preclinical personalized medicine for distinct renal diseases and renal electrolyte transport proteins.

Evidences for redox reaction driven charge transfer and mass transport in metal-assisted chemical etching of silicon.

In this work, we investigate the transport processes governing the metal-assisted chemical etching (MacEtch) of silicon (Si). We show that in the oxidation of Si during the MacEtch process, the transport of the hole charges can be accomplished by the diffusion of metal ions. The oxidation of Si is subsequently governed by a redox reaction between the ions and Si. This represents a fundamentally different proposition in MacEtch whereby such transport is understood to occur through hole carrier conduction followed by hole injection into (or electron extraction from) Si. Consistent with the ion transport model introduced, we showed the possibility in the dynamic redistribution of the metal atoms that resulted in the formation of pores/cracks for catalyst thin films that are ≲30 nm thick. As such, the transport of the reagents and by-products are accomplished via these pores/cracks for the thin catalyst films. For thicker films, we show a saturation in the etch rate demonstrating a transport process that is dominated by diffusion via metal/Si boundaries. The new understanding in transport processes described in this work reconcile competing models in reagents/by-products transport, and also solution ions and thin film etching, which can form the foundation of future studies in the MacEtch process.

Measurement of the refractive index of electrically poled soda-lime glass layers using leaky modes.

Electrically poled layers have been formed in soda-lime glass using graphite electrodes in air. The refractive index and thickness of the poled glass layers have been measured by the analysis of leaky optical modes. These modes are supported by the poled layer and can be determined by analysis of the optical reflectivity measured with a prism coupler arrangement. A relatively constant refractive index of ∼1.486 in the poled glass region is measured, which is ∼0.03 below the substrate index. The reflectivity data shows that the transition between poled and unpoled glass is very sharp and is consistent with ion transport models. The thickness of the poled glass region is consistent with the removal of Na+ and K+ ions from the poled region. The index and depth data are confirmed by interferometric measurements. The tensile stress in the poled glass layer is also estimated from optical birefringence measurements and is estimated to be ∼0.3 GN/m2.

A microscopic investigation of ion and electron transport in lithium-ion battery porous electrodes using the lattice Boltzmann method

Improving the cycle life and reliability of a battery is an important issue in lithium-ion battery (LIB) applications. Except for the material properties of the battery electrodes, the morphological features of LIBs also have a great influence on battery performance. In order to identify the relation between the morphological features of the electrodes and the macroscopic battery performance, a two-dimensional (2D) lattice Boltzmann model of ion and electron transport within LIB porous electrodes is presented in this study. The proposed model is superior to previous finite element method (FEM)-based models by providing a more convenient geometry generation process and a more efficient calculation technique. In the simulation, the lattice Boltzmann method (LBM) is utilized to solve the governing equations for ion and electron transport. The quartet structure generation set (QSGS) is employed to generate the electrode geometry with circular particles. The effects of the electrode micro-structure on the local concentration distribution, electric potential, and macroscopic discharge performance are investigated. Results show that the LBM is an optional approach in solving problems related to mass transport and electrochemical reactions. For the electrode particles, the obvious variations in local lithium concentration and electric potential prove that the electrode microstructure can influence the microscopic lithium transport; specifically, the lithium exchange is improved for smaller particle sizes. As for discharge performance, larger discharge depth can be achieved by a smaller cathode particle size and a larger cathode porosity. Meanwhile, a larger anode particle size and a smaller anode porosity both contribute to a larger discharge depth.

Nernst\u2013Planck modeling of multicomponent ion transport in a Nafion membrane at high current density

A mathematical model of multicomponent ion transport through a cation-exchange membrane is developed based on the Nernst–Planck equation. A correlation for the non-linear potential gradient is derived from current density relation with fluxes. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface, taking into account the convective flow. Effective diffusivities are used in the model based on the correlation of tortuosity and ionic diffusivities in free water. The model predicts the effect of an increase in current density on the ion concentrations inside the membrane. The model is fitted to the previously published experimental data. The effect of current density on the observed increase in voltage drop and the decrease in permselectivity has been analyzed using the available qualitative membrane swelling theories. The observed non-linear behavior of the membrane voltage drop versus current density can be explained by an increase in membrane pore diameter and an increase in the number of active pores. We show how the membrane pore diameter increases and dead-end pores open up when the current density is increased.Graphical

Investigation of Triple-Phase Boundary Region in Partially Immersed Pt Segmented Electrode As a Model Electrode of Air Electrodes for Metal-Air Secondary Batteries

Introduction There has been increasing interest in metal-air secondary batteries such as Zn-air secondary batteries and Fe-air secondary batteries. These batteries are expected to have high energy density and light weight since they can utilize ambient air as their cathode material. They are also expected to satisfy high safety standard because they can utilize non-flammable aqueous electrolyte. Therefore, metal-air secondary batteries are attractive power sources for large energy storage systems. However, large overpotential of air electrode hinders their widely use. In air electrode, the electrochemical reactions, oxygen reduction and oxygen evolution, only occur at the regions where the three different species, the electron, the electrolyte and the oxygen, can be transported, so-called triple-phase boundary (TPB) region. Therefore, observation of its property can lead to some improvement of the large overpotential. However, it is difficult to investigate the property of the TPB region using practical gas-diffusion electrodes, because their microstructure is too complicated to be analyzed in detail. Therefore, partially immersed electrode system has been applied for the investigation of the property of TPB region[1 - 3]. In these systems, mass transport of the gases and ions in the gas diffusion electrodes can be simulated. Previously, we have investigated current distributions in TPB region using partially immersed Pt segmented electrode (Fig. 1)[3]. In this research, we measure local ionic resistance of TPB regions using the electrode so as to investigate the basic properties of TPB region. Experimental Electrochemical two- or three-electrode cells were used for electrochemical measurements. In the two-electrode configuration, each platinum segment was used as working and counter electrode. In the three-electrode configuration, Pt segment, Pt wire and Hg, HgO electrode (Hg/HgO) were used as working, counter and reference electrodes, respectively. Solutions of 0.10 mol dm- 3 KOH (saturated with O2 or Ar ) was used as an electrolyte solution. We carried out AC-impedance measurement as electrochemical measurement. Before the measurement, we fully immersed Pt-supporting area of the segmented electrode (h = 0 mm) and vertically raised the micrometer head to h = 10 mm. Results and discussion First, we measured AC-impedance between 3 CH and upper segments in order to characterize thin liquid film on the electrode. Solution resistance (Rsol) between the segments showed linear behaviors. This means that cross-sectional area of the film was not changed with the heights. From the slopes and the ionic conductivities of KOH solutions, the cross-sectional area of the thin liquid film was estimated at 5.3 ± 0.1 × 10- 3 cm2 [4]. Second, we investigated local ionic resistance variations with oxygen reduction reaction (ORR). When ORR is occurred, electrode potential is decreased and OH- is transported through the film. Therefore, we investigated local ionic resistance variations with both electrode potential and ionic current in the film. For the investigations of the effects of electrode potential, we measured impedance of 5 CH at various electrode potentials using the three-electrode cell configuration under Ar atmosphere. We found that the electrode potential hardly affected the impedance. In the case of ionic current, we carried out AC impedance measurement between 5 and 6 CH under oxygen atmosphere while performing cathodic galvanostatic measurements using 7 ~ 10 CH and Pt wire as working and counter electrode respectively. Figure 2 shows variation of Rsol with cathodic galvanostatic current. We can see that the ionic resistance decreased with the decrease of the DC-current. It was proposed by Bennion et al. that OH- was concentrated in the film during ORR[1]. Therefore, we simulate the KOH concentration and the ionic resistance of the thin film using ion transport model constructed by Bennion et al. We can see in Fig. 2 that the simulated resistances show good agreement with measured ones. This result shows that we have successfully measured OH- concentration gradient predicted by Bennion et al. as ionic resistance. Reference D. N. Bennion, C. W. Tobias, J. Electrochem. Soc., 113, 593 (1966).A. Ikezawa, K. Miyazaki, T. Fukutsuka, T. Abe., J. Electrochem. Soc., 162, A1646 (2015).A. Ikezawa, K. Miyazaki, T. Fukutsuka, T. Abe., ECS meeting abstracts, MA2014-02, abstract 32 (2014).R. J. Gilliam, J. W. Graydon, D. W. Kirk, S. J. Thorpe, Int. J. Hydrogen Energy, 32, 359 (2007). Figure 1

Determination of Physico-Chemical Parameters for Simulation of Lithium Ion Batteries

For understanding of existing battery systems such as lithium-ion batteries and for the development of future battery systems, advanced numerical simulation tools are important. One beneficial aspect of computational methods is that they can provide insight into physical and chemical aspects, which sometimes cannot be probed by experimental methods. Accuracy and reliability are key issues for such numerical simulations and depend on appropriate physical models, boundary conditions, and accurately determined physico-chemical parameters1. For numerical simulations of battery systems, the ion-transport model for concentrated electrolyte solutions introduced by Newman and Thomas-Alyea is frequently used and depends on three ion transport parameters, namely the conductivity, the transference number and the binary diffusion coefficient. In addition to the transport parameters, the thermodynamic factor which is derived from the mean molar activity coefficient is required for the correct description of the thermodynamic behavior of a binary electrolyte solution. Since the microscopic geometry of actually used porous electrodes and separators are largely unknown, a homogenization approach is applied for the macroscopic description of porous media. In this case, the influence of the microstructure on the macroscopic behavior is modelled by additional geometric parameters such as the porosity ε and the tortuosity τ. For an accurate description of the interface reactions the intercalation and deintercalation kinetics have to be known, often described by a Butler-Volmer behavior. Lastly solid state diffusion of lithium ions within the active materials may limit the battery performance, especially at high charge and discharge currents. A vast spectrum of physico-chemical parameters can be found in the literature (e.g., Valoen and Reimers2), but since the investigated electrolytes and the experimental techniques differ from study to study, it is difficult to find a consistent parameter set for a given electrolyte. In addition, some of the parameters are often fitted to match experimental performance data and may thus be fitting parameters rather than intrinsic physico-chemical parameters with predictive capability. We will present an overview of the necessary physico-chemical parameters for simulation of lithium ion battery performance and will show methods by which they can be measured rigorously. For example, novel methods will be shown with which one can determine transport, thermodynamic and geometrical properties like for instance the transference number, the thermodynamic factor and the separator and electrode tortuosity3-5. Figure 1 exemplarily shows one of those results, namely the determination of electrode tortuosities based on impedance spectroscopy measurements in symmetrical cells. Our concentration and temperature dependent studies of physico-chemical parameters as well as the methodology for their unambiguous deter-mination will allow for an improved correlation between lithium ion battery experiments and simulations. More importantly, the use of intrinsic physico-chemical paramters will enable predictive simulations rather than data fitting models, which helps in understanding as well as predicting present and future lithium ion battery technologies. Figure 1: Comparison of determined tortuosities for different electrodes at porosities between 30% and 35% and comparison with the tortuosity obtained by the commonly used Bruggeman estimate (τ=ε -0.5). Acknowledgements We gratefully acknowledge the funding by the Bavarian Ministry of Economic Affairs and Media, Energy, and Technology for its financial support under the auspices of the EEBatt project.

Effects of energetic particle phase space modifications by instabilities on integrated modeling

Tokamak plasmas can feature a large population of energetic particles (EP) from neutral beam injection or fusion reactions. In turn, energetic particles can drive instabilities, which affect the driving EP population leading to a distortion of the original EP distribution function and of quantities that depend on it. The latter include, for example, neutral beam (NB) current drive and plasma heating through EP thermalization. Those effects must be taken into account to enable reliable and quantitative simulations of discharges for present devices as well as predictions for future burning plasmas. Reduced models for EP transport are emerging as an effective tool for long time-scale integrated simulations of tokamak plasmas, possibly including the effects of instabilities on EP dynamics. Available models differ in how EP distribution properties are modified by instabilities, e.g. in terms of gradients in real or phase space. It is therefore crucial to assess to what extent different assumptions in the transport models affect predicted quantities such as EP profile, energy distribution, NB driven current and energy/momentum transfer to the thermal populations. A newly developed kick model, which includes modifications of the EP distribution by instabilities in both real and velocity space, is used in this work to investigate these issues. Coupled to TRANSP simulations, the kick model is used to analyze NB-heated NSTX and DIII-D discharges featuring unstable Alfvén eigenmodes (AEs). Results show that instabilities can strongly affect the EP distribution function, and modifications propagate to macroscopic quantities such as NB-driven current profile and NB power transferred to the thermal plasma species. Those important aspects are only qualitatively captured by simpler fast ion transport models that are based on radial diffusion of energetic ions only.

Modeling of ion transport through a porous separator in vanadium redox flow batteries

Abstract In this work, we develop a two-dimensional, transient model to investigate the mechanisms of ion-transport through a porous separator in VRFBs and their effects on battery performance. Commercial-available separators with pore sizes of around 45 nm are particularly investigated and effects of key separator design parameters and operation modes are explored. We reveal that: i) the transport mechanism of vanadium-ion crossover through available separators is predominated by convection; ii) reducing the pore size below 15 nm effectively minimizes the convection-driven vanadium-ion crossover, while further reduction in migration- and diffusion-driven vanadium-ion crossover can be achieved only when the pore size is reduced to the level close to the sizes of vanadium ions; and iii) operation modes that can affect the pressure at the separator/electrode interface, such as the electrolyte flow rate, exert a significant influence on the vanadium-ion crossover rate through the available separators, indicating that it is critically important to equalize the pressure on each half-cell of a power pack in practical applications.

Modeling Root Zone Effects on Preferred Pathways for the Passive Transport of Ions and Water in Plant Roots.

We extend a model of ion and water transport through a root to describe transport along and through a root exhibiting a complexity of differentiation zones. Attention is focused on convective and diffusive transport, both radially and longitudinally, through different root tissue types (radial differentiation) and root developmental zones (longitudinal differentiation). Model transport parameters are selected to mimic the relative abilities of the different tissues and developmental zones to transport water and ions. For each transport scenario in this extensive simulations study, we quantify the optimal 3D flow path taken by water and ions, in response to internal barriers such as the Casparian strip and suberin lamellae. We present and discuss both transient and steady state results of ion concentrations as well as ion and water fluxes. We find that the peak in passive uptake of ions and water occurs at the start of the differentiation zone. In addition, our results show that the level of transpiration has a significant impact on the distribution of ions within the root as well as the rate of ion and water uptake in the differentiation zone, while not impacting on transport in the elongation zone. From our model results we infer information about the active transport of ions in the different developmental zones. In particular, our results suggest that any uptake measured in the elongation zone under steady state conditions is likely to be due to active transport.

Numerical Analysis of the Source of Excessive Na+ and Cl- Species in Flowback Water From Hydraulically Fractured Shale Formations

Summary Fracture fluid is composed of fresh water, proppant, and a small percentage of other additives, which support the hydraulic-fracturing process. Excluding situations in which flowback water is recycled and reused, the total dissolved solids in fracture fluid is limited to the fluid additives, such as potassium chloride (1 to 7 wt% KCL), which is used as a clay stabilizer to minimize clay swelling and clay-particle migration. However, the composition of recovered fluid, especially as it relates to the total dissolved solids (TDS), is always substantially different from the injected fracture fluid. The ability to predict flowback-water volume and composition is useful when planning for the management or reuse of this aqueous byproduct stream. In this work, an ion-transport and halite-dissolution model was coupled with a fully implicit, dual-porosity, numerical simulator to study the source of the excess solutes in flowback water and to predict the concentration of both Na+ and Cl− species seen in recovered water. The results showed that mixing alone, between the injected fracture fluid and concentrated in-situ formation brine, could not account for the substantial rise in TDS seen in flowback water. Instead, the results proved that halite dissolution is a major contributor to the change in TDS seen in fracture fluid during injection and recovery. Halite dissolution can account for as much as 81% of Cl− and 86.5% of Na+ species seen in 90-day flowback water; mixing, between the injected fracture fluid and in-situ concentrated brine, accounts for approximately 19% of Cl− and 13% of Na+.

Poisson–Nernst–Planck model of multiple ion transport across an ion-selective membrane under conditions close to chlor-alkali electrolysis

The assumption of electrochemical equilibrium at membrane–electrolyte interfaces is frequently accepted in a mathematical simulation of multiple ion transport (MIT) across a single-layer perfluorinated sulfonated cation-selective membrane (CM). This assumption is obviously inaccurate at high electric current loads typical of industrial applications, e.g. brine electrolysis. An assessment of this problem is one of the main objectives of this contribution. For this purpose, a one-dimensional stationary Poisson–Nernst–Planck (PNP) model was employed to describe MIT across a CM. The model input parameters used correspond closely to industrial chlor-alkali electrolysis. The model results are compared with those of an equivalent model published earlier that considered the classical Nernst–Planck equation and Donnan equilibrium at the CM–electrolyte interfaces (denoted as the DNP model). Both the DNP and the PNP models provide identical results at low current loads. However, a comparison at high current loads close to ‘industrial scale’ was impossible due to convergence problems of the DNP model. The ion transport numbers and membrane permselectivity were estimated by means of the PNP model. This model predicts conditions at the membrane interfaces close to thermodynamic equilibrium even in a current density range up to 10,000 A m−2. Additionally, the PNP model takes into account the kinetics of water autoprotolysis. It was shown that a high flux of OH− ions across a CM effectively alkalizes the catholyte diffusion layer, ensuring a precipitation of alkaline earth cations outside the CM and thus minimizing internal CM blockage.