Aqueous Mixed Electrolyte Solutions Research Articles

Reflection coefficient of a natural sodium bentonite in aqueous mixed electrolyte solutions: positive and negative anomalous osmosis

A natural sodium bentonite was tested in the laboratory to measure its reflection coefficient, ω, in equilibrium with mixed aqueous solutions of sodium chloride (NaCl) and potassium chloride (KCl), with the aim of assessing the relative contribution of chemico-osmosis and diffusion induced electro-osmosis to the non-hydraulic component of the liquid flux in the presence of two cationic species, which diffuse at different rates in the pore solution. The former chemico-osmotic contribution is only related to the ionic partition effect in the bentonite pores, and causes ω to vary in the 0 to 1 range, whereas the latter electro-osmotic contribution is controlled by the diffusion potential, which spontaneously builds up across the bentonite layer in response to the different aqueous-phase diffusion coefficients of the ionic species. The theoretical interpretation of the obtained test results demonstrated that chemico-osmosis was the major contribution to ω when the testing solutions only comprised KCl. However, significant deviations in the values of ω from those expected for pure chemico-osmosis were observed for mixtures of NaCl and KCl, with both negative ( ω = −1.234) and positive ( ω = 1.040) anomalous values of the reflection coefficient, resulting from the enhanced influence of diffusion induced electro-osmosis.

Improving gas dispersion and decreasing bubble size in saline water with oscillatory air supply

The present paper describes gas dispersion in an air-sparged laboratory scale bubble column containing aqueous solutions of single electrolytes (NaCl, CaCl2, MgCl2, MgSO4, and AlCl3) and mixed electrolytes (NaCl-CaCl2 and NaCl-CaCl2-MgCl2-AlCl3) at different ionic strengths and air flow rates, with oscillatory air supply and conventional steady air supply, respectively. The gas dispersion was investigated by a light-scattering technique (turbidity measurement) and bubble size measurement. The oscillatory air supply was generated from steady air flow using a fast-switching solenoid valve and was characterized by measuring the pressure of the output air of the solenoid valve as a function of time. It was found that for each electrolyte solution tested, oscillatory air supply at a certain frequency and amplitude could give better gas dispersion than steady air supply, and the degree of improvement of gas dispersion varied with the electrolyte type and concentration and air flow rate. At each air supply mode tested, either the intensity of scattered light or the Sauter mean diameter of bubbles would scale with the ionic strength, following a decreasing trend. A cooperative effect of electrolyte addition and oscillatory air supply on gas dispersion was generally found. The combined effect of electrolyte addition and oscillatory air supply on bubble size was significant, being up to almost a 2/3 decrease in the Sauter mean diameter. The present work highlights the importance of flow condition for controlling bubble generation and coalescence in saline water and has significant implications for seawater flotation of minerals.

The role of diffusion induced electro-osmosis in the coupling between hydraulic and ionic fluxes through semipermeable clay soils

Most of the experimental research conducted to date has provided evidence on the semipermeable membrane behaviour of smectite-rich clay soils, the extent of which is typically quantified through the reflection coefficient, when the permeant (electrolyte) solution contains a single monovalent or divalent salt. Under such conditions, the osmotic flow of solution is controlled to a great extent by the different accessibility of ions and water molecules to the soil porosity, which is referred to as the chemico-osmotic effect. However, theoretical simulations of coupled solute and solvent transport suggest that, when two or more cations that diffuse in water at different rates are present simultaneously in the permeant solution, the electro-osmotic effect, which stems from the condition of null electric current density through the porous medium, can be enhanced compared to the case of a single salt to such an extent that it becomes comparable to or even greater than the chemico-osmotic effect. An original closed-form analytical solution to the problem of calculating the diffusion potential, which in turn controls the magnitude of the electro-osmotic effect, is here illustrated, and the relative importance of the aforementioned contributions to multi-electrolyte systems is examined through the interpretation of laboratory test results from the literature pertaining to a bentonite amended clay soil in equilibrium with aqueous mixtures of potassium chloride (KCl) and hydrochloric acid (HCl). The proposed mechanistic model is shown to be able to quantitatively capture the impact of both chemico-osmosis and electro-osmosis on the measured reflection coefficient of smectite clays, thereby breaking new ground in the experimental and theoretical research on the osmotic properties of engineered clay barriers in contact with mixed aqueous electrolyte solutions.

Competitive specific ion effects in mixed salt solutions on a thermoresponsive polymer brush

HypothesisGrafted poly(ethylene glycol) methyl ether methacrylate (POEGMA) copolymer brushes change conformation in response to temperature ('thermoresponse'). In the presence of different ions the thermoresponse of these coatings is dramatically altered. These effects are complex and poorly understood with no all-inclusive predictive theory of specific ion effects. As natural environments are composed of mixed electrolytes, it is imperative we understand the interplay of different ions for future applications. We hypothesise anion mixtures from the same end of the Hofmeister series (same-type anions) will exhibit non-additive and competitive behaviour. ExperimentsThe behaviour of POEGMA brushes, synthesised via surface-initiated ARGET-ATRP, in both single and mixed aqueous electrolyte solutions was characterised with ellipsometry and neutron reflectometry as a function of temperature. FindingsIn mixed fluoride and chloride aqueous electrolytes (salting-out ions), or mixed thiocyanate and iodide aqueous electrolytes (salting-in ions), a non-monotonic concentration-dependent influence of the two anions on the thermoresponse of the brush was observed. A new term, δ, has been defined to quantitively describe synergistic or antagonistic behaviour. This study determined the specific ion effects imparted by salting-out ions are dependent on available solvent molecules, whereas the influence of salting-in ions is dependent on the interactions of the anions and polymer chains.

Correlation and prediction of surface tension in single and mixed aqueous electrolyte solutions based on the mean ionic activity coefficient: A comparative analysis of Pitzer, E-NRTL and E-UNIQUAC models

Li and Lu's model to calculate the surface tension of single and mixed aqueous electrolyte solutions, coupled with Pitzer, e-NRTL and e-UNIQUAC activity coefficient models, is critically evaluated in this paper. Parameters of these activity coefficient models were taken from vapor-liquid equilibrium data available in the literature. The effect of the mean ionic activity coefficient model on the surface tension calculation is investigated in order to obtain low deviations from experimental data with emphasis on salt reservoir applications. An evaluation is made of the magnitude of the percentage surface tension increment relative to the surface tension of pure water, which occurs due to an increase in salt concentration. The feasibility of interpolation and extrapolation of the surface tension model with respect to the temperature was investigated for single electrolyte solutions at several temperatures. A sensitivity analysis of the initial guesses of the Li and Lu's model when adjusting the model parameters was performed. A new approach is also proposed to estimate the Pitzer parameters for some systems. This study explores the Li and Lu's model as never found in the literature before and is generally able to provide more accurate surface tension calculations compared with previous works. The results show that for single electrolyte solutions, the Pitzer and e-NRTL models provide similar deviations with an overall AAPD of 0.49%. For mixed electrolyte solutions, the e-NRTL model performed better than the Pitzer and e-UNIQUAC, providing an overall AAPD of 0.42%. The simulated increments of surface tension due to addition of salt are in accordance with the literature. The sensitivity analysis demonstrates the relevance of well adjusting the initial guesses for parameter estimation. Interpolation and extrapolation analysis yielded quite acceptable deviations with all overall AAPDs lower than 1.40% and also indicated that e-NRTL model is the most accurate. The proposed approach to fit the Pitzer model parameters provided an average deviation of 0.75%.

Modified McKay–Perring Equation and Its Two Particular Solutions

Zdanovskii’s rule is the simplest isopiestic molality relation of mixed electrolyte aqueous solutions and the McKay–Perring equation is a differentio-integral equation particularly suitable for calculating solute activity coefficients from isopiestic measurements. However, they have two unsolved problems, which have puzzled solution chemists for several decades: (1) Zdanovskii’s rule has been verified by precise isopiestic measurements. But, several scientists suggested that the rule contradicts the Debye–Huckel limiting law for extremely dilute unsymmetrical mixtures. (2) In the McKay–Perring equation, a solute activity coefficient is multiplied by a solute composition variable. Different scientists have suggested that the composition variable may be the total ionic strength, common ion concentration, total ionic concentration, or an additive function with arbitrary proportionality constants. But, the different choices of the composition variable may lead to different activity coefficient results. Here, I derive a modified McKay–Perring equation in which the composition variable has the exclusive physical meaning of total ionic concentration for mixed electrolyte solutions (or of total solute particle concentration for the mixed solutions containing nonelectrolyte solutes). I also demonstrate that Zdanovskii’s rule is consistent with the Debye–Huckel limiting law for extremely dilute unsymmetrical mixtures. I derive two particular solutions of the modified McKay–Perring equation: one for the systems obeying Zdanovskii’s rule and another for the systems obeying a limiting linear concentration rule. These theoretical results have been verified with literature experiments and model calculations.

Poisson-Fermi modeling of ion activities in aqueous single and mixed electrolyte solutions at variable temperature.

The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-Hückel models to calculate activity coefficients of aqueous mixtures of the most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-Hückel theory that does not take steric and correlation effects of ions and water into account. By contrast, the Poisson-Fermi theory developed in recent years treats ions and water molecules as nonuniform hard spheres of any size with interstitial voids and includes ion-water and ion-ion correlations. We present a Poisson-Fermi model and numerical methods for calculating the individual or mean activity coefficient of electrolyte solutions with any arbitrary number of ionic species in a large range of salt concentrations and temperatures. For each activity-concentration curve, we show that the Poisson-Fermi model requires only three unchanging parameters at most to well fit the corresponding experimental data. The three parameters are associated with the Born radius of the solvation energy of an ion in electrolyte solution that changes with salt concentrations in a highly nonlinear manner.

The PVTx properties of aqueous electrolyte solutions containing Li+, Na+, K+, Mg2+, Ca2+, Cl− and SO42− under conditions of CO2 capture and sequestration

Based on the Pitzer electrolyte theory, an accurate density model of binary sulfate-water systems (Li2SO4-H2O, Na2SO4-H2O, K2SO4-H2O and MgSO4-H2O) has been established. Corresponding model parameters are obtained by the least square method. Compared with reliable experimental data of the Li2SO4-H2O, Na2SO4-H2O, K2SO4-H2O and MgSO4-H2O systems, the average density deviations are 0.046%, 0.036%, 0.051%, 0.038%, respectively, which are within or close to experimental uncertainties. Combined a simple mixing rule with the density models of binary sulfate-water systems and previous chloride-water systems (LiCl-H2O, NaCl-H2O, KCl-H2O, MgCl2-H2O and CaCl2-H2O), a predictive density model is proposed for aqueous mixed electrolyte solutions containing Li+, Na+, K+, Mg2+, Ca2+, Cl− and SO42− under conditions of CO2 capture and sequestration (CCS) (generally less than 473 K and 300 bar). Compared to experimental density data of multi-component water-salt systems, the average density deviation of each system is usually less than 0.1%. The model can be used to calculate the apparent molar volume at infinite dilution and the volumetric properties of CO2-bearing multi-component electrolyte solutions under the CCS conditions. A computer code for the volumetric properties of multi-component aqueous electrolyte solutions can be obtained from the corresponding author.

Extrapolation of surface tensions of electrolyte and associating mixtures solutions

A new surface tension model is proposed, based on the Gibbs phenomenological surface-phase method, coupled with Ion-based Statistical Associating Fluid Theory (Ion-based SAFT2). The model was used to extrapolate the surface tensions of aqueous electrolyte solutions and mixed electrolyte solutions, as well as systems of associating mixtures at different temperatures and concentrations, and was found to give good agreement with experimental data from the literature.

Rigorous modeling of gypsum solubility in Na–Ca–Mg–Fe–Al–H–Cl–H2O system at elevated temperatures

Precipitation and scaling of calcium sulfate have been known as major problems facing process industries and oilfield operations. Most scale prediction models are based on aqueous thermodynamics and solubility behavior of salts in aqueous electrolyte solutions. There is yet a huge interest in developing reliable, simple, and accurate solubility prediction models. In this study, a comprehensive model based on least-squares support vector machine (LS-SVM) is presented, which is mainly devoted to calcium sulfate dihydrate (or gypsum) solubility in aqueous solutions of mixed electrolytes covering wide temperature ranges. In this respect, an aggregate of 880 experimental data were gathered from the open literature in order to construct and evaluate the reliability of presented model. Solubility values predicted by LS-SVM model are in well accordance with the observed values yielding a squared correlation coefficient (R 2) of 0.994. Sensitivity of the model for some important parameters is also checked to ascertain whether the learning process has succeeded. At the end, outlier diagnosis was performed using the method of leverage value statistics to find and eliminate the falsely recorded measurements from assembled dataset. Results obtained from this study indicate that LS-SVM model can successfully be applied in predicting accurate solubility of calcium sulfate dihydrate in Na---Ca---Mg---Fe---Al---H---Cl---H2O system over temperatures ranging from 283.15 to 371.15 K.

Volumetric Properties of Mixed Electrolyte Aqueous Solutions at Elevated Temperatures and Pressures. The System KCl–NaCl–H2O to 523.15 K, 40 MPa, and Ionic Strength from (0.1 to 5.8) mol·kg–1

The densities of KCl–NaCl aqueous mixtures were determined at temperatures from (298.15 to 523.15) K, pressures up to 40 MPa, and over a range of compositions at ionic strengths from (0.1 to 5.8) mol·kg–1. A vibrating-tube densimeter used for the experimental measurements provides the accuracy on density better than 2·10–4 g·cm–3. The mean apparent molar volumes of the mixed electrolytes, Vmeanϕ, were calculated from the experimental data. At 523.15 K, the change in Vmeanϕ from saturated vapor pressure to 40 MPa is comparable to the change with temperature at 10 MPa from ambient conditions to 523.15 K. A Pitzer-type equation was fit to the data set and used to evaluate the individual partial molar volumes of NaCl and KCl in the solutions. The volume of mixing computed from the equation is always positive and displays a nearly symmetrical increase between the NaCl and KCl end-members. It also increases with increasing salt concentration and pressure, and decreases with increasing temperature. The results o...

Theoretical analysis of aqueous solutions of mixed strong electrolytes by a smaller-ion shell electrostatic model

In spite of the great importance of mixed electrolytes in science and technology, no compelling theoretical explanation has been offered yet for the thermodynamic behavior of such systems, such as their deviation from ideality and the variation of their excess functions with ionic composition and concentration. Using the newly introduced Smaller-ion Shell treatment - an extension of the Debye-Hückel theory to ions of dissimilar size (hence DH-SiS) - simple analytic mathematical expressions can be derived for the mean and single-ion activity coefficients of binary electrolyte components of ternary ionic systems. Such expressions are based on modifying the parallel DH-SiS equations for pure binary ionic systems, by adding to the three ion-size parameters - a (of counterions), b+ (of positive coions), and b- (of negative coions) - a fourth parameter. For the (+ + -) system, this is "b++," the contact distance between non-coion cations. b++ is derived from fits with experiment and, like the other b's, is constant at varying ion concentration and combination. Four case studies are presented: (1) HCl-NaCl-H2O, (2) HCl-NH4Cl-H2O, (3) (0.01 M HX)-MX-H2O with X = Cl, Br, and with M = Li, Na, K, Cs, and (4) HCl-MCln-H2O with n = 2, M = Sr, Ba; and n = 3, M = Al, Ce. In all cases, theory is fully consistent with experiment when using a of the measured binary electrolyte as the sole fitting parameter. DH-SiS is thus shown to explain known "mysteries" in the behavior of ternary electrolytes, including Harned rule, and to adequately predict the pH of acid solutions in which ionized salts are present at different concentrations.

Application of modified PHSC model in prediction of phase behavior of single and mixed electrolyte solutions

The modified perturbed hard sphere chain (e-PHSC) equation of state (EoS) has been used for correlation and prediction of thermo-physical properties of single and mixed aqueous electrolyte solutions. In order to take electrostatic contribution into account, the primitive mean spherical approximation (MSA) term has been utilized. The proposed electrolyte equation of state (e-EOS) has two ion-based parameters per each ion. Ion specific parameters were obtained by simultaneous adjustment using mean ionic activity coefficient (MIAC) and solution liquid density experimental data of single electrolyte solutions. In order to check the accuracy of the model, water activity, osmotic coefficient and vapor pressure of single electrolyte solutions have been calculated using adjusted parameters. Finally water activities, MIACs, solution liquid densities, osmotic coefficients and vapor pressures of various mixed electrolyte solutions were predicted. The results showed that using e-PHSC model, MIACs, osmotic coefficient, water activity and vapor pressure and liquid density of mixed electrolyte solutions up to 6.5, 10, 10, 10 and 5 of ionic strength can be well predicted without any additional adjustable parameters.

An Investigation of Zdanovskii’s Rule for Predicting the Water Activity of Multicomponent Aqueous Strong Electrolyte Solutions

The effectiveness of Zdanovskii’s rule as a fundamental method of predicting water activities in mixed aqueous strong electrolyte solutions has been investigated. Unfortunately, when literature data available for more than 100 ternary systems (i.e., two electrolytes plus water) were examined, sufficient measurements were rarely available to test Zdanovskii’s rule conclusively. This is because few mixed systems have been studied by more than one (independent) investigator and, in these few cases, the differences between reported water activities are generally much larger than typical estimates of experimental uncertainty. Most of the electrolyte systems considered in this work are found statistically to conform with Zdanovskii’s rule but often only within a worryingly large tolerance in residuals. However, when data are taken from a single source, deviations from Zdanovskii’s rule, significant in comparison to the stated experimental precision, can often be attributed equally well to small, unrecognized, systematic errors. This dilemma can only be resolved by more experimental measurements of sufficient accuracy to achieve better agreement between independent observers. Our findings imply that (a) confidence in deviations from Zdanovskii’s rule typically depends on a subjective judgment of data quality and (b) Zdanovskii’s rule, albeit often difficult to validate, provides an impressively general method for estimating water activities in mixed aqueous strong electrolyte solutions, with a certainty that, objectively, is as good as or better than current experimental capability.

A modified mean spherical approximation model for prediction of mean ionic activity coefficient in mixed electrolyte solution at different temperatures

In this work, the Dehghani–Modarress mean spherical approximation model has been modified and extended for prediction of the mean ionic activity coefficient in mixed aqueous electrolyte solutions at different temperatures. In the DM-MSA model the cationic diameter as well as the dielectric constant of water are considered to be concentration dependent. In order to make the DM-MSA model applicable in engineering applications, a binary interaction parameter has been introduced. Using these parameters, the mean ionic activity coefficient of electrolytes can be predicted applying a linear mixing rule. To calculate the activity coefficient of single electrolytes at different temperatures, a temperature dependency has been considered for cationic size as well as dielectric constant. Utilizing the obtained parameters for single electrolytes at different temperatures, the mean ionic activity coefficients of mixed electrolytes have been predicted. The accuracy of the model is also compared with those results produced by extended UNIQUAC model. In order to have a fair judgment, the same experimental data and minimization algorithm have been used for comparison.

Membrane Potentials across the Cation Exchange Membrane in Aqueous Mixed Electrolyte Solutions

Membrane Potentials across the Cation Exchange Membrane in Aqueous Mixed Solutions Made of Two Kinds of Electrolytes Were Experimentally Studied. Effects of both the Concentration and the Species of Electrolytes on Membrane Potentials Were Presented. for any Mixed Solution Made of Two Kinds of Electrolytes, when the Total Electrolyte Concentration at Right Side of the Membrane Is Fixed, the Membrane Potential Increases with the Total Electrolyte Concentration at Left Side of the Membrane. however, such Increase Is Rather Slight at both Low and High Concentrations. when the Concentrations at each Side of the Membrane Are Equivalent for Three Mixed Solution Systems, the Membrane Potential Decreases with such Order: ΦKCl+NaCl>ΦKCl+MgCl2>ΦKCl+AlCl3.

Osmotic and activity coefficient of 1-ethyl-3-methylimidazolium chloride in aqueous solutions of tri-potassium phosphate, potassium carbonate, and potassium chloride at [formula omitted

Vapour–liquid equilibrium data (water activity, vapour pressure, osmotic coefficient, and activity coefficient) of the mixed electrolyte aqueous solutions, 1-ethyl-3-methylimidazolium chloride, (EmimCl) + tri-potassium phosphate, EmimCl + potassium carbonate, EmimCl + potassium chloride and their corresponding binary aqueous solutions have been measured by the isopiestic method at a temperature of 298.15 K. The osmotic coefficients for binary aqueous solutions were correlated to the Pitzer, modified Pitzer and TCPC models. The osmotic coefficient of mixed electrolyte with common anion was correlated to the Pitzer model. From these data, the corresponding mean activity coefficients, γ ± , have been calculated. The activity coefficients of mixed electrolytes were calculated by Scatchard’s neutral electrolyte method. A modified Pitzer model has been used to predict the osmotic and activity coefficients of mixed electrolyte solution with common anion.

Experimental study and modelling of saturation molality of NaCl in quaternary aqueous electrolyte solutions at various temperatures

Saturation molality of sodium chloride in mixed aqueous electrolyte solutions containing NaCl, CaSO 4 and Na 2SO 4 was measured at atmospheric pressure over the wide range of temperatures using an equilibrium cell equipped with an accurate temperature control system. The measurements were carried out at different CaSO 4 and Na 2SO 4 concentrations. In order to check the repeatability of the experimental data for the saturation molality of NaCl, the experiments were replicated three times and the values reported were the average of the replicas. To model the data generated in this work, the PDH+UNIFAC-Dortmund activity coefficient model was used. The model used to predict the mean ionic activity coefficients of NaCl at the saturation molality at various temperatures and at different concentrations for CaSO 4 and Na 2SO 4. The PDH term of the model accounts for the long range interactions between ionic species in solutions, while the modified UNIFAC-Dortmund activity coefficient model was used to account for the short range interactions between the species in solutions. It is worth noting that no new adjustable parameters were introduced into the model and the previously reported values for the interaction parameters of the binary and ternary electrolyte systems were directly used to predict the experimental data of the mean ionic activity coefficients of NaCl at saturation molality. The results showed that the PDH+UNIFAC-Dortmund activity coefficient model can accurately predict the mean ionic activity coefficients for the quaternary electrolyte solutions studied in this work.

Measurement and correlation of the saturation concentrations for single and mixed aqueous electrolyte solutions at various temperatures

Saturation molality for a number of single and mixed aqueous electrolyte solutions containing NaCl, CaSO 4, and Na 2SO 4, was measured at atmospheric pressure over a wide range of temperature. In order to check the repeatability of the experimental data, the experiments were replicated three times and average of the results was considered as final saturation molality. Experimental data of saturation molality for single electrolyte solutions were correlated using the modified UNIFAC–Dortmund model to account for the short-range interaction. Binary interaction parameters, between water molecules and ionic species were also reported. For the long-range interactions between the ionic species in solutions, the Pitzer–Debye–Hückel (PDH) model was used. The results showed that the PDH + UNIFAC–Dortmund activity coefficient model can accurately correlate the mean ionic activity coefficients for the single aqueous systems studied at saturation molality. In case of mixed electrolyte solutions, the PDH model was used to correlate the mean ionic activity coefficients of the electrolytes. Ternary interaction parameters, between the ionic species in solution, introduced in the PDH model were also reported. The results obtained from the PDH model were in good agreement with those of data collected in this work.

Comparison of activity coefficient models for electrolyte systems

AbstractThree activity coefficient models for electrolyte solutions were evaluated and compared. The activity coefficient models are: The electrolyte NRTL model (ElecNRTL) by Aspentech, the mixed solvent electrolyte model (MSE) by OLI Systems, and the Extended UNIQUAC model from the Technical University of Denmark (DTU). Test systems containing a single salt (NaCl), multiple salts, and mixed solvent aqueous electrolyte solutions were chosen. The performance of the activity coefficient models were compared regarding the accuracy of solid–liquid and vapor–liquid equilibrium calculations for the test systems. © 2009 American Institute of Chemical Engineers AIChE J, 2010