Pitzer Equations Research Articles

Volume properties of the ternary systems (LiCl + LiB5O8 + H2O) and (Li2SO4 + LiB5O8 + H2O) from 283.15 to 363.15 K and 101.325 kPa

In this study, densities of the two ternary aqueous solution systems (LiB5O8 + LiCl + H2O) and (LiB5O8 + Li2SO4 + H2O) were measured using an accurate digital vibrating-tube densimeter from 283.15 to 363.15 K at an interval of 5 K and 101.325 kPa. B5O8- in aqueous solution was in the form of [B5O6(OH)4]-. Therefore, the complex aqueous solution of LiB5O8 is in the form of Li[B5O6(OH)4]. Subsequently, the mean apparent molar volume (VΦθ) and mixing ion-interaction parameters (θa,a′v and Ψc,a,a′v, c = Li+, a = B5O6(OH)4-, a′= Cl- or SO42-) against temperature were obtained using the Pitzer equation for the first time. And then, the temperature-dependence equations for the Pitzer mixing ion-interaction parameters and the relevant temperature correlation coefficients of the equation aj, i.e. [f (ai, T) = a1 + a2ln(T/298.15) + a3(T − 298.15) + a4/(620 − T) + a5/(T − 227)] were also obtained through the least square fitting. These volumetric properties and parameterization Pitzer parameters obtained in this work could hopefully be used for the quantitatively predictive calculation of the physicochemical properties of the mixed electrolytes containing lithium, chloride, and sulfate ions at any temperature.

Experimental determination and thermodynamic modeling of solid–liquid equilibria in the system NaCl–Na2SO4–H3BO3–H2O at 323.15 K and its application in industry

The solubilities and refractive indices in the systems NaCl–Na2SO4–H3BO3–H2O and NaCl–H3BO3–H2O at 323.15 K were investigated with the isothermal dissolution equilibrium method. The phase diagram of the ternary system consists of two single-salt crystallization fields of NaCl and H3BO3, two solubility univariant curves, and one invariant point. The dry-salt diagram of the quaternary system is composed of three single-salt crystallization fields corresponding to NaCl, Na2SO4 and H3BO3, three solubility univariant curves, and one invariant point. A comparison of the diagrams of the quaternary system at (298.15, 323.15 and 373.15) K shows that areas of sodium chloride and sodium sulfate salts region increases whereas the area of H3BO3 region decreases distinctly with temperature increasing. Combining the Pitzer parameters and solubilities in the ternary systems in this study and literatures, the lacking Pitzer parameters for H3BO3 were fitted on the basis of Pitzer model. The calculated solubilities with the model agree well with the experimental data. The phase diagrams and Pitzer model for the quaternary system at 298.15 and 323.15 K were then used to conduct a computer simulation of brine separation. All H3BO3 and most of Na2SO4 can be separated from the solution with segmental evaporation method.

Mean activity coefficients of KCl in the KCl + SrCl2 + H2O solutions at 278.15 K determined by cell potential method and their application to the prediction of solid-liquid equilibria of the KCl + SrCl2 + H2O system

The cell potentials were determined by the cell without liquid junction K-ISE |KCl (m0) |Cl-ISE firstly. Using Nernst equation and the measured cell potentials, the response slope κ of the single-salt electrode and the standard cell potential E0 were fitted well. The total ionic strengths range from 0.0100 to 1.0000 mol·kg−1, the cell without liquid junction K-ISE |KCl (m1), SrCl2 (m2) |Cl-ISE is used to determine the mean activity coefficients of KCl in the KCl + SrCl2 + H2O solutions, the ionic strength fractions yb of SrCl2 are 0.8, 0.6, 0.4, 0.2 and 0. According to the measured cell potentials, the mean activity coefficients of KCl in the KCl + SrCl2 + H2O solutions were calculated by Nernst equation, and the relationship diagrams between the mean activity coefficients and total ionic strengths of the mixed solutions are drawn at 278.15 K. The mixed interaction parameters θK,Sr, and ψK,Sr,Cl in the Pitzer model were also obtained by regression of the mean activity coefficients of KCl in the mixed solutions. The mean activity coefficients of SrCl2, the osmotic coefficients, the water activities, and the excess Gibbs free energies of the mixed solutions were also calculated by Pitzer equations. Additionally, in order to verify the mixed ion parameters of Pitzer model fitted in this work, the isothermal dissolution equilibrium method is used to measure experimentally the phase equilibria of the mixed solutions at 278.15 K, and then the Pitzer equations and the mixed ion parameters are used to predict the solubilities of the salts in the mixed solutions at 278.15 K. The experimental and predicted phase diagrams are good agreement.

Crystal Structures and Solution Chemical Properties of Two Lactate Complexes Mn[(C3H5O3)2(H2O)2]⋅H2O(s) and Cu(C3H5O3)2(s)

Trihydrated manganese lactate Mn[(C3H5O3)2(H2O)2]⋅H2O(s) and anhydrous copper lactate Cu(C3H5O3)2(s) were synthesized. Crystal structures of the two compounds were characterized by X-ray single crystal diffraction technique. The compositions, spatial structures and coordination modes of the two compounds were determined by analysis of their molecular structures and crystal structures. Lattice potential energies of the compounds were calculated by using the crystallographic data. Molar enthalpies of dissolution of these metal complexes in the ultrapure water were measured by an isoperibol solution-reaction calorimeter with an accuracy of ±0.3%. On the basis of Pitzer's electrolyte solution theory, infinite dilution molar enthalpies of dissolution and Pitzer's parameters of the two lactate complexes soluble in water at T = 298.15 K were calculated. The infinite dilution molar enthalpies (ΔsHm∞) of dissolution of the title compounds were combined with lattice potential energies (UPOT) by a designed thermodynamic cycle, and the average molar enthalpy of hydration of the common lactate ion was calculated to be (407.207 ± 0.038) kJ·mol−1. The mechanism of thermal decomposition or dehydration of the trihydrated manganese lactate was explored by TG-DSC technique, and the difference between molar enthalpies (ΔsHm) of dissolution of trihydrated manganese lactate and anhydrous copper lactate at the same concentration was revealed.

Crystal structure and solution thermodynamics of the lactate complex Zn[(C3H5O3)2(H2O)2]⋅H2O(s)

An important trihydrated lactate complex Zn[(C3H5O3)2(H2O)2]⋅H2O(s) was synthesized. Crystal structure was characterized by X-ray single crystal diffractometer, and molecular structure, spatial structure and coordination mode of the complex were determined. The lattice potential energy of the complex was calculated by crystal data. The enthalpy of dissolution of the compound in the water was measured by isoperibol reaction calorimeter with an accuracy of ±0.3%. According to the Pitzer electrolyte solution theory, molar enthalpy of dissolution at the infinite dilution and Pitzer parameters of the compound soluble in water at T = 298.15 K were calculated. Combined with molar enthalpy of dissolution in the infinite dilution (ΔsHm∞) and lattice potential energy (UPOT), enthalpy of hydration of lactate ion was calculated. Mechanism of thermal analysis or dehydration of the compound was explained by TG-DSC technique.

Procedure to determine the phase region of high-pressure, high-temperature binary salt-water mixtures

A decision tree to determine the phase region of high-pressure, high-temperature binary salt-water mixtures was developed. Based on the temperature, pressure and feed concentration of binary salt-water mixtures, the phase regions of either a type I or II salt were identified for a selected condition range. The Anderko and Pitzer equation of state (AP EoS) was used to calculate the equilibrium concentrations of the respective salt-water mixtures under high-pressure (P > 220 bar) and high-temperature (T > 300 ºC) conditions. The EoS was adapted to calculate the thermodynamic properties of KCl-H2O and Na2SO4-H2O mixtures, in addition to the properties of NaCl-H2O. The developed decision tree was able to accurately identify the phase regions and indicate the transition from one phase to another for different feed concentrations. The developed decision tree can be useful in determining operating conditions and preventing solid deposition for processes operating under the supercritical conditions of water.

A Simple 1–1 Electrolyte: Volumetric Properties of Aqueous Solutions of Sulfuric Acid at Elevated Temperatures

Densities of aqueous solutions of sulfuric acid (H2SO4) have been measured by vibrating tube densimetry at molalities m varying from 0.02 to 3.0 mol·kg–1, at temperatures over the range 323.15 ≤ T/K ≤ 523.15 at 10 MPa pressure. These results were used to calculate the corresponding apparent molar volumes Vϕ(H2SO4,aq) and appear to be the first-ever systematic study of the volumetric properties of this important acid at elevated temperatures. At T ≤ 373.15 K, the present results aligned well with recent literature data and with values reported in the 1926 International Critical Tables. No reliable experimental data were found for comparison at higher temperatures. The present results confirm that at lower concentrations and temperatures, sulfuric acid solutions exist as a variable mixture of H+(aq) + HSO4–(aq) + SO42–(aq). However, at higher temperatures, the degree of association increases markedly such that at T ≥ 448.15 K, sulfuric acid solutions behave like a simple 1:1 electrolyte [H+(aq) + HSO4–(aq)] even at low concentrations. The variation of Vϕ(H2SO4,aq) over the entire experimental region was well modelled using a simple Pitzer equation that specifically included (where appropriate) the effects of chemical speciation. Combination of this model with relevant literature data enabled estimation of the standard ionic volume V°(HSO4–,aq) and the standard volume change ΔrV° for the reaction H+(aq) + SO42–(aq) → HSO4–(aq) at temperatures up to 523 K.

A Review of Geochemical Modeling for the Performance Assessment of Radioactive Waste Disposal in a Subsurface System

Radionuclides are inorganic substances, and the solubility of inorganic substances is a major factor affecting the disposal of radioactive waste and the release of concentrations of radionuclides. The degree of solubility determines whether a nuclide source migrates to the far field of a radioactive waste disposal site. Therefore, the most effective method for retarding radionuclide migration is to reduce the radionuclide solubility in the aqueous geochemical environment of subsurface systems. In order to assess the performance of disposal facilities, thermodynamic data regarding nuclides in water–rock systems and minerals in geochemical environments are required; the results obtained from the analysis of these data can provide a strong scientific basis for maintaining safety performance to support nuclear waste management. The pH, Eh and time ranges in the environments of disposal sites cannot be controlled, in contrast to those under experimental conditions in laboratories. Using a hypothetical error mechanism for the safety assessment of disposal sites may engender incorrect assessment results. Studies have focused on radionuclide reactions in waste disposal, and have offered evidence suggesting that these reactions are mainly affected by the geochemical environment. However, studies have not examined the thermodynamics of chemical reactions or interactions between water and minerals, such as the surface complexation and adsorption of various nuclide-ion species. Simple coefficient models have usually been applied in order to obtain empirical formulas for deriving Kd to describe nuclide distributions in the solid or liquid phase in water–rock geochemical systems. Accordingly, this study reviewed previous research on the applications of geochemical models, including studies on the development of geochemical models, sources of thermodynamic databases (TDBs) and their applications in programs, the determination of the adequacy of TDBs in surface complexation models and case studies, and the selection and application of activity coefficient equations in geochemical models. In addition, the study conducted case studies and comparisons of the activity coefficients derived by different geochemical models. Three activity coefficient equations, namely the Davies, modified Debye–Hückel, and Pitzer equations, and four geochemical models, namely PHREEQC, MINEQL+, MINTEQA2, and EQ3/6, were used in the study. The results demonstrated that when the solution’s ionic strength was <0.5 m, the differences in the activity coefficients between the Davies and modified Debye–Hückel equations were <5%. The difference between the Pitzer and Davies equations, or between the Pitzer and modified Debye–Hückel equations in terms of the calculated activity coefficients was <8%. The effect of temperature on the activity coefficient slightly influenced the modeling outputs of the Davies and modified Debye–Hückel equations. In the future, the probability distribution and uncertainty of parameters of Kd and the equilibrium constant can be used in geochemical and reactive transport models to simulate the long-term safety of nuclear waste disposal sites. The findings of this study can provide a strong scientific basis for conducting safety assessments of nuclear waste disposal repositories and developing environmental management or remediation schemes to control sites marred by near-surface contamination.

Pitzer Equations and a Model-Free Version of the Ion Interaction Approach for the Activity of Individual Ions

This work presents values of the Ion Interaction Function (IIF) which makes the activity coefficient of the cation to be different from the activity of the anion of a 1:1 electrolyte in aqueous solution and, in addition to the Debye-Hückel-type contribution, determines the very different dependence on ionic strength of the activity coefficients of the cation and the anion in 1:2, 2:1 electrolytes. The IIF cancels out in the mean ionic and osmotic coefficients due to the condition of electroneutrality. As was foreseen by K. S. Pitzer, the evaluation of the IIF was possible thanks to the availability of the activity coefficients of the individual ions. Values of the IIF, which were previously invisible, are presented and a self-consistent method to back calculate the activity of individual ions is developed.

Raman Spectroscopy Coupled with Chemometric Analysis for Speciation and Quantitative Analysis of Aqueous Phosphoric Acid Systems.

Complex chemical systems that exhibit varied and matrix-dependent speciation are notoriously difficult to monitor and characterize online and in real-time. Optical spectroscopy is an ideal tool for in situ characterization of chemical species that can enable quantification as well as species identification. Chemometric modeling, a multivariate method, has been successfully paired with optical spectroscopy to enable measurement of analyte concentrations even in complex solutions where univariate methods such as Beer's law analysis fail. Here, Raman spectroscopy is used to quantify the concentration of phosphoric acid and its three deprotonated forms during a titration. In this system, univariate approaches would be difficult to apply due to multiple species being present simultaneously within the solution as the pH is varied. Locally weighted regression (LWR) modeling was used to determine phosphate concentration from spectral signature. LWR results, in tandem with multivariate curve resolution modeling, provide a direct measurement of the concentration of each phosphate species using only the Raman signal. Furthermore, results are presented within the context of fundamental solution chemistry, including Pitzer equations, to compensate for activity coefficients and nonidealities associated with high ionic strength systems.

Solubility measurement and thermodynamic modeling of solid–liquid equilibria in quaternary system NaCl–Na2SO4–NaBO2–H2O at 323.15 K

The solubilities and refractive indices in the systems Na2SO4–NaBO2–H2O and NaCl–Na2SO4–NaBO2–H2O at 323.15 K were studied by the isothermal dissolution method. The phase diagram of the ternary system is composed of two single-salt crystallizations for Na2SO4 and NaBO2·4H2O. A comparison of the diagrams of system Na2SO4–NaBO2–H2O from 288.15 K to 323.15 K shows that the crystallization region of NaBO2·4H2O changes greatly as the temperature increasing, and the solid phase of mirabilite at 288.15 K and 298.15 K transforms into the nardite at 308.15 K and 323.15 K. The dry-salt diagram of the quaternary system consists of four salt crystallization fields for NaCl, NaBO2·4H2O, NaCl·NaBO2·2H2O and Na2SO4, five univariant solubility curves and two invariant points. On the basis of the Pitzer model, the lacking Pitzer parameters and dissolution equilibrium constants of the solid phases in this quaternary system were fitted with the solubilities and other thermodynamic properties in this study and literature. The calculated solubilities in the two systems are in good agreement with the experimental data.

Thermodynamic description of the chemical leavening in biscuits

In this paper we describe the chemical reactions of leavening agents in baking biscuits on a sound thermodynamic basis. The model is part in a sequel targetted at physical understanding of biscuit baking with the purpose of reformulation of biscuits with respect to sucrose and sodium levels. The chemical leavening gases, CO2 and NH3, originate from the dissociation of sodium and ammonium bicarbonate. Next to water vapour, these produced gases create gas bubbles in the biscuit dough. The concentrations of the leavening agents and added salt lead to high ionic strength. Consequently, the activities of ions participating in the leavening reaction deviate strongly from ideality. The non-idealities are described using the Pitzer equations. The values of many parameters of the Pitzer model and equilibrium constants are obtained from the strong developed field of CO2 sequestering in ammonia solutions. The model describing the chemical reactions is coupled to a cell model describing the expansion of gas bubbles. Model simulations show that most of the produced gas originates from the bicarbonate, and the ammonium contributes significantly less. The functionality of ammonium as leavening agent is not quite clear, but it may help in reducing sodium levels.

Experiment and Calculation of Solid Liquid Phase Equilibria in the Ternary System KCl−KBr−H2O at T = 273 K

In this work, the solid-liquid phase equilibrium in the ternary system KCl−KBr−H2O at T = 273 K has been investigated by using the isothermal dissolution equilibrium method. Based on determined solubility data of saturated liquid phase and corresponding humid residue composition, the experimental phase diagram has been constructed. The result shows that the type of the system is classified as completely solid solution type due to the existence of solid solution K(Cl, Br). The phase diagram of the ternary system KCl−KBr−H2O at 273 K is divided into an unsaturated liquid phase filed and one solid crystalline phase region corresponding to K(Cl, Br) by an univariant solubility curve on which there is without any invariant point. The function which described the relationship between the composition of solid solution and the solubility of two salts in saturated liquid phase was constructed by multiple regression. The Pitzer equation has been selected to calculate the solubility data in the ternary system KCl−KBr−H2O at T = 273 K. The solubility modelling approach agrees with experimental solubility data.

A Comparative Study for Application of Pitzer and ePC-SAFT Equations to Predict Volumetric and Saturation Properties in “Formation” Water

Predictions of salt solubility, brine vapor pressure and density are necessary to plan subsurface and surface operations. In this work, a comparative study was conducted to investigate prediction capabilities for salt solubility, equilibrium and volumetric properties of several minerals in “Formation” water by the Pitzer model (a commonly used industrial model) and by the ePC-SAFT equation of state (EOS). To achieve this, several validation and comparison steps were considered for reliable implementation of both models. Firstly, solubility, brine densities and vapor pressures for single-salt solutions were predicted. Afterward, the models’ applications were extended to several mixtures of two salts to predict solubility compared to experimental data from available literature. ePC-SAFT shows promising accuracy. The average relative deviation for prediction of liquid density (which cannot be estimated with the Pitzer model) for single-salt solutions of NaBr, KCl, NaCl and Na2SO4 are 1.13%, 0.70%, 1.02% and 0.36%, respectively. The average relative deviation from experimental data of vapor pressure for mixtures of NaCl and KBr is 0.75% and for mixtures of NaBr and KCl is 0.74% for systems with different concentrations. Moreover, a stochastic regression procedure is presented to evaluate the ePC-SAFT parameters. This technique is used for strontium in different salt solutions. The average relative deviation for mean ionic activity coefficients calculated by ePC-SAFT from experimental data using the ePC-SAFT parameters of strontium from the work of Held et al. [1] for single-salt solutions of strontium chloride, strontium bromide, strontium iodide, strontium nitrate and strontium perchlorate are 19.73%, 19.96%, 15.15%, 14.95% and 25.70%, respectively. These values using the ePC-SAFT parameters of strontium regressed in this work are 6.98%, 10.13%, 8.33%, 9.59% and 10.08%, respectively. Finally, the solubility of different salts was studied for mixing of formation water (FW) and injection water (SW).

Measurements and theoretical simulations of phase equilibria in the quaternary systems NaBr + KBr + SrBr2 + H2O, NaBr + MgBr2 + SrBr2 + H2O and their subsystems at 273.15 K

Since various mineral elements (such as sodium, potassium, strontium, bromine) are rich in underground brine in Sichuan Basin of China, to utilize the bromine resources rationally, the phase equilibria of the quaternary systems NaBr + KBr + SrBr2 + H2O, NaBr + MgBr2 + SrBr2 + H2O and their subsystems at 273.15 K were studied with the means of isothermal dissolution equilibrium method. The research systems are three ternary systems (NaBr + SrBr2 + H2O, KBr + SrBr2 + H2O and MgBr2 + SrBr2 + H2O) and two quaternary systems (NaBr + KBr + SrBr2 + H2O and NaBr + MgBr2 + SrBr2 + H2O). The corresponding solubility phase diagrams of the research systems listed above were plotted based on the measured experimental data.The experimental results indicate that there is no formation of solid solution or double salts in five systems. Five phase diagrams all belong to hydrate type I and contain one invariant point. In three ternary systems, there are two isothermal solubility curves and two crystallization fields, and the equilibrium solid phases are NaBr•2H2O and SrBr2•6H2O in the ternary system NaBr + SrBr2 + H2O, KBr and SrBr2•6H2O in the ternary system KBr + SrBr2 + H2O, and MgBr2•6H2O and SrBr2•6H2O in the ternary system MgBr2 + SrBr2 + H2O, respectively. There are three isothermal solubility curves and three crystallization fields in two quaternary systems. The equilibrium solid phases are NaBr•2H2O, KBr, and SrBr2•6H2O in the quaternary system NaBr + KBr + SrBr2 + H2O. In the quaternary system NaBr + MgBr2 + SrBr2 + H2O, the salts NaBr•2H2O, MgBr2•6H2O and SrBr2•6H2O coexist at the invariant point.The unreported mixing ion-interaction parameters of Pitzer equations θMg, Sr, ΨMg, Sr, Br, ΨNa, Sr, Br, and ΨK, Sr, Br are fitted with the solubility data at 273.15 K. The Pitzer ionic interaction model and the required parameters were employed to predict the solubilities of salts in five systems. The calculated results show that the predicted values are in accordance with the measured data, which verify the reliability of the selected parameters.

Uso das equações generalizadas de pitzer para avaliação termodinâmica de gases

A equação do tipo Virial foi a base para a proposta da equação generalizada de Pitzer e que consideram as forças de interação molecular do gás, como preponderantes no comportamento mecânico do sistema. A equação do tipo Virial foi baseada na proposição de um polinómio cujo grau leva em consideração o número de moléculas que interagem entre si. A ausência de dados experimentais para a aplicação da equação do tipo Virial resultou na proposta de correlações generalizadas que possibilitam determinar os parâmetros termodinâmicos, a partir das propriedades críticas e reduzidas de cada gás, além do fator acêntrico que relaciona o tamanho das moléculas. Desta forma, este trabalho tem como objectivo avaliar o comportamento do factor de compressibilidade (Zi) de gases, em função da pressão e da temperatura, baseado num estudo numérico realizado a partir de um programa computacional, desenvolvido em linguagem C++, que usa a equação generalizada de Pitzer. Dos resultados obtidos, foi possível observar a similaridade qualitativa do comportamento e a dependência da pressão e da temperatura do sistema com o factor de compressibilidade. Para estas avaliações, concluiu-se que as forças de atração e repulsão moleculares são mais efetivas para sistemas com alta pressão, pois genericamente, para pressões menores que 200 bar, as forças atrativas são mais intensas e acima desta pressão, prevalecem as forças repulsivas, que resultam na liquefação dos gases. Concluiu-se, também, que o comportamento termodinâmico dos gases tem relação direta com o tipo e as características do gás avaliado.

Isopiestic measurements and thermodynamic model for the ternary system {Li2B4O5(OH)4) + LiB5O6(OH)4 + H2O} and its subsystem at 288.15 K and ambient pressure

The isopiestic equilibria for the systems {Li2B4O5(OH)4 + H2O}, {LiB5O6(OH)4 + H2O} and {Li2B4O5(OH)4 + LiB5O6(OH)4 + H2O} at 288.15 K and ambient pressure were measured by the isopiestic method using a modified gravimetric isopiestic apparatus. The water activities and osmotic coefficients were determined based on the sodium chloride standard reference solution. On the basis of Pitzer model, an extended Pitzer model was developed to describe the thermodynamic properties of the aqueous systems containing different forms of lithium borates, then the Pitzer single salt parameters β(0), β(1), β(2) and Cϕ for the binary systems {Li2B4O5(OH)4 + H2O} and {(LiB5O6(OH)4 + H2O} and mixing ion-interaction parameters θB4O5OH4,B5O6OH4 and ψLi,B4O5OH4,B5O6OH4 for the ternary system {Li2B4O5(OH)4 + LiB5O6(OH)4 + H2O} were fitted with the experimental osmotic coefficients using the Fortran 97 program. Meanwhile, the water activities were calculated by the Pitzer parameters, and the good agreement between the calculated water activities and experimental results of this ternary system indicated that the Pitzer parameters obtained in this work were reliable.

Brine Management: Techno-economic Analysis of a Mechanical Vapor Compression Energy System for a Near-Zero Liquid Discharge Application

Fresh water availability is gradually decreasing and may limit the primary needs of drinking water and irrigation, as well as other activities, such as energy conversion, tourism, etc. A high number of desalination plants are being built to provide clean water. One of the main strategies is the brine volume minimization by means of either membrane or thermal processes. The present study focuses on the development of a techno-economic analysis of a Single Effect-Mechanical Vapor Compression (SE-MVC) system for purposes of brine volume minimization. The aim is to evaluate the thermodynamic and economic performances as well as the capital and operating expenditures of the brine concentrator when being part of a near zero liquid discharge (near-ZLD) application. This is achieved by developing the thermodynamic and economic models of the system, which are then combined together in a single integrated procedure. Brackish water analysis is used as starting point for this work. Water properties are modeled using Pitzer's equations as well as correlations found in the literature. The economic evaluation of the investment is performed by calculating the Net Present Value and Internal Rate of Return, key parameters to assess the investment viability of the project. The evaporator model provides the necessary input variables for the economic model. For a feed flow of 10.147 kg∙s-1 and a heat duty of 18080 kW, the annualized capital cost of equipment is 594.93 k€∙y-1, while the operating expenses are 854.40 k€∙y-1 The total annualized cost of the process is 1449.33 k€∙y-1.

Modeling of the Competition between Uranyl Nitrate and Nitric Acid upon Extraction with Tri-n-butyl Phosphate.

Uranium is a strategic element and plays an important role in energy resources. A H2O–HNO3–UO2(NO3)2–TBP (tri-n-butyl phosphate)–diluent system is commonly used for uranium separation and purification in liquid–liquid extraction. Uranyl nitrate is promoted by the existence of nitrate at low HNO3 concentrations but is inhibited at high HNO3 concentrations. Considering the competitive extraction between HNO3 and UO2(NO3)2, a generic extraction model is developed. The activities of components in the aqueous phase were estimated using Pitzer models. The thermodynamic equilibrium constants and Pitzer parameters were regressed by experimental data. The resulting model was able to successfully predict uranyl nitrate, nitric acid, and water extraction over a large range of conditions (U, 0–1.8 mol/L; HNO3, 0–10 mol/L; TBP, 5–100 vol %) within average absolute relative deviations of 11.2, 15.7, and 23.8%, respectively. The predicted results show that water and nitric acid were extracted as di-solvates HNO3·(TBP)2·H2O and (TBP)2·2H2O at low nitric acid concentrations, with the formation of mono-solvates HNO3·TBP and HNO3·TBP·H2O as the acid concentration increased. Uranyl nitrate was shown to be rejected from the organic phase as the formation of HNO3·TBP and HNO3·TBP·H2O in acid was extracted at high acid concentrations.

A Two-Parameter Theoretical Model for Predicting the Activity and Osmotic Coefficients of Aqueous Electrolyte Solutions

A thermodynamic model of electrolyte solutions is proposed. The model consists of a long-range term expressed by the Pitzer–Debye–Huckel equation (PDH) and a short-range term expressed by the molecular interaction volume model (MIVM). The new model was fitted with 39 different types of single electrolyte systems and was compared with the Pitzer equation, and the mean standard deviation (SD) and the mean average relative deviation (ARD%) are 0.0264, 0.0040 and 2.09%, 0.40%, respectively. Meanwhile, the physical meaning of the two electrolyte-specific interaction parameters ( $$B_{ca,s}$$ and $$B_{s,ca}$$ ) of the new model is also discussed. By further comparison with the Pitzer equation and a state-of-the-art model, eUNIQUAC-NRF, the new model exhibits relatively robust extrapolation capability, and also shows the potential ability to predict the activity coefficients of individual ions. In addition, only using binary parameters to predict 29 different types of ternary systems, the overall prediction results of the new model are slightly better than those of the Pitzer equation, and the mean SD and ARD% are 0.0288, 0.0396 and 2.88%, 3.81%, respectively. For some cases involving Rb and Cs, the Pitzer equation needs two ternary adjustable parameters ( $$\theta$$ and $$\psi$$ ) to achieve the prediction accuracy of the new model. Furthermore, we also compared the predictions of the new model with the eUNIQUAC-NRF model for several ternary systems; the new model also shows better performance, and its overall prediction accuracy was about twice that of the eUNIQUAC-NRF model, with the average SD and ARD% values being 0.0261, 0.0546 and 2.63%, 5.80%, respectively.