Activity Coefficient Equations Research Articles

Thermodynamic modeling and process evaluation of advanced ionic liquid-based solvents for CO2/CH4 separation

Carbon capture technology is a prospective strategy to address the increasing concentration of CO2 in the atmosphere, with the core challenge of developing new cost-effective processes. In this work, the energy analysis and economic evaluation were conducted based on rigorous thermodynamic models and the process simulation results of a novel chemical absorption-dominated hybrid solvent which consists of functional ionic liquid of choline triazole ([Cho][Triz]) and sulfolane (TMS) to separate CO2 from shale gas. The solubility of CO2 and CH4 in different solvents were calculated using phase equilibrium model including the NRTL activity coefficient equation, the RK equation of state, chemical reaction equilibrium equations, and the mass balance equation. The physical properties of the ionic liquid-based solvent systems were calculated with empirical equations which was corrected using experimental data. The results obtained from the thermodynamic models exhibited good agreement with experimental data. Subsequently, the established models and the parameters obtained were embedded into Aspen Plus for further analysis. The total CO2 capture energy consumption of 1.65 GJ·t−1 CO2 and the cost of 48.07 $·t−1 CO2 were achieved using the new solvent when the mass fraction of IL was 60 wt%. Compared with the commercial 30 wt% MDEA carbon capture process, it reduced the energy consumption and economic cost of 64.16 % and 45.59 %, respectively.

Thermodynamic modeling and process evaluation of advanced ionic liquid-based solvents for CO2/CH4 separation

Carbon capture technology is a prospective strategy to address the increasing concentration of CO2 in the atmosphere, with the core challenge of developing new cost-effective processes. In this work, the energy analysis and economic evaluation were conducted based on rigorous thermodynamic models and the process simulation results of a novel chemical absorption-dominated hybrid solvent which consists of functional ionic liquid of choline triazole ([Cho][Triz]) and sulfolane (TMS) to separate CO2 from shale gas. The solubility of CO2 and CH4 in different solvents were calculated using phase equilibrium model including the NRTL activity coefficient equation, the RK equation of state, chemical reaction equilibrium equations, and the mass balance equation. The physical properties of the ionic liquid-based solvent systems were calculated with empirical equations which was corrected using experimental data. The results obtained from the thermodynamic models exhibited good agreement with experimental data. Subsequently, the established models and the parameters obtained were embedded into Aspen Plus for further analysis. The total CO2 capture energy consumption of 1.65 GJ·t−1 CO2 and the cost of 48.07 $·t−1 CO2 were achieved using the new solvent when the mass fraction of IL was 60 wt%. Compared with the commercial 30 wt% MDEA carbon capture process, it reduced the energy consumption and economic cost of 64.16 % and 45.59 %, respectively.

A comprehensive thermodynamic modeling of the solubility of sugar alcohols in ionic liquids

Environmental regulations have recently drawn attention from fossil sources to green materials, among which sugar alcohols (SA) have particular importance due to their vast use in the nutrition, pharmaceutical, and chemical industries. Their properties and equilibrium conditions, including the extraction and solubility behavior utilizing novel solvents such as ionic liquids (ILs), are essential for developing further processes and their optimization. On account of this, the present study aims to develop a comprehensive thermodynamic approach based on simple and accurate tools such as activity coefficient models (ACMs) and equations of state (EoSs), which have not been hitherto addressed. To this end, eleven calculation schemes based on these two approaches were applied to the largest databank investigated thus far (13 SAs, 21 ILs, and 653 data points), and the performance of the models was analyzed. NRTL, free-volume Flory-Huggins (FVFH), and Redlich-Kister (RK) ACMs with different schemes, as well as athermal and ideal solution models, were evaluated and compared against well-known cubic EoSs such as Peng-Robinson (PR) and Valderrama-Patel-Teja (VPT). Benefitting from three adjustable parameters and a simple form, the three-parameter RK model yielded the best results with a 0.82 % (2.77 K) deviation in the entire databank. Moreover, employing temperature-dependent interaction parameters with FVFH ACM (3.55 K, 1.05 %), PR EoS (3.60 K, 1.07 %), and VPT EoS (3.66 K, 1.08 %) improved the accuracy of the calculations remarkably. The results of this contribution prove that thermodynamic models based on NRTL, FVFH, and RK ACMs are the best options for calculating solid–liquid conditions equilibrium of SA-IL systems with a simple and precise calculation procedure, and can therefore be employed for the simulation and optimization tools. This study investigates the most extensive SA-IL databank, a large number of models from different routes, and the nature of SA-IL pairs employing the obtained parameters.

Calculating Thermodynamic Factors for Diffusion Using the Continuous Fractional Component Monte Carlo Method.

Thermodynamic factors for diffusion connect the Fick and Maxwell-Stefan diffusion coefficients used to quantify mass transfer. Activity coefficient models or equations of state can be fitted to experimental or simulation data, from which thermodynamic factors can be obtained by differentiation. The accuracy of thermodynamic factors determined using indirect routes is dictated by the specific choice of an activity coefficient model or an equation of state. The Permuted Widom's Test Particle Insertion (PWTPI) method developed by Balaji et al. enables direct determination of thermodynamic factors in binary and multicomponent systems. For highly dense systems, for example, typical liquids, it is well known that molecular test insertion methods fail. In this article, we use the Continuous Fractional Component Monte Carlo (CFCMC) method to directly calculate thermodynamic factors by adopting the PWTPI method. The CFCMC method uses fractional molecules whose interactions with their surrounding molecules are modulated by a coupling parameter. Even in highly dense systems, the CFCMC method efficiently handles molecule insertions and removals, overcoming the limitations of the PWTPI method. We show excellent agreement between the results of the PWTPI and CFCMC methods for the calculation of thermodynamic factors in binary systems of Lennard-Jones molecules and ternary systems of Weeks-Chandler-Andersen molecules. The CFCMC method applied to calculate the thermodynamic factors of realistic molecular systems consisting of binary mixtures of carbon dioxide and hydrogen agrees well with the NIST REFPROP database. Our study highlights the effectiveness of the CFCMC method in determining thermodynamic factors for diffusion, even in densely packed systems, using relatively small numbers of molecules.

Separation of ethyl acetate and ethanol by imidazole ionic liquids based on mechanism analysis and liquid–liquid equilibrium experiment

Azeotrope of ethyl acetate (EAC) and ethanol (EA) generated in the synthesis of ethyl acetate (EAC), was difficult to separate by general distillation. Liquid-liquid extraction using ionic liquids (ILs) as extractants is a green and efficient method for separating azeotropes. To select the suitable ILs, the σ-profiles of EAC, EA, and different anions of imidazole ILs were obtained through the COSMO-SAC model. Then, the extraction mechanism of ILs in the EAC-EA system was discussed from the micro perspective, the interaction between ILs and EA was analyzed graphically by the interaction region indicator (IRI) using the Multiwfn and VMD, the interaction energy between ILs and EA/EAC were calculated by Gaussian 09. Finally, we selected 1-ethyl-3-methyl-imidazolium dihydrogen phosphate ([EMIm][H2PO4]), 1-butyl-3-methyl-imidazolium dihydrogen phosphate ([BMIim][H2PO4]), 1-ethyl-3- methyl-imidazolium hydrogen sulfate ([EMIm][HSO4]), and 1-butyl-3-methyl- imidazolium hydrogen sulfate ([BMIm][HSO4]) as the extractants based on the mechanism analysis. The Liquid-liquid equilibrium(LLE) data of EAC-EA-ILs were measured at 298.15 K under atmospheric pressure; the effects of ILs with different alkyl chain lengths of cations on the extraction efficiency were investigated, and the influence of ILs with different anions was also verified through experiments. Meanwhile, we adopted the NRTL activity coefficient equation to regress the experiment data, and the interaction parameters were optimized by the least square method using Matlab 2014.

Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties. III. Seawater from the freezing point to 45 °C, including acid-base equilibria

A quantitative understanding of pH, acid-base equilibria, and chemical speciation in natural waters including seawater is needed in applications ranging from global change to environmental and water quality management. In a previous study (Humphreys et al., 2022) we implemented a model of solutions containing the ions of artificial seawater, based upon the use of the Pitzer equations for the calculation of activity coefficients and including, for the first time, the propagation of uncertainties. This was extended (Clegg et al., 2022) to include the Tris buffer solutions that are used to calibrate the seawater total pH scale. Here we apply the same methods to develop a model of solutions containing the ions of standard reference seawater, based upon studies by Millero and co-workers. We compare the predictions of the model to literature data for: the dissociation of dissolved CO2 and bicarbonate ion; boric acid dissociation; saturation with respect to calcite, the ion product of water, and osmotic coefficients of seawater. Estimates of the uncertainty contributions of all thermodynamic equilibrium constants and Pitzer parameters to the variance of the calculated quantity are used to determine which elements of the model need improvement, with the aim of agreeing with properties noted above to within their experimental uncertainty. Further studies are recommended. Comparisons made with several datasets for carbonate system dissociation in seawater suggest which are the most reliable, and identify low salinity waters (S < 10) as a region for which dissociation constants of bicarbonate are not yet accurately known. At present, the model is likely to be most useful for the direct calculation of equilibria in natural waters of arbitrary composition, or for adjusting dissociation constants known for seawater media to values for natural waters in which the relative compositions of the major ions are different.

Thermodynamic study of solubility of B6 hydrochloride in water + co-solvent systems with UNIQUAC model at different temperatures

In this study, due to the importance of the solubility of this vitamin in solvents, based on the UNIQUAC activity coefficient equation, its solubility in the presence of water, acetonitrile, n-propanol and isopropanol has been studied. To investigate the interaction behavior of components in the system, the desired thermodynamic equations were optimized based on experimental results with a combined Genetic + PSO algorithm. Based on the objective function, the value of the theoretical and experimental model was acceptable. Therefore, the optimized model can be significant for formulating and investigating solubility of B6 hydrochloride based on the design of a computer program.

Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties: Artificial seawater from 0 to 45 °C

Accurate chemical speciation models of solutions containing the ions of seawater have applications in the calculation of carbonate system equilibria and trace metal speciation in natural waters, and the determination of pH. Existing models, based on the Pitzer formalism for the calculation of activity coefficients, do not yet agree with key experimental data (potentiometric determinations of H+ and Cl− activity products in acidified artificial seawaters) and, critically, do not include uncertainty estimates. This hampers applications of the models, and also their further development (for which the uncertainty contributions of individual ion interactions and equilibrium constants need to be known). We have therefore implemented the models of Waters and Millero (Mar. Chem. 149, 8-22, 2013) and Clegg and Whitfield (Geochim. et Cosmochim. Acta 59, 2403-2421, 1995) for artificial seawater, within a generalised treatment of uncertainties, as a first step towards a more complete model of standard seawater and pH buffers. This addition to the models enables both the total uncertainty of any model-calculated quantity (e.g., pH, speciation) to be estimated, and also the contributions of all interaction parameters and equilibrium constants. Both models have been fully documented (and some corrections made). Estimates of the variances and covariances of the interaction parameters were obtained by Monte Carlo simulation, with simplifying assumptions. The models were tested against measured electromotive forces (EMFs) of cells containing acidified artificial seawaters. The mean offsets (measured – calculated) at 25 °C for the model of Waters and Millero are: 0.046 ± 0.11 mV (artificial seawater without sulphate, 0.280 mol kg−1 to 0.879 mol kg−1 ionic strength); and −0.199 ± 0.070 mV (artificial seawater, salinities 5 to 45). Results are similar at other temperatures. These differences compare with an overall uncertainty in the measured EMFs of about 0.04 mV. Total uncertainties for calculated EMFs of the solutions were dominated by just a few contributions: mainly H+-Cl−, Na+-Cl−, and H+-Na+-Cl− ionic interactions, and the thermodynamic dissociation constant of HSO4−. This makes it likely that the accuracy of the models can readily be improved, and recommendations for further work are made. It is shown that standard EMFs used in the calibration of the marine ‘total’ pH scale can be accurately predicted with only slight modification to the original models, suggesting that they can contribute to the extension of the scale to lower salinities.

Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties. II. Tris buffers in artificial seawater at 25 °C, and an assessment of the seawater ‘Total’ pH scale

The substance Tris (or THAM, 2-amino-2-hydroxymethyl-1,3-propanediol, CAS 77–86-1), and its protonated form TrisH+, is used in the preparation of pH buffer solutions for applications in seawater chemistry. The development of an acid-base chemical speciation model of buffer solutions containing Tris, TrisH+, and the major ions of seawater is desirable so that: (i) the effects of changes in the composition of the medium on pH can be calculated; (ii) pH on the free (a measure of [H+]) and total (a measure of ([H+] + [HSO4−])) scales can be interconverted; (iii) approximations inherent in the definition of the total pH scale can be quantified; (iv) electrode pairs such as H+/Cl− and H+/Na+ can more easily be calibrated for the measurement of pH. As a first step towards these goals we have extended the Pitzer-based speciation model of Waters and Millero (Mar. Chem. 149, 8–22, 2013) for artificial seawater to include Tris and TrisH+, at 25 °C. Estimates of the variances and covariances of the additional interaction parameters were obtained by Monte Carlo simulation. This enables the total uncertainty of any model-calculated quantity (e.g., pH, speciation) to be estimated, as well as the individual contributions of all interaction parameters and equilibrium constants. This is important for model development, because it allows the key interactions to be identified. The model was tested against measured EMFs of cells containing Tris buffer in artificial seawater at 25 °C, and the mean deviation was found to be 0.13 ± 0.070 mV for salinities 20 to 40. Total variances for calculated electromotive forces of the buffer solutions are dominated by contributions from just a few interaction parameters, making it likely that the model can readily be improved. The model was used to quantify the difference between various definitions of total pH and –log10([H+] + [HSO4−]) in Tris buffer solutions at 25 °C, for the first time (item (iii) above). The results suggest that the total pH scale can readily be extended to low salinities using the established approach for substituting TrisH+ for Na+ in the buffer solutions, especially if the speciation model is used to quantify the effect on pH of the substitution. The relationships between electromotive force (EMF), and pH on the total scale, with buffer molality in artificial seawater at constant salinity are shown to be linear above about 0.01 to 0.02 mol kg−1 buffer molality. The pH of Tris buffers containing ratios of TrisH+ to Tris that vary from unity can be calculated very simply. Technical aspects of the total pH scale, such as the extrapolation of pH to zero buffer (at constant salinity), are clarified. Recommendations are made for further work to extend the model to the temperature range 0–45 °C, and improve accuracy, so that requirements (i) to (iv) above can be fully met.

Conclusions from Round Table Discussion during IUT of ESAT 2021 electrolyte thermodynamics challenges - From industrial needs to academic research

Electrolyte thermodynamics is considered one of the most challenging areas of applied thermodynamics. It is an area with a wide range of applications in science and engineering. There are numerous models, both activity coefficient models and equations of state, but despite great successes and achievements of many models for several applications there is little consensus on which are the more generally applicable approaches. There are many controversial aspects, both related to models and to fundamentals. Over many years the Working Party of the Thermodynamics and Transport Properties of the European Federation of Chemical Engineering has organized IUT (Industrial Use of Thermodynamics) workshops in different topics of actual interest. The most recent of these IUTs, 5th in the series, was held (virtually) during the ESAT 2021 conference in Paris. Panellists and participants from both academia and industry attended allowing to include views from a very wide spectrum. This manuscript summarizes the most important points from this workshop in terms of status and needs for electrolyte data and models and concludes with some recommendations for the community, which we hope can accelerate future studies in the field. The target of this work is not to present a general account of successes and shortcomings of electrolyte thermodynamic models, rather it is mostly to focus on the expert views of the IUT participants from industry and academia related to the challenges concerning data, models and applications of electrolyte thermodynamics.

Thermodynamic modeling of calcium carbonate scale precipitation: aqueous Na+-Ca2+-Cl–-HCO3–-CO32–-CO2 system

To allow for accurate calculations of calcium carbonate scaling in highly saline produced waters, we present a comprehensive thermodynamic model based on the electrolyte nonrandom two-liquid (eNRTL) activity coefficient equation for the aqueous Na+-Ca2+-Cl–-HCO3–-CO32–-CO2 system. The eNRTL binary interaction parameters for the H2O:(Na+-CO32–) pair, the H2O:(Na+-HCO3–) pair, the (Na+-Cl–):(Na+-CO32–) pair, and the (Na+-Cl–):(Na+-HCO3–) pair are identified in this work via the regression of thermodynamic, calorimetric, and phase equilibria experimental data. The binary interaction parameters associated with the H2O:(Na+-Cl–) pair, the CO2:(Na+-Cl–) pair, the H2O:(Ca2+-Cl–) pair, and the (Na+-Cl–):(Ca2+-Cl–) pair are retrieved from the literature. The remaining binary interaction parameters are retrieved from Aspen Plus or set to zero. In addition, the solubility product constants are identified for Na2CO3•10H2O(s), Na2CO3•7H2O(s), Na2CO3•H2O(s), Na2CO3•NaHCO3•2H2O(s), Na2CO3•3NaHCO3(s), and CaCO3(s) via regression of solubility data. The model is capable of accurately calculating all phase equilibria and calorimetric properties at temperatures up to 473.15 K and salt concentrations up to saturation.

Solubility Prediction of Etodolac, Lamotrigine, Diazepam and Clonazepamin in Cosolvent Mixtures Using UNIQUAC Model

Etodolac, Lamotrigine, diazepam, and clonazepamine are four important drugs in the pharmaceutical industry that optimizing the solvent concentration in the least amount can reduce the cost and toxicity of these drugs. Due to the lack of thermodynamic modeling based on the activity coefficient equation in previous studies for solubility of Etodolac, Lamotrigine, diazepam, and clonazepamine in aqueous solution, in this study, based on thermodynamic equations and UNIQUAC model, their solubility is optimized with the presence of water and ethanol. Based on the objective function defined, the error rate of the model optimization value was acceptable for each system. The results of this study can be used to better understand the intermolecular reaction of Etodolac, Lamotrigine diazepam, and clonazepamine in the presence of ethanol and water solvents. Also, the importance of the optimization results of this study in order to design a computer program to predict the solubility of these drugs is significant.

An improved model for CO2 solubility in aqueous Na+–Cl−–SO42− systems up to 473.15 K and 40 MPa

This article contributes to the development of a thermodynamic model for simulating CO2 solubility in pure water and aqueous brines under different conditions of temperature, pressure and ionic strength. The modeling activity-fugacity (γ-φ) approach allows calculating CO2 solubility, based on the Pitzer electrolyte theory for activity coefficient and Peng-Robinson's equation of state for fugacity. The present work proposes a new set of Pitzer interaction parameters through the set of CO2 solubility data in saline systems such as CO2-H2O-NaCl and CO2-H2O-Na2SO4. The determined model is capable of covering a wide T − P − I range (273.15–473.15 K, 0.1–40 MPa and 0–6 mol/kg). Average absolute deviation of CO2 solubility is about 5% compared to a large number of experimental data available (more than 700 data analyzed). New experimental solubility data for the CO2-H2O-NaCl-Na2SO4 system were also acquired in this study (303.15–423.15 K, 1.5–20 MPa and 0–6 mol/kg) to test the model's capacity: it is able to describe the CO2 solubility in aqueous salt mixtures without any further optimizations of interaction parameters.

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 &lt;0.5 m, the differences in the activity coefficients between the Davies and modified Debye–Hückel equations were &lt;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 &lt;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.

A comparative study of thermodynamic models to describe the VLE of the ternary electrolytic mixture H2O–NH3–CO2

Abstract This study aims to ascertain the influence of the activity coefficient model and equation of state for predicting the vapor–liquid equilibrium (VLE) of the multi-electrolytic system H2O–NH3–CO2. The non-idealities of the liquid phase are described by the eUNIQUAC and eNRTL models. The vapor phase is modeled with the Nakamura equation, which is compared with the ideal gas assumption. The models are validated with experimental data from literature on total pressure and ammonia partial pressure. Results show that the models UNIQUAC and NRTL without dissociation can only reproduce the experimental conditions in the absence of CO2. When the electrolytic term is considered, the eUNIQUAC model is able to reproduce the experimental data with greater accuracy than the eNRTL. The equation of state which describes the vapor phase plays no major role in the accuracy of the VLE prediction in the operational conditions evaluated here. Indeed, the accuracy relies on the activity coefficient, therefore the ideal gas equation can be considered if the non-idealities of the liquid phase are described by a well-tuned model. These findings could be useful for equipment design, flowsheet simulations and large-scale simultaneous optimization problems.

A general thermodynamic model for eutectics of phase change molten salts in concentrating solar power applications

• Development of a thermodynamic simulation tool • Design of innovative molten salts-based phase change materials • Practical modeling method to determine eutectic points • Calorimetric and theoretical investigation of ternary phase diagrams • Employment of NRTL and Wilson equations for activity coefficients

Liquid + liquid equilibria of the ternary system water + glycerol + 1-butanol system: experimental data and modeling

In this study, solubility and tie-line data of ternary system water + glycerol + 1-butanol were determined at 293.2, 298.2 and 303.2 K and atmospheric pressure. This thermodynamic system is relevant for the production and purification of biofuels. Phase equilibrium data have been determined by cloud-point titration method and the tie-lines were obtained by correlating the refractive index of the binodal curves as a function of mixture composition. All measured LLE data were modeled by UNIQUAC and NRTL activity coefficient equations obtaining a satisfactory accuracy with modeling errors lower than 0.4%. Binary interaction parameters of tested thermodynamic models were estimated to predict the value of tie lines using a hybrid bio-inspired swarm intelligence optimization algorithm, that is, MAKHA without and with closure equation. This hybrid method was reliable to solve the global optimization problem for the binary interaction parameter identification of this ternary system. Results of this paper provide useful information for the design and modeling of industrial units for glycerol recovery, which is a relevant industrial feedstock.

Design of ESR slag for remelting 9CrMoCoB steel through experiments and thermodynamic calculations

To control the chemically active boron (B) in 9CrMoCoB within a narrow target range, thermodynamic calculations using FactSage 7.2 and equilibrium reaction experiments were conducted between slag and steel. First, equilibrium reaction experiments between 9CrMoCoB and slag of 55%CaF2–20%CaO–3%MgO–22%Al2O3–x%B2O3 (x ≤ 3) were conducted to supplement and optimize the Henrian activity coefficient γ (lgγ = A/T + C, where A and C are constants) of B2O3 in the solution phase of FToxid-OXYL in FactSage 7.2. Second, the equilibrium reactions between 9CrMoCoB steel and slag of 55%CaF2–20%CaO–3%MgO–22%Al2O3–x%SiO2–y%B2O3 (x ≤ 3, y ≤ 3) were calculated by using FactSage 7.2 to study the effects of B2O3, SiO2, and O2 in the atmosphere on the contents of B, Si, and O in steel. Then, equilibrium reaction experiments were conducted to validate the calculated results. Finally, suitable slag was designed, and electroslag remelting (ESR) experiments were conducted for verification. Results showed that A = −6582 and C = 0 in the Henrian activity coefficient equation were suitable to the slag of 55%CaF2–20%CaO–3%MgO–22%Al2O3–x%SiO2–y%B2O3 (x ≤ 3, y ≤ 3), and the appropriate slag for ESR remelting the 9CrMoCoB steel was 55%CaF2–20%CaO–3%MgO–22%Al2O3–1%SiO2–1%B2O3. The volume percent of O2 had a stronger influence on the Si content, compared with B content. The volume percent of O2 should be less than 0.05% to produce the qualified 9CrMoCoB ingot when using the designed proper slag.

Measurement and Correlational Study of Phase Equilibria in Aqueous Solutions of N,N-Dimethylacetamide with 1-Pentanol and 1-Hexanol at 298.15 and 308.15 K

Tie-line data were determined for the systems (water + N,N-dimethylacetamide + 1-pentanol) and (water + N,N-dimethylacetamide + 1-hexanol) at the temperatures of 298.15 and 308.15 K under 101.1 KPa. The phase diagrams for these systems are of type I according to the Treyball classification. The thermodynamic consistency of the measured tie-line data was verified using the Hand and Othmer–Tobias equations. The distribution ratios (D) and selectivity (S) values were computed according to the measured tie-line data to assess the extracting behaviors of the selected solvents. The experimental data were correlated using the nonrandom two liquid and the universal quasichemical activity coefficient equations and the Elephant Herding Optimization Algorithm (EHA). EHA is an emerging nature-inspired stochastic global optimization method, and it has been used for liquid–liquid equilibrium (LLE) parameter estimation of local composition models in multicomponent mixtures. The performance of this new swarm-based metaheuristic search method for LLE modeling with and without the closure equation has been analyzed.

Dispersion activity coefficient models. Part 1: Cubic equations of state

An explicit expression for dispersion in activity coefficient models can be derived from cubic equations of state (cEoS). Here we show that all the two-parameter cEoS deliver a van Laar type of equation. The difference between these equations can be characterized by a single parameter K, which can be computed directly from the cEoS characteristic parameters. The theoretical values for K are always higher than experimental activity coefficient data of alkane mixtures indicate. We show that mixtures of linear and branched alkanes require K=4.13 and K=3.04, respectively, while the lowest theoretical value, K=9, is given by the van der Waals equation. This mismatch in results is caused by the assumptions, which are made in the derivation of the van der Waals equation of state and which remain present in later developed cEoS. One of these is that all molecules are spherical, which leads to the inconsistency that the ratio of the covolume and the van der Waals volume is always 4, while this ratio for linear alkanes decreases rapidly to nearly 2 with increasing chain length. Another assumption is that all molecules experience the same number of external interactions, which neglects the fact that polyatomic molecules have less intermolecular interactions per spherical segment due to presence of covalent bonds and the occurrence of intramolecular interaction. Therefore, the van Laar type of activity coefficient equations are limited in their use as predictive model for dispersion. Perturbed hard-sphere chain equation of state will be discussed in part 2.