Temperature-dependent Binary Interaction Parameters Research Articles

Viscosity database for ternary Cu–Cr–X (X=Ni, Si, Zr) alloys based on CALPHAD-type modeling

A viscosity model with composition and temperature dependence for the liquid alloys of the Cu–Cr–X (X = Ni, Si, Zr) systems was developed using the CALPHAD (CALculation of PHAse Diagrams) approach. Based on the critical review of the available experimental data for pure metal viscosity, the viscosities of pure liquid Cu, Cr, Zr, Ni and Si were simulated with the Arrhenius formula. The viscosities of the binary liquid alloys of the Cu–Ni, Cu–Si, Cu–Zr, Cr–Ni, Cr–Si and Ni–Zr systems at different temperatures were evaluated using the CALPHAD-type formalism. The non-linear viscosity behavior resulting from chemical short-range order was described using temperature-dependent binary interaction parameters. The viscosities of the Cu–Cr and Cr–Zr liquid alloys were predicted employing the Hirai equation. The viscosities of the Cu–Cr–Zr, Cu–Cr–Ni and Cu–Cr–Si ternary liquids were directly extrapolated using the Redlish-Kister-Muggianu equation from the parameters of the binary systems. A comprehensive understanding of the temperature-composition-solidification phase-viscosity relationship was established for ternary melts. The satisfactory agreement observed between calculations and experimental data validates the use of CALPHAD-type viscosity modeling, supporting the suitability of the constructed viscosity database for predicting the viscosity of high-performance Cu-based alloys.

Evaluation of cubic, PC-SAFT, and GERG2008 equations of state for accurate calculations of thermophysical properties of hydrogen-blend mixtures

Hydrogen (H2) is a clean fuel and key enabler of energy transition into green renewable sources and a method of achieving net-zero emissions by 2050. Underground H2 storage (UHS) is a prominent method offering a permanent solution for a low-carbon economy to meet the global energy demand. However, UHS is a complex procedure where containment security, pore-scale scattering, and large-scale storage capacity can be influenced by H2 contamination due to mixing with cushion gases and reservoir fluids. The literature lacks comprehensive investigations of existing thermodynamic models in calculating the accurate transport properties of H2-blend mixtures essential to the efficient design of various H2 storage processes. This work benchmarks cubic equations of state (EoSs), namely Peng–Robinson (PR) and Soave Redlich–Kwong (SRK) and their modifications by Boston–Mathias (PR-BM) and Schwartzentruber–Renon (SR-RK), for their reliability in predicting the thermophysical properties of binary and ternary H2-blend mixtures, including CH4, C2H6, C3H8, H2S, H2O, CO2, CO, and N2, in addition to Helmholtz-energy-based EoSs (i.e., PC-SAFT and GERG2008). The benchmarked models are regressed against the experimental data for vapor–liquid equilibrium (VLE) that covers a wide range of pressures (0.01 to 101 MPa), temperatures (92 K to 367 K), and mole fractions (0.001 to 0.90) of H2. The novelty of this work is in benchmarking and optimizing the parameters of the mentioned EoSs to study VLE envelopes, densities, and other critical transport properties, such as heat capacity and the Joule–Thomson coefficient of H2 mixtures in a wide range of associated conditions. The results highlight the significant effect of the temperature-dependent binary interaction parameters on the calculations of thermophysical properties. The SR-RK EoS demonstrated the highest agreement with VLE data among the cubic EoSs with a low root mean square error and absolute average deviation. The PC-SAFT VLE models demonstrated results comparable to the SR-RK. The sensitivity analysis highlighted the high influence of impurity on changing the thermophysical behavior of H2-blend streams during the H2 storage process.

Experimental data and modeling of the CO2 solubility in 2-methylimidazole aqueous solution

CO2 capture plays a critical role in reducing carbon emissions. Novel chemical absorption media, such as imidazole aqueous solutions, have been extensively studied as potential candidates. In this work, new experimental data of CO2 solubility in 5–30 wt% 2-methylimidazole (2-MeIm) aqueous solutions at 293.15–313.15 K were measured. The Cubic-Plus-Association equation of state (CPA EoS) with the pseudo chemical reaction approach has been proposed to model the CO2 solubility in the 2-MeIm aqueous solutions. The CPA model can describe well the saturated vapor pressure (1.1%), liquid density (0.5%) and vapor–liquid equilibrium data (14%) of 2-MeIm aqueous solutions. Temperature dependent binary interaction parameters between 2-MeIm and CO2 are needed in order to satisfactorily represent the phase equilibrium data of the 2-MeIm-H2O-CO2 ternary systems (11%) in the temperature range of 293.15–393.15 K, which covers all the decarbonization process operation conditions. With the pseudo chemical reaction approach within CPA EoS, it is possible to distinguish the physical and chemical effects of CO2 solubility in chemical absorbents. This work provides the experimental and model basis for further research and application of the novel imidazole-based separation media for CO2 capture.

Fluid phase equilibria in asymmetric model systems. Part II: CO2 + 2,2,4,4,6,8,8-heptamethylnonane

The experimental phase behavior of carbon dioxide and 2,2,4,4,6,8,8-heptamethylnonane mixtures was studied at T = (293.15–378.15) K and at pressures of up to 20 MPa. The carbon dioxide content varied from 20.0 to 95.0 mol%, and phase transitions were determined using the synthetic variable volume method along 11 different isopleths. These results suggest that the system studied could present a type I or II phase behavior according to the classification of van Konynenburg and Scott for binary mixtures. Experimental data were successfully described by the Peng-Robinson equation of state using temperature-dependent binary interaction parameters.

The impressive impact of including enthalpy and heat capacity of mixing data when parameterising equations of state. Application to the development of the E-PPR78 (Enhanced-Predictive-Peng-Robinson-78) model.

PPR78 (Predictive-Peng-Robinson78) is a well-established cubic equation of state in which, the temperature-dependent binary interaction parameters (bips) between two molecules i and j [kij(T)] are predicted by a group-contribution method. In such a model, two group-binary-interaction parameters (G-bips), noted Akl and Bkl, are required per (k,l) pair of groups. The purpose of this article is to demonstrate that the inclusion of enthalpy and heat capacity of mixing data in the process of optimisation of the G-bips leads to a remarkable overall reduction of the error on such properties, from 841.51% to 51.42%, while keeping constant the accuracy in the prediction of VLE data, 8.6% (without inclusion of mixing properties) to 8.8% (with inclusion of mixing thermal properties). This new version of the PPR78 model (with the new sets of Akl and Bkl G-bips) has thus been called Enhanced-PPR78 (E-PPR78) model. From 2013 to 2017, this model was continuously developed and it is currently based on 40 groups. The many G-bips were fitted over 131,207 vapour liquid equilibrium data and 33,629 mixing properties data (hM and cPM) belonging to 1301 binary systems. After almost 18 years from the initial development of the PPR78 model, this paper summarizes for the first time the overall accuracy of the E-PPR78 model.

Thermodynamic modeling of pharmaceuticals solubility in pure, mixed and supercritical solvents

In this study, the capability of the PHSC model was evaluated to predict the solubility of the pharmaceuticals in pure, mixed, and supercritical solvents over a wide range of temperatures and pressures. The PHSC model was utilized for fifteen pharmaceutical compounds in pure and mixed solvents. The prediction results of the PHSC model were compared to PC-SAFT, COSMO-RS, and COSMO-SAC models. Twenty-one ternary systems were considered to study the solubility of pharmaceuticals in the mixed solvents. Finally, the solubility of five pharmaceuticals in supercritical CO2 at different temperatures was estimated using an adjustable temperature-dependent binary interaction parameter. The obtained results show that the solubility of pharmaceuticals in different solvents and supercritical CO2 can be estimated using the PHSC model satisfactory.

High-Pressure Phase Equilibria Measurements of the Carbon Dioxide + Cycloheptane Binary System

The phase behavior of the carbon dioxide + cycloheptane binary system for which no literature data are available has been examined at temperatures ranging from 292.6 to 372.8 K. Saturation pressures, ranging from 23.9 to 154.8 bar, were acquired by a synthetic and visual method. In concrete terms, an adjustable-volume high-pressure cell was utilized to measure bubble and dew point pressures by visual detection of phase transitions at constant overall composition. A total of 11 different mixtures with mole fractions of carbon dioxide ranging from 0.20 to 0.96 were prepared, and a total of 99 experimental points were reported. The experimental results obtained in this work reveal the absence of liquid–liquid immiscibility in the studied temperature range and make it possible to conclude that the vapor–liquid critical line of the binary system is continuous and uninterrupted between the two pure compounds. Experimental data were correlated with the Peng–Robinson equation of state and classical van der Waals mixing rules with temperature-dependent binary interaction parameters. They were also compared to the PPR78 model, an entirely predictive group contribution method in which the kij depends on temperature.

Fluid phase equilibria for the CO2 + 2,3-dimethylbutane binary system from 291.9 K to 373.1 K

The phase behavior of the CO2 (1)+2,3-dimethylbutane (2) binary mixture has been experimentally studied between 293 and 373 K. Saturation pressures, ranging from 14.0 to 112.2 bar, were visually measured using a high-pressure cell at carbon dioxide mole fractions between 0.20 and 0.93. 78 experimental points have been measured: 67 bubble points and 11 dew points. Experimental results reveal that the vapor-liquid critical locus is a continuous curve between the two pure compounds, meaning that the studied binary system exhibits a type I or II phase behavior in the classification scheme of Van Konynenburg and Scott. The experimental data can be very satisfactorily represented by the Peng-Robinson equation of state with mixing rules that embed a temperature-dependent binary interaction parameter.

Solubility of Ethanethiol in Water

There are limited data in the open literature for the solubility of ethanethiol in water. A comprehensive literature review showed voids in the data set. The gaps in the literature data set were addressed with new experimental solubility measurements at temperatures in the range (298.15 to 413.15) K at pressures up to 1.75 MPa. The Peng-Robinson equation of state, with a temperature dependent binary interaction parameter, was used to correlate the new and existing data. The new solubility data were correlated to an average absolute percentage deviation of 1.3% in pressure and 8.1% in ethanethiol mole fraction. The VLLE phase boundary pressures of ethanethiol + water at (298.15, 313.15, 343.15, 373.15, and 413.15) K were also measured. Henry’s law constants, from the literature and those calculated from the Peng-Robinson equation of state, were correlated with a Clarke and Glew model over the (273.15 to 588.7) K temperature range. This model could correlate all of the Henry’s law constants to within an overall average absolute percentage deviation of 13.1%.

Boil-off calorimetry enthalpy measurements and equation of state of an aqueous pyridine azeotrope

We present measurement and modeling of the thermo-physical properties of an aqueous pyridine azeotrope for evaluation as a working fluid for power and thermal management applications. The enthalpy values of the Pyridine/water azeotrope were measured using an electrical matching boil-off flow calorimeter in the range of P = 0.101 to 11 MPa and T = 373 to 575 K. A Peng-Robinson equation of state model for mixtures was fitted to the experimental data using a temperature-dependent binary interaction parameter. The results were used to develop a pressure-enthalpy diagram with isotherms in both the liquid and vapor states.

Modeling the Vapor-Liquid equilibria of binary and ternary systems comprising associating and non-Associating compounds by using Perturbed-Chain Statistical association fluid Theory. Part I

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was implemented for modeling the vapor–liquid equilibrium of binary and ternary systems of carbon dioxide (CO2) + fatty oil, CO2 + ionic liquids (IL), CO2 + perfluoroalkanes, CO2 + HFE-449mec-f, CO2 + water + IL, CO2 + thiophene, and alcohols + thiophene at temperatures between 298.15 and 543.15 K and at pressures up to 200 bar. ILs studied in this work contain 1-octyl-3-methylimidazolium hexafluorophosphate [OMIM][PF6] and N-methyl-2-hydroxyethylammonium propionate [m-2HEA][Pr]. The PC-SAFT pure-component parameters were fitted to the experimental density and vapor pressure data of pure-components. For ILs, only liquid density data were used to obtain pure-IL PC-SAFT parameters, because of the negligible values of the vapor pressure of ILs. Temperature-dependent binary interaction parameters of the binary and ternary systems were fitted to vapor–liquid equilibrium data taken from experimental literature data. These parameters were then used to describe the VLE of other binary and ternary systems. Correlation results of the PC-SAFT were found to be in qualitative agreement with the available experimental data and improved the modeling accuracy of past models in the literature. The overall value of the absolute average relative deviation in pressure (ARDP) and vapor-phase mole fraction (ARDy) of 12.05% and 6.13%, respectively, reveals the goodness of the developed models for modeling the phase behavior of other associating or non-associating mixtures with the same parameters reported in this work.

Asphaltene precipitation from heavy oil mixed with binary and ternary solvent blends

Abstract Models are required to predict the onset and precipitation of asphaltenes from mixtures of heavy oil and solvents for a variety of heavy oil applications. The regular solution approach is well suited for this objective but has not yet been tested on solvent mixtures. To do so, the onset and amount of asphaltene precipitation were measured and modeled for mixtures of heavy oil with solvent blends made up from n-alkanes, cyclohexane, and toluene at temperatures of 21 and 180 °C and pressures of 0.1 and 10 MPa. Temperature dependent binary interaction parameters (BIP) between the cyclohexane/asphaltene and toluene/asphaltene pseudo-component pairs were proposed to match the data. All other BIP were set to zero. The model with BIP determined from asphaltene precipitation in heavy oil and binary solvents predicted asphaltene precipitation from heavy oil and ternary solvent blends, generally to within the experimental error.

Experimental determination and modelling of high-pressure phase behavior for the binary system CO2 + cyclooctane

Using a synthetic method, the phase behavior of the CO2 (1) + cyclooctane (2) binary system was for the first time experimentally studied between 292.95 K and 373.55 K. In this temperature range, the bubble- and dew-point pressures, ranging from 13.2 to 183.4 bar were measured for carbon dioxide mole fractions between 0.1014 and 0.9701. A total of 96 experimental data points were acquired. The experimental data were obtained using a high-pressure cell by visual observation of phase transitions. These measurements made it possible to conclude that the studied binary system probably exhibits a type V phase behavior in the classification scheme of Van Konynenburg and Scott. In particular, the experimental temperature of the suspected lower critical end point (LCEP) was found to be 303 K. Despite the complexity of the phase behavior, the experimental data could be accurately correlated with the Peng-Robinson equation of state combined with sophisticated mixing rules that either involve temperature-dependent binary interaction parameters (kij(T)) or that embed the residual part of the Wilson activity coefficient model.

Modelling Sorption Thermodynamics and Mass Transport of n-Hexane in a Propylene-Ethylene Elastomer.

Optimization of post polymerization processes of polyolefin elastomers (POE) involving solvents is of considerable industrial interest. To this aim, experimental determination and theoretical interpretation of the thermodynamics and mass transport properties of POE-solvent mixtures is relevant. Sorption behavior of n-hexane vapor in a commercial propylene-ethylene elastomer (V8880 VistamaxxTM from ExxonMobil, Machelen, Belgium) is addressed here, determining experimentally the sorption isotherms at temperatures ranging from 115 to 140 °C and pressure values of n-hexane vapor up to 1 atm. Sorption isotherms have been interpreted using a Non Random Lattice Fluid (NRLF) Equation of State model retrieving, from data fitting, the value of the binary interaction parameter for the n-hexane/V8880 system. Both the cases of temperature-independent and of temperature-dependent binary interaction parameter have been considered. Sorption kinetics was also investigated at different pressures and has been interpreted using a Fick’s model determining values of the mutual diffusivity as a function of temperature and of n-hexane/V8880 mixture composition. From these values, n-hexane intra-diffusion coefficient has been calculated interpreting its dependence on mixture concentration and temperature by a semi-empiric model based on free volume arguments.

Measurements and correlation of vapor-liquid equilibrium for difluoromethane (R-32) + 2,3,3,3-tetrafluoroprop-1-ene (R-1234yf) and pentafluoroethane (R-125) + propane (R-290)

A new set of recirculation-analytical type vapor-liquid equilibrium (VLE) apparatus was built, and the verification experiment of the R-125+R-290 system was carried out along three isotherms in the range of temperature from 273.15 K to 293.15 K. The experimental data is consistent with the literature data, which proves the reliability of the experimental system and method. In the temperature range of from 273.15 K to 358.15 K, the VLE measurement of the R-32+R-1234yf system was carried out along eight isotherms. The VLE data above 333.15 K was reported for the first time, and the measurement uncertainties of temperature, pressure, mole fraction were determined. Using the PRSV equation of state (EoS) combined with the W.S. mixing rule and NRTL activity coefficient model, the experimental VLE data of the R-32+R-1234yf system were correlated, and the temperature-dependent binary interaction parameters (BIP) within 273.15 to 343.15 K is obtained. For the R-32+R-1234yf system, the average relative deviation of the pressure ARD(p) is 0.34%, and the average absolute deviation of the vapor phase mole fraction AAD(y) is 0.0050. The experimental data in this work are in good agreement with the literature data.

Vapor-liquid equilibria, solid-vapor-liquid equilibria and H2S partition coefficient in (CO2 + CH4) at temperatures between (203.96 and 303.15) K at pressures up to 9 MPa

Vapor-liquid equilibrium (VLE) measurements of the (CO2 + CH4) system are reported along seven isotherms at temperatures varying from just above the triple point to just below the critical point of CO2 at pressures from the vapor pressure of pure CO2 to approximately 9 MPa, including near-critical states. From these data, the critical locus has been determined and correlated over its entire length. The VLE data are correlated with the Peng-Robinson equation of state (PR-EoS), using a temperature-dependent binary interaction parameter, and also compared with the predictions of the GERG-2008 equation of state. The former represents the phase compositions across all isotherms with a root-mean-square mole-fraction deviation of S = 0.0075 while, for the latter, S = 0.0126. Measurements of the three-phase solid-vapor-liquid equilibrium (SVLE) line are reported at temperatures from approximately (204 to 216) K and a new correlation is developed which is valid from 145 K to the triple point of CO2. Additionally, we report the partitioning of trace levels of H2S between coexisting liquid and vapor phases of the (CO2 + CH4) system and compare the results with the predictions of the PR-EoS.

Benchmark Database Containing Binary-System-High-Quality-Certified Data for Cross-Comparing Thermodynamic Models and Assessing Their Accuracy

In the last two centuries, equations of state (EoSs) have become a key tool for the correlation and prediction of thermodynamic properties of fluids. They not only can be applied to pure substances as well as to mixtures but also constitute the heart of commercially available computer-aided-process-design software. In the last 20 years, thousands of publications have been devoted to the development of sophisticated models or to the improvement of already existing EoSs. Chemical engineering thermodynamics is thus a field under steady development, and to assess the accuracy of a thermodynamic model or to cross-compare two models, it is necessary to confront model predictions with experimental data. In this context, the importance of a reliable free-to-access benchmark database is pivotal and becomes absolutely necessary. The goal of this paper is thus to present a database, specifically designed to assess the accuracy of a thermodynamic model or cross-compare models, to explain how it was developed and to enlighten how to use it. A total of 200 nonelectrolytic binary systems have been selected and divided into nine groups according to the associating character of the components, i.e., their ability to be involved in a hydrogen bond (the nature and strength of the association phenomena are indeed considered a measure of the complexity to model the thermodynamic properties of mixtures). The methodology for assessing the performance of a given model is then described. As an illustration, the Peng− Robinson EoS with classical van der Waals mixing rules and a temperature-dependent binary interaction parameter (k ij) have been used to correlate the numerous data included in the proposed database, and its performance has been assessed following the proposed methodology.

Solubility of methane in octamethylcyclotetrasiloxane: Experimental measurement and thermodynamic modeling

Liquid storage is a potential method for low-pressure storage of natural gas. In this work, octamethylcyclotetrasiloxane (OMCTS) was selected as a solvent for methane storage. Experimental measurements were carried out in a Cailletet apparatus, according to the synthetic method, from low to high pressures. One hundred experimentally-measured phase equilibrium data points are presented for methane + OMCTS in the form of bubble-points. The pressure, temperature, and methane mole fraction ranges are (0.61–8.07) MPa, (287.73–368.25) K, and (0.0534–0.4038), respectively. Furthermore, phase equilibrium calculations based on the ϕ−ϕ approach were carried out to model the methane + OMCTS binary system. In this regard, the Peng-Robinson EoS (PR EoS), coupled with the classical van der Waals (vdW) mixing rule, was applied. The vdW mixing rule was used in three modes: a) with no binary interaction parameters (kij=0,lij=0), b) with one constant binary interaction parameter (kij=constant), and c) with one temperature-dependent binary interaction parameter (kij=a+bT). It was concluded that both modes (b) and (c) give accurate results for methane solubility in OMCTS, with AAD(MPa) values of 0.11 and 0.10, respectively.

Towards accurate phase behavior modeling for hydrogen sulfide/water mixtures

Many deep gas wells contain acid gas components. Hydrogen sulfide (H2S) is one of the typical acid gases. Accurate flow simulations for H2S/H2O mixtures in reservoirs and wellbores requires a proper thermodynamic model that is capable of accurately modeling the H2S/H2O mixtures under in-situ conditions. This study aims at screening and developing cubic-equation-of-state-based thermodynamic models that can well describe the phase behavior of H2S/H2O mixtures. Peng-Robinson equation of state (PR EOS) (Peng and Robinson, 1976) and the Huron-Vidal (HV) (Huron and Vidal, 1979) mixing rule are used as the primary modeling framework. The temperature-dependent binary interaction parameter (BIP) correlations in the HV mixing rule are established by matching the measured vapor-liquid equilibria (VLE) data for H2S/H2O mixtures collected from the literature. The experimental VLE data cover a temperature range of 273.15–627.85 K and a pressure range of 0.41–303 bar, while the experimental density data cover a temperature range of 294.35–705.30 K and pressures up to 350 bar. Different volume translation strategies are examined in terms of their accuracy in reproducing the measured density data for H2S/H2O mixtures. We employ PR EOS together with the optimal BIP strategy in the HV mixing rule to reproduce the mutual solubility of H2S and H2O in VLE. The calculated results show a good agreement with the experimental data, especially at high temperatures and pressures; the average absolute percentage deviation (%AAD) of 4.90% and 4.95% can be obtained for reproducing the vapor-phase H2O solubility and the aqueous-phase H2S solubility, respectively. With the inclusion of the volume translation model proposed by Abudour et al. (2013), PR EOS together with the optimal BIP strategy in the HV mixing rule shows a good performance in estimating the aqueous-phase density for H2S/H2O VLE, i.e., an %AAD of 5.42% in reproducing the measured density data.

Evaluation of the Peng\u2013Robinson and the Cubic-Plus-Association Equations of State in Modeling VLE of Carboxylic Acids with Water

The performance of the classic Peng–Robinson (PR) and the modern Cubic-Plus-Association (CPA) equations of state were evaluated in modeling isobaric and isothermal vapor–liquid equilibria (VLE) of binary mixtures of carboxylic acids (formic, acetic, propanoic or butanoic) + water. Two functionalities of the alpha term were tested in PR, the original term proposed by Soave and the Matthias–Copeman term specially developed for modeling polar compounds. Within the Soave functionality, two generalized forms of the acentric factor were studied, the original general form and the Robinson and Peng modification for values of the acentric factor larger than 0.491. In addition, the case of PR with fitted parameters from saturated properties (as commonly obtained for modern equations of state) was also evaluated. VLE calculations without the use of a binary interaction parameter are in general more accurate with the modern CPA due to the association term; however, when a binary interaction parameter is used, the performance of the PR versions studied here are on average similar to those of CPA, and in some cases even superior. The original alpha function used in the PR equation and the original generalized form of the acentric factor are the best options for modeling organic acids + water systems when the binary interaction parameter is available. Temperature-dependent binary interaction parameters are provided as a database in modeling these complex systems.