A thermodynamic model for calculating nitrogen solubility,gas phase composition and density of the N2–H2O–NaCl system

A thermodynamic model is presented to calculate N₂ solubility in pure water (273–590 K and 1–600 bar) and aqueous NaCl solutions (273–400 K, 1–600 bar and 0–6 mol kg⁻¹) with or close to experimental accuracy. This model is based on a semi-empirical equation used to calculate gas phase composition of the H₂O–N₂ system and a specific particle interaction theory for liquid phase. With the parameters evaluated from N₂–H₂O–NaCl system and using a simple approach, the model is extended to predict the N₂ solubility in seawater accurately. Liquid phase density of N₂–H₂O–NaCl system at phase equilibrium and the homogenization pressure of fluid inclusions containing N₂–H₂O–NaCl can be calculated from this model. A computer code is developed for this model and can be downloaded from the website: www.geochem-model.org/programs.htm.     

Modelling of the phase behaviour for the direct synthesis of dimethyl carbonate from CO2 and methanol at supercritical or near critical conditions

This study is focused on modelling the phase equilibrium behaviour of the reaction mixture (CO₂ + methanol + DMC + H₂O) at high pressure–temperature conditions using the Patel–Teja (PT) and Peng–Robinson–Stryjek–Vera (PRSV) equations of state along with the van der Waals One-Fluid (1PVDW) mixing rule. The optimum values of the binary interaction parameters (k_ij) were calculated from VLE data found in the literature, and then adjusted to a lineal temperature equation. As a result, the temperature-dependent model was applied to predict the fluid phase equilibria of the corresponding binary a ternary sub-systems and, later, successfully contrasted with experimental data. In addition, phase equilibrium data were experimentally measured at high pressure (8 MPa to 15 MPa) for the ternary system (CO₂ + methanol + DMC), in order to confirm the ability of the model to predict the phase behaviour of the ternary system at high pressure–temperature. The agreement between the experimental data and the proposed model enables to predict the phase equilibrium behaviour of the mixture (CO₂ + methanol + DMC + H₂O), and thus, optimise the operation conditions in several reaction and separation processes.     

(Liquid + liquid) equilibria of the (water + butyric acid + dodecanol) ternary system

(Liquid + liquid) equilibrium (LLE) data for the (water + butyric acid + dodecanol) ternary system have been determined experimentally at T = (298.2, 308.2 and 318.2) K. Complete phase diagrams were obtained by determining binodal curves and tie lines. The reliability of the experimental tie lines was confirmed by using the Othmer–Tobias correlation. The UNIFAC method was used to predict the phase equilibrium in the ternary system using the interaction parameters determined from experimental data of CH₃, CH₂, COOH, OH and H₂O functional groups. Distribution coefficients and separation factors were evaluated for the immiscibility region.     

Vapor–liquid equilibria for the ternary mixture of carbon dioxide + 1-propanol + propyl acetate at elevated pressures

Vapor–liquid equilibrium (VLE) data for the ternary mixture of carbon dioxide, 1-propanol and propyl acetate were measured in this study at 308.2, 313.2, and 318.2 K, and at pressures ranging from 4 to 10 MPa. A static type phase equilibrium apparatus with visual sapphire windows was used in the experimental measurements. New VLE data for CO₂ in the mixed solvent were presented. These ternary VLE data at elevated pressures were also correlated using either the modified Soave–Redlich–Kwong or Peng–Robinson equation of state (EOS), and by employing either the van der Waals one-fluid or Huron–Vidal mixing model. Satisfactory correlation results from both EOS models are reported with temperature-independent binary interaction parameters. It is observed that at 318.2 K and 10 MPa, 1-propanol may probably be separated from propyl acetate into the vapor phase at the entire concentration range in the presence of high pressure CO₂.     

Phase diagram of the ternary system NMMO/water/cellulose

The phase diagram of the system N-methylmorpholine-N-oxide(NMMO)/H₂O/cellulose has been measured at 80 °C by establishing a solubility map (observation of the mixtures under the microscope), by the analysis of coexisting phases and determining the critical point. These experiments manifest a continuous reduction of the two phase area existing for the subsystem H₂O/cellulose upon the addition of NMMO, where a weight fraction of NMMO in the mixed solvent exceeding 75 wt% is required for Solucell 400 to reach the critical composition. The critical cellulose concentration is only 0.34 wt%, i.e., more than an order of magnitude lower than for the solutions of typical vinyl polymers in mixed solvents. All experimental observations can be well modeled on the basis of composition dependent binary interaction parameters by means of recently established mixing rules. For the subsystems H₂O/cellulose and NMMO/water the corresponding data are known from independent earlier measurements. The adjustment of two parameters to the ternary phase diagram was required to obtain this information for NMMO/cellulose, the third binary subsystem.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + ZnCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases and relevant gaseous species of the (NaCl + KCl + MgCl₂ + CaCl₂ + ZnCl₂) system, and optimized model parameters have been found. The (NaCl + KCl + MgCl₂ + CaCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase.     

Isobaric Vapor–Liquid Equilibrium for the Mixture of Neohexane,Cyclopentane and N,N-Dimethylformamide at 101.3 kPa

The vapor–liquid phase equilibrium (VLE) data for binary systems of neohexane?+?cyclopentane, neohexane?+?N,N-dimethylformamide (DMF), cyclopentane?+?DMF and ternary system of neohexane?+?cyclopentane?+?DMF were determined with a modified Rose still at 101.3 kPa, and all the binary data passed the Wisniak’s test (D?<?5), which accorded with the thermodynamic consistency. Three activity coefficient models namely, Wilson, NRTL and UNIQUAC were used to correlate VLE data and get binary interaction parameters, then the ternary VLE data of neohexane?+?cyclopentane?+?DMF were estimated based on these model parameters using Aspen Plus software. The estimation values of the three models agree well with the experimental data (σ(T)?<?0.5 K). Moreover, the analysis of the effect of DMF on the vapor–liquid phase equilibrium shows that DMF can act as an effective extractant for the system studied.

     

Thermodynamic evaluation and optimization of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaNO₃ + KNO₃ + Na₂SO₄ + K₂SO₄) ternary reciprocal system, and optimised model parameters have been found. The model parameters obtained for the four binary common-ion subsystems (i.e. (NaNO₃ + Na₂SO₄), (KNO₃ + K₂SO₄), (NaNO₃ + KNO₃) and (Na₂SO₄ + K₂SO₄)) are used to predict thermodynamic properties and phase equilibria for the entire system. The Modified Quasichemical Model in the Quadruplet Approximation for short-range ordering was used for the molten salt phase, and the Compound Energy Formalism was used for the various solid solutions.     

Thermodynamic optimization of the (Na2O + SiO2 + NaF + SiF4) reciprocal system using the Modified Quasichemical Model in the Quadruplet Approximation

All available thermodynamic and phase diagram data for the condensed phases of the ternary reciprocal system (NaF + SiF₄ + Na₂O + SiO₂) have been critically assessed. Model parameters for the unary (SiF₄), the binary systems and the ternary reciprocal system have been found, which permit to reproduce the most reliable experimental data. The Modified Quasichemical Model in the Quadruplet Approximation was used for the oxyfluoride liquid solution, which exhibits strong first-nearest-neighbor and second-nearest-neighbor short-range ordering. This thermodynamic model takes into account both types of short-range ordering as well as the coupling between them. Model parameters have been estimated for the hypothetical high-temperature liquid SiF₄.     

Phase equilibria involved in extractive distillation of dipropyl ether + 1-propyl alcohol using 2-ethoxyethanol as entrainer

Consistent vapour–liquid equilibrium data at 101.3 kPa have been determined for the ternary system dipropyl ether + 1-propyl alcohol + 2-ethoxyethanol and two constituent binary systems: dipropyl ether + 2-ethoxyethanol and 1-propyl alcohol + 2-ethoxyethanol. The dipropyl ether + 2-ethoxyethanol system shows positive deviations from ideal behaviour and 1-propyl alcohol + 2-ethoxyethanol system exhibits no deviation from ideal behaviour. The activity coefficients and the boiling points were correlated with their compositions by the Wilson, NRTL and UNIQUAC equations. It is shown that the models allow a very good prediction of the phase equilibria of the ternary system using the pertinent parameters of the binary systems. The parameters obtained from binary data were utilized to predict the phase behaviour of the ternary system. The results showed a good agreement with the experimental values. Moreover, the entrainer capabilities of 2-ethoxyethanol were compared with 1-pentanol, butyl propionate and N,N-dimethylformamide, concluding that N,N-dimethylformamide is the best entrainer.     

(Liquid + liquid) equilibria of three ternary systems: (heptane + benzene + N-formylmorpholine), (heptane + toluene + N-formylmorpholine), (heptane + xylene + N-formylmorpholine) from T = (298.15 to 353.15) K

(Liquid + liquid) equilibrium (LLE) data for ternary systems: (heptane + benzene + N-formylmorpholine), (heptane + toluene + N-formylmorpholine), and (heptane + xylene + N-formylmorpholine) have been determined experimentally at temperatures ranging from 298.15 K to 353.15 K. Complete phase diagrams were obtained by determining solubility and tie-line data. Tie-line compositions were correlated by Othmer–Tobias and Bachman methods. The universal quasichemical activity coefficient (UNIQUAC) and the non-random two liquids equation (NRTL) were used to predict the phase equilibrium in the system using the interaction parameters determined from experimental data. It is found that UNIQUAC and NRTL used for LLE could provide a good correlation. Distribution coefficients, separation factors, and selectivity were evaluated for the immiscibility region.     

Equilibrium solubility of carbon dioxide in a 30 wt.% aqueous solution of 2-((2-aminoethyl)amino)ethanol at pressures between atmospheric and 4400 kPa: An experimental and modelling study

New experimental equilibrium data were obtained for the solubility of carbon dioxide in an aqueous solution with 30 wt.% of 2-((2-aminoethyl)amino)ethanol (AEEA) at temperatures ranging from (313.2 to 368.2) K and CO₂ partial pressures ranging from above atmospheric to 4400 kPa. A thermodynamic model based on the Deshmukh–Mather method was applied to correlate and predict the CO₂ solubility in aqueous AEEA solutions. The binary interaction parameters and equilibrium constants for the proposed reactions were determined by data regression. Using the adjusted parameters, equilibrium partial pressures of CO₂ were calculated and compared with the corresponding experimental values at the selected temperatures and pressures. Values of carbon dioxide solubility at other temperatures reported in the literature were also calculated. The average absolute deviation for all of the data points was found to be 8.2%. The enthalpy change of the absorption of CO₂ in the 30 wt.% aqueous solution of AEEA was also estimated with our model.     

Correlation of CO2 solubility in N-methyldiethanolamine + piperazine aqueous solutions using extended Debye–Hückel model

Solubility data of CO₂ in aqueous N-methyldiethanolamine (MDEA) solutions of concentration (2.52, 3.36, and 4.28) kmol/m³ were obtained at temperatures (313, 323, and 343) K and partial pressures ranging from about (30 to 5000) kPa. A thermodynamic model based on extended Debye–Hückel theory was applied to predict and correlate of CO₂ solubility in various aqueous amine solutions. The effect of piperazine (PZ) concentration on CO₂ loading in MDEA solutions was determined at PZ concentration (0.36, 0.86, and 1.36) kmol/m³. Using experimental data in various temperatures the interaction parameters of activity coefficient model for these systems were determined. The results show the model consistency with experimental and literature data and PZ is beneficial to the CO₂ loading. The comparison of results of this study with previous data work shows the wide range of CO₂ loading considered in this work and the better agreement of model with experimental data. The average absolute relative deviation percent (δ_AAD) for all data points were 8.11%.     

Phase equilibria for the extraction of sec-butylbenzene from dodecane with N,N-dimethylformamide

The phase equilibria for the ternary system: dodecane + sec-butylbenzene + N,N-dimethylformamide (DMF) was studied over a temperature range of 288–318 K and at atmospheric pressure. Such a system is found in the extraction of aromatics in the middle distillate production. The system studied exhibits type I liquid–liquid phase diagram. The values of distribution coefficients and selectivities were calculated from the equilibrium data. The effect of temperature and solute concentration in the feed upon solubility, distribution coefficient, and selectivity were investigated experimentally and theoretically. The experimental results of the studied system was regressed to estimate the interaction parameters between each of the three pairs of components with NRTL and UNIQUAC models as a function of temperature. Both models satisfactorily correlate the experimental data, and they are equally the same.     

Thermodynamic evaluation and optimization of the (LiF + NaF + KF + MgF2 + CaF2 + SrF2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (LiF + NaF + KF + MgF₂ + CaF₂ + SrF₂) system, and optimized model parameters have been found. The (LiF + NaF + KF + MgF₂ + CaF₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase, and the low-temperature and high-temperature (CaF₂ + SrF₂) solid solutions were modelled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Li, Na, K)(Mg, Ca, Sr)F₃ perovskite phase was modelled using the Compound Energy Formalism.     

Cloud-point measurements of the {H2O + poly(ethylene glycol) + NaNO3} system

The cloud-point (CP) temperatures and phase separation of {H₂O + poly(ethylene glycol) + NaNO₃} ternary system is studied by the turbidimetry method using a reaction calorimeter. The phase separation was also observed by visual inspection. Differences between the CP measured using the turbidimetry method and visual inspection, was up ±0.5 K. The Flory–Huggins model with a temperature and concentration-dependent interaction parameter was employed to correlate the phase diagram of the system. As a result of the correlation an average absolute deviation of 0.002 is obtained.     

A density model based on the Modified Quasichemical Model and applied to the (NaCl + KCl + ZnCl2) liquid

A theoretical model for the density of multicomponent inorganic liquids based on the Modified Quasichemical Model has been presented previously. By introducing in the Gibbs free energy of the liquid phase temperature-dependent molar volume expressions for the pure components and pressure-dependent excess parameters for the binary (and sometimes higher-order) interactions, it is possible to reproduce, and eventually predict, the molar volume and the density of the multicomponent liquid phase using standard interpolation methods. In the present article, this density model is applied to the (NaCl + KCl + ZnCl₂) ternary liquid and a Kohler–Toop-like asymmetric interpolation method is used. All available density data for the (NaCl + KCl + ZnCl₂) liquid were collected and critically evaluated, and optimized pressure-dependent model parameters have been found. This new volumetric model can be used with Gibbs free energy minimization software, to calculate the molar volume and the density of (NaCl + KCl + ZnCl₂) ternary melts.     

Vapor–liquid equilibria for the ternary system of carbon dioxide + ethanol + ethyl acetate at elevated pressures

Vapor–liquid equilibrium (VLE) data for the ternary system of carbon dioxide, ethanol and ethyl acetate were measured in this study at 303.2, 308.2, and 313.2 K, and at pressures from 4 to 7 MPa. A static type phase equilibrium apparatus with visual sapphire windows was used in the experimental measurements. New VLE data for CO₂ in the mixed solvent were presented. These ternary VLE data at elevated pressures were also correlated using either the modified Soave–Redlich–Kwong or Peng–Robinson equation of state, with either the van der Waals one-fluid or Huron–Vidal mixing model. Satisfactory correlation results are reported with temperature-independent binary parameters. It is observed that at 313.2 K and 7 MPa, ethanol can be separated from ethyl acetate into the vapor phase at all concentrations in the presence of high pressure CO₂.     

Ebulliometric determination and prediction of (vapor + liquid) equilibria for binary and ternary mixtures containing alcohols (C1–C4) and dimethyl carbonate

(Vapor + liquid) equilibrium (VLE) data for a ternary mixture, namely {methanol + propan-1-ol + dimethyl carbonate (DMC)}, and four binary mixtures, namely an {alcohol (C₃ or C₄) + DMC}, containing the binary constituent mixtures of the ternary mixture, were measured at p = (40.00 to 93.32) kPa using a modified Swietoslawski-type ebulliometer. The experimental data for the binary systems were correlated using the Wilson model. The Wilson model was also applied to the ternary system to predict the VLE behavior using parameters from the binary mixtures. The modified UNIFAC (Dortmund) model was also tested for the predictions of the VLE behavior of the binary and ternary mixtures. In addition, the experimental VLE data for the ternary and constituent binary mixtures were correlated using the extended Redlich–Kister (ERK) model, which can completely represent the azeotropic points. For the ternary system, a comparison of the experimental and the predicted or correlated boiling points obtained using the Wilson and ERK models showed that the ERK model is more accurate. The valley line, i.e., the curve which divides the patterns of vapor–liquid tie lines, was found in the (methanol + propan-1-ol + DMC) system. This valley line could be represented by the ERK model. Finally, the composition profile for simple distillation of this ternary mixture was obtained by analysis of the residue curves from the estimated Wilson parameters of the constituent binary mixtures.     

(Liquid + liquid) equilibria of (sulfolane + benzene + n-hexane), (N-formylmorpholine + benzene + n-hexane), and (sulfolane + N-formylmorpholine + benzene + n-hexane) at temperatures ranging from (298.15 to 318.15) K: Experimental results and correlation

The experimental (liquid + liquid) equilibrium (LLE) properties for two ternary systems containing (N-formylmorpholine + benzene + n-hexane), (sulfolane + benzene + n-hexane) and a quaternary mixed solvent system (sulfolane + N-formylmorpholine + benzene + n-hexane) were measured at temperature ranging from (298.15 to 318.15) K and at an atmospheric pressure. The experimental distribution coefficients and selectivity factors are presented to evaluate the efficiency of the solvents for extraction of benzene from n-hexane. The LLE results obtained indicate that increasing temperature decreases selectivity for all solvents. The LLE results for the systems studied were used to obtain binary interaction parameters in the UNIQUAC model by minimizing the root mean square deviations (RMSD) between the experimental and calculated results. Using the interaction parameters obtained, the phase equilibria in the systems were calculated and plotted. The calculated compositions based on the UNIQUAC model were found to be in good agreement with the experimental values. The result of the RMSD obtained by comparing the calculated and experimental two-phase compositions is 0.0163 for (N-formylmorpholine + benzene + n-hexane) system and is 0.0120 for (sulfolane + benzene + n-hexane) system.