Computing all the azeotropes in refrigerant mixtures through equations of state

Azeotropic mixtures of fluorocarbon (FC) and hydro fluorocarbon (HFC) with hydrocarbons are gaining popularity as drop-in substitutes for CFCs and HCFCs. A method to compute all the azeotropes in a refrigerant mixture through the equation of state approach is described. The method allows prediction of all the azeotropes in a refrigerant mixture and is in close agreement with the experimental data. Both the vapor and the liquid phase non-idealities are incorporated through fugacity coefficients modeled using Peng–Robinson–Stryjek–Vera equation of state with Wong-Sandler and van der Waals mixing rules. Homotopy continuation based methodology guarantees computation of all the solutions of necessary and sufficient condition of azeotropy in multicomponent refrigerant mixtures. The method establishes the pressure dependency of azeotropic composition allowing prediction of bifurcation pressure where refrigerant azeotropes may appear or disappear and predicts azeotropes at elevated pressures. The approach is independent of equation of state and mixing rules but rely on their ability to represent the phase behavior. The approach is tested with R23–R13, propane–R227ea binary mixtures and a ternary mixture of R32–R125–R143a.     

High-pressure phase equilibria for the carbon dioxide–2-methyl-1-butanol,carbon dioxide–2-methyl-2-butanol,carbon dioxide–2-methyl-1-butanol–water,and carbon dioxide–2-methyl-2-butanol–water systems

High-pressure vapor–liquid equilibria for the binary carbon dioxide–2-methyl-1-butanol and carbon dioxide–2-methyl-2-butanol systems were measured at 313.2 K. The phase equilibrium apparatus used in this work is of the circulation type in which the coexisting phases are recirculated, on-line sampled, and analyzed. The critical pressure and corresponding mole fraction of carbon dioxide for the binary carbon dioxide–2-methyl-1-butanol system at 313.2 K were found to be 8.36 MPa and 0.980, respectively. The critical point of the binary carbon dioxide–2-methyl-2-butanol was also found 8.15 MPa and 0.970 mole fraction of carbon dioxide. In addition, the phase equilibria of the ternary carbon dioxide–2-methyl-1-butanol–water and carbon dioxide–2-methyl-2-butanol–water systems were measured at 313.2 K and several pressures. These ternary systems showed the liquid–liquid–vapor phase behavior over the range of pressure up to their critical point. The binary equilibrium data were all reasonably well correlated with the Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), and Patel–Teja (PT) equations of state with eight different mixing rules the van der Waals, Panagiotopoulos–Reid (P&R), and six Huron–Vidal type mixing rules with UNIQUAC parameters.     

Correlation of gas solubilities in water and methanol at high pressure

A random—nonrandom—mixture equation for the Helmholtz energy of a fluid mixture is shown to correlate the solubility of inert and acidic gases in water and methanol quite accurately at pressures up to 300 bar. Further, the calculated Henry's law constants of the gases in water show good agreement with experimental data.The gas solubility models is a modification of our previous model. It contains three binary interaction parameters, one in the reduced density term and two in the attractive terms. When the nonrandom parameter vanishes the model reduces to the classical mixing rule. The model correlates vapour—liquid equilibria in binary and ternary hydrocarbon—methanol systems quite accurately.The results of the correlation are compared with results obtained using the classical van der Waals quadratic mixing rule. The random—nonrandom model is, in all cases, superior to the van der Waals model. Finally, a comparison of computer time consumption for the two models is given.     

The experiments and correlations of the solubility of ethylene in toluene solvent

Polymer cyclic olefin copolymer (COC) is produced from the reaction of attaching ethyl groups to the norbornene monomer in liquid phase. The first step of process is dissolving ethylene in a liquid phase where toluene is present as a cosolvent. Thus, the solubility of ethylene in liquid toluene is the most important factor affecting the production of COC. In this study, the solubility of ethylene in toluene was measured in the temperature range from 323.15 to 423.15 K and pressure range from 5 to 25 bar. The experiments were conducted by the method of pressure decaying with a newly designed apparatus. The experimental results show that the solubility of ethylene in toluene increases with increasing pressure but decreases with increasing temperature.The experimental solubility data were expressed in the vapor–liquid equilibrium relationship and correlated fairly well by the bubble–pressure calculation with the Peng–Robinson equation of state (PR EOS) incorporated with the van der Waals one-fluid and the Zhong–Masuoka mixing rules with the consideration of binary interaction parameters. The results showed the van der Waals (vdW-1) mixing rule is slightly better than the Z–M mixing rule for pressure correlation but the Z–M mixing rule is slightly better for vapor composition correlation.A semi-empirical solubility equation with four parameters for the present binary system was proposed in this study. This proposed model estimates the solubility easier and as accurate as the PR EOS does for the present system.     

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.     

Patterns of solid–fluid phase equilibria: new possibilities?

Thermodynamic phase space patterns of solid–liquid–vapor (slg) behavior in binary systems are reviewed. The van der Waals equation of state is used in combination with a common mathematical artifice for the solid–phase fugacity function to map out the slg loci for a model binary homologous series of solvent+solute mixtures as a function of the solute characterization. The computational results suggest the possible existence of a richer thermodynamic phase space topography than previously envisioned.     

Application of a generalized van der Waals equation of state to several nonpolar mixtures

A generalized van der Waals equation of state, applied recently (Nguyen Van Nhu and Kohler, 1995) to the calculation of excess properties and phase equilibria for the mixture methane + ethane, is now extended to several nonpolar binary mixtures.Improved mixing rules for the van der Waals attractive term and for the correction term are proposed. With these mixing rules, the equation gives good agreement for vapour-liquid and liquid-liquid equilibria over a large temperature range for 29 binary mixtures. The agreement of mixture volumes and cross second virial coefficients is also satisfactory.     

Vapor-liquid equilibria for alcohol/hydrocarbon systems using the CPA Equation of state

The recently developed Cubic-Plus-Association Equation of State (CPA EoS) is extended in this study to binary systems containing one associating compound (alcohol) and an inert one (hydrocarbon). CPA combines the Soave-Redlich-Kwong (SRK) equation of state for the physical part with an association term based on perturbation theory. The classical van der Waals one-fluid mixing rules are used for the attractive and co-volume parameters, and b, while the extension of the association term to mixtures is rigorous and does not require any mixing rules. Excellent correlation of Vapor-Liquid Equilibria (VLE) is obtained using a small value for the interaction parameter (k_ij) in the attractive term of the physical part of the equation of state even when it is temperature-independent. CPA yileds much better results than SRK and its performance is similar to that of other association models, like the Anderko EoS, and the more complex SAFT and Simplified SAFT EoS.     

Calculation of high pressure vapour—liquid equilibria for systems containing polar substances with the use of an augmented van der Waals equation of state

An augmented van der Waals equation of state based on a perturbation theory has been applied to the calculation of high pressure vapour—liquid equilibria for systems containing polar substances. The equation of state comprises four terms, which imply the contributions from repulsion, symmetric, non-polar asymmetric, and polar asymmetric interactions. The characteristic parameters of each pure substance have been determined by three methods with the use of vapour pressures and saturated liquid densities. Mixing models for the terms of the repulsion, symmetric, and non-polar asymmetric interactions are the same as used previously. Two types of mixing models based on a three-fluid model and/or a one-fluid model are developed for the polar asymmetric term. The polar asymmetric term has a large effect on the prediction of the vapour—liquid equilibrium. With the introduction of a binary interaction parameter, the equation is found to be useful in correlating the vapour—liquid equilibria for a system containing a polar substance except near a critical region.     

Experimental measurement and modeling of the vapor–liquid equilibrium of carbon dioxide + chloroform

Isothermal bubble and dew points, saturated molar volumes, and mixture critical points for binary mixtures of carbon dioxide+chloroform (trichloromethane) (CO₂/CHCl₃) have been measured in the temperature region 303.15–333.15 K and at pressures up to 100 bar. Mixture critical points are reported at 313.15, 323.15, and 333.15 K. The data were modeled with the Peng–Robinson equation of state using both the van der Waals-1 (vdW-1) mixing rule and the Wong–Sandler (WS) mixing rule incorporating the UNIQUAC excess free energy model. The WS mixing rule provided a better representation of the data than did the vdW-1 mixing rule, though with three adjustable parameters instead of one. The extrapolating ability of both of the mixing rules was investigated. Using the parameters regressed at 323.15 K, the WS mixing rule yielded better extrapolations for the composition dependence at 303.15, 313.15, and 333.15 K than the vdW-1 mixing rule.     

Phase equilibrium calculations of highly polar systems

It is well known that highly polar and hydrogen bonding mixtures pose a serious challenge to equations of state. In the present report it is shown that excellent correlations and predictions of complex systems can be achieved when the van der Waals mixing rules are properly associated with an equation of state. In this report the proper form of the van der Waals mixing rules is used with the Peng—Robinson equation of state to predict the vapor—liquid equilibrium properties of water—ketone, water—alcohol, alcohol—ketone, and other complex mixtures, which exhibit either positive or negative azeotropy, with an accuracy which was not achievable by the original form of Peng—Robinson equation of state of mixtures.     

Volume expansion and vapour–liquid equilibrium of toluene and ethanol with carbon dioxide at high pressures for the selection of optimum operational condition in the GAS process

High-pressure equilibrium data (vapour–liquid equilibria) were measured for CO₂ + toluene and CO₂ + ethanol systems between 298.15K and 318.15K and pressures up to 7.8 MPa. Based on reported relative volume expansion of solvents, the optimum operational condition for production of fine particles in Gas Anti-Solvent process has been suggested. Moreover, thermodynamic modelling of phase equilibria has been done using Peng-Robinson and Soave-Redlich-Kwong (SRK) equations of state along with van der Waals and Huron Vidal (HV) mixing rules. The results showed that the SRK–HV combination has the best accuracy between studied models and is capable of simulating the binary systems investigated in current research.     

Isothermal vapor–liquid equilibria of the ternary system formed by ethanol,tert-amyl methyl ether and toluene

Vapor–liquid equilibrium (VLE) data are presented for the ternary system ethanol–tert-amyl methyl ether (TAME)–toluene at 333.15 K. The experimental results were measured by using a Boublik vapor–liquid recirculation still. The results are compared with values predicted from the PRSV equation of state with the modified Huron–Vidal first order (MHV1) and Wong–Sandler (WS) mixing rules. Good agreement is obtained.     

A local composition extension of the van der Waals mixing rule for PR cubic equation of state

New mixing rules (VWLC-I and II) capable of connecting van der Waals (VDW) to CEOS/A^E mixing rule models were developed. These models are able to incorporate the same multi-component mixture parameters obtained for the van der Waals and CEOS/A^E models simultaneously. The VWLC mixing rules directly incorporate local compositions into the cubic equations of state (CEOS). The energy parameters required for the local compositions are calculated from the CEOS parameters. The Peng–Robinson (PR) CEOS was used for this study. Binary interactions parameters were obtained by adjusting the vapor pressure of the binary mixture for several low and high-pressure systems. The predictive capabilities of the VWLC mixing rules were tested by vapor–liquid equilibria calculations for low and high-pressure multicomponent systems. The results were compared with the predictions of the VDW mixing rule and a Huron–Vidal (HV) kind of CEOS/A^E-NRTL mixing rule. The VWLC mixing rules are consistent models giving good results in a broad range of pressures and temperatures in binary and multicomponent mixtures. They compare favorably with the CEOS/A^E-NRTL mixing rule for low-pressure systems. In high-pressure ternary systems VWLC-I and II give good predictions, much better, in fact, than the CEOS/A^E-NRTL mixing rule.     

Clathrate hydrate dissociation conditions of refrigerants R404A,R406A,R408A and R427A: Experimental measurements and thermodynamic modeling

Clathrate hydrate dissociation conditions were measured for four “alternative” refrigerants, viz. R404A, R406A, R408A and R427A. The experimental measurements were performed within the pressure range of (0.079 to 9.995) MPa and temperatures ranging from (272.7 to 288.7) K. An isochoric pressure-search method was used to perform the measurements. A thermodynamic model based on the van der Waals–Platteeuw (vdW–P) model was applied for the prediction of the dissociation conditions which were compared to the experimental measurements. The fluid phase was modeled using the MHV2 G^E-EoS mixing rule along with the UNIFAC (original) activity model. The van der Waals–Platteeuw (vdW–P) model was used for the modeling of the hydrate phase. There was reasonable agreement between the experimental and predicted values.     

聚合物流体的范德华凝聚行为

研究了由聚合物的范德华作用导致的凝聚行为. 研究发现, 尽管聚合物同小分子的相行为的形成原因不同(聚合物体系的相行为是由动能、构象熵项和范德华作用能三项相互竞争的结果, 而小分子的相行为是由动能和范德华作用能相互竞争的结果), 但是它们表现出了极为相似的相行为.     

Comparison of different mixing rules for prediction of density and residual internal energy of binary and ternary Lennard–Jones mixtures

Mixing rules are necessary when equations of state for pure fluids are used to calculate various thermodynamic properties of fluid mixtures. The well-known van der Waals one-fluid (vdW1) mixing rules are proved to be good ones and widely used in different equations of state. But vdW1 mixing rules are valid only when molecular size differences of components in a mixture are not very large. The vdW1 type density-dependent mixing rule proposed by Chen et al. [1] is superior for the prediction of pressure and vapor–liquid equilibria when components in the mixture have very different sizes. The extension of the mixing rule to chain-like molecules and heterosegment molecules was also made with good results. In this paper, the comparison of different mixing rules are carried out further for the prediction of the density and the residual internal energy for binary and ternary Lennard–Jones (LJ) mixtures with different molecular sizes and different molecular interaction energy parameters. The results show that the significant improvement for the prediction of densities is achieved with the new mixing rule [1], and that the modification of the mixing rule for the interaction energy parameter is also necessary for better prediction of the residual internal energy.     

Applicability of cubic equation of state mixing rules on correlation of excess molar volume of Non-Electrolyte binary mixtures

The excess molar volume V ^E data of the binary liquid systems were correlated by the Peng–Robinson–Stryjek–Vera equation of state coupled with two different types of mixing rules: composition dependent van der Waals mixing rule (vdW) and the mixing rule based on the Gupta–Rasmussen–Fredenslund method (GRF), with the NRTL equation as G ^E model. The results obtained by these models show that type of applied mixing rule, a number and position of interaction parameters are of great importance for a satisfactory correlation of V ^E data. The GRF mixing rules coupled with the NRTL model gave mostly satisfactory results for V ^E correlation of the nonideal binary systems of diverse complexity.     

Vapor‐Liquid Phase Equilibria for Carbon Dioxide+Isopentanol Binary System at Elevated Pressure

High‐pressure vapor‐liquid phase equilibrium data for carbon dioxide+isopentanol were measured at temperatures of 313.2, 323.1, 333.5 and 343.4 K in the pressure range of 4.64 to 12.71 MPa in a variable‐volume high‐pressure visual cell. The experimental data were well correlated with Peng‐Robinson equation of state (PR‐EOS) together with van der Waals‐2 two‐parameter mixing rule, and the binary interaction parameters were obtained. Henry coefficients and partial molar volumes of CO₂ at infinite dilution were estimated based on Krichevsky‐Kasarnovsky equation, and Henry coefficients increase with increasing temperature, however, partial molar volumes of CO₂ at infinite dilution are negative and the magnitudes decrease with temperature.     

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.