High-pressure Vapor-liquid Equilibria Research Articles

High-pressure vapor–liquid equilibria in the nitrogen– n-nonane system

New experimental vapor–liquid equilibrium data of the N 2– n-nonane system were measured over a wide temperature range from 344.3 to 543.4 K and pressures up to 50 MPa. A static-analytical apparatus with visual sapphire windows and pneumatic capillary samplers was used in the experimental measurements. Equilibrium phase compositions and vapor–liquid equilibrium ratios are reported. The new results were compared with those reported by other authors. The comparison showed that the pressure-liquid phase composition data reported in this work are in good agreement with those determined by others. The experimental data were modeled with the PR and PC-SAFT equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results of the modeling showed that the PC-SAFT equation was superior to the PR equation in correlating the experimental data of the N 2– n-nonane system.

High-pressure Vapor-Liquid Equilibrium Studies for DME-CO 2-CH 3OH and DME-CO 2-C 2H 5OH Systems

In this study, the Gibbs-Duhem equation was applied to make the thermodynamic consistency test and thermodynamic model estimation for systems of CO 2-DME (dimethyl ether), DME-CH 3OH, CO 2-CH 3OH and C 2H 5OH systems on the basis of the vapor-liquid equilibrium (VLE) experimental data in published reports. And the NRTL binary interaction parameters of the systems mentioned above were regressed by the VLE data and were subjected to a thermodynamic consistency test because the study showed that PR-NRTL model combination was appropriate for the four systems mentioned above. The regressed binary interaction parameters were used to estimate the VLE for DME-CO 2-CH 3OH at temperatures of 313.15K and 333.15K, and the estimated result was coincident with the experimental data. On the basis of the predicted VLE data for systems of DME-CO 2-CH 3OH and DME-DME-CO 2-C 2H 5OH, the VLE behaviors of the two systems were studied by the phase diagrams of these two ternary systems, with the forms of both the two dimensional and three dimensional phase diagrams, respectively.

High pressure vapor–liquid equilibrium measurements of carbon dioxide with naphthalene and benzoic acid

High pressure vapor–liquid equilibrium data for binary systems of carbon dioxide with naphthalene and benzoic acid were measured at three different temperatures for each system. Experimental temperatures and pressures ranged from 373 to 458 K and 0 to 22 MPa, respectively. Dew points were also measured for naphthalene in the CO 2 rich region. The data measured provides valuable solubility information and is used to derive gas–solvent group interaction parameters for the predictive Soave–Redlich–Kwong equation of state.

Determination and modelling of the high-pressure vapour–liquid equilibrium carbon dioxide–methyl acetate

Experimental data for the high-pressure vapour–liquid equilibrium of the binary system of carbon dioxide and methyl acetate have been measured. Equilibrium data were needed for investigation of acetic acid esterification with methanol. Pressure–composition ( P– x) isotherms were determined at 308, 318 and 328 K and an operation pressure up to 9 MPa. Data were modelled using the Peng–Robinson equation of state. Van der Waals one-fluid mixing rules were used for the temperature-dependent function a and for parameter b in the Peng–Robinson equation. One parameter van der Waals model for the cross coefficient terms a ij and b ij was used, which both contain one adjustable binary interaction parameter k ij and l ij , respectively. In a second modelling method the temperature dependence of k ij and l ij was determined. A comparison of experimental results with calculations obtained from PR equation showed a reasonable accordance of the data over a wide range of composition.

An algorithm for convergent solutions in vapor–liquid equilibrium calculations using an equation of state

In high-pressure vapor–liquid equilibrium calculations using an equation of state, two types of convergence problems may be encountered as the critical region is approached. One is the trivial solution in which compositions and densities for equilibrium phases become identical and the other is the divergence problem. In the present study, an efficient algorithm was proposed to remove these difficulties in the extended regions by introducing auxiliary loops for composition and pressure (or temperature) iterations. The algorithm was found to extend the region of convergence to near critical points efficiently without using the information on adjacent equilibrium points.

Styrene–carbon dioxide phase equilibria at high pressures

High pressure vapor–liquid equilibrium data for the binary system styrene and carbon dioxide were measured using the static method. Experiments were carried out at temperatures and pressures between 333.15 and 348.15 K, and 6 and 13 MPa, respectively. Experimental results were correlated with the Peng–Robinson equation of state using conventional mixing rules with one interaction parameter.

Measurements and modeling of high-pressure phase behavior of binary CO 2–amides systems

High-pressure vapor–liquid equilibrium (VLE) data were measured for binary CO 2– N, N-dimethylformamide, CO 2– N, N-diethylformamide and CO 2– N, N-dibutylformamide systems at various temperatures (318.2–398.2 K) and pressure up to 25 MPa. These CO 2– N, N-dimethylformamide, CO 2– N, N-diethylformamide and CO 2– N, N-dibutylformamide systems exhibits type-I phase behavior, which is characterized by an uninterrupted critical mixture curve which has a maximum in pressure. The solubility of N, N-dimethylformamide, N, N-diethylformamide and N, N-dibutylformamide for the CO 2– N, N-dimethylformamide, CO 2– N, N-diethylformamide and CO 2– N, N-dibutylformamide systems increases as the temperatures increases at constant pressure. The CO 2– N, N-dimethylformamide, CO 2– N, N-diethylformamide and CO 2– N, N-dibutylformamide systems have continuous critical mixture curves that exhibit maximums in pressure at temperatures between the critical temperatures of CO 2 and N, N-dimethylformamide, N, N-diethylformamide or N, N-dibutylformamide. Also, three phases were not observed of any of the systems studied. In each systems, the mixture critical point increases as the temperatures increases, and also the mixture critical pressure does as molecular weight increases. The experimental results for CO 2– N, N-dimethylformamide, CO 2– N, N-diethylformamide and CO 2– N, N-dibutylformamide systems is modeled using the Peng–Robinson equation of state. A good fit of the calculated data is obtained with the Peng–Robinson equation of state.

An apparatus for high-pressure VLE measurements using a static mixer. Results for (CO 2+limonene+citral) and (CO 2+limonene+linalool)

A new flow apparatus for high-pressure vapour–liquid equilibrium measurements was assembled. Its main feature is the use of a static mixer followed by a cyclone separator. Phase equilibrium ratios were determined, at 323.2 K and at pressures up to the vicinity of the mixture critical pressure, for the following systems: carbon dioxide+limonene, carbon dioxide+citral, carbon dioxide+linalool, carbon dioxide+limonene+citral and carbon dioxide+limonene+linalool. The results compare well with available literature data.

High pressure vapor–liquid equilibrium data for the systems carbon dioxide/2-methyl-1-propanol and carbon dioxide/3-methyl-1-butanol at 288.2, 303.2 and 313.2 K

In this work, we report vapor–liquid equilibrium data for the systems carbon dioxide (CO 2)/ iso-butanol and CO 2/ iso-pentanol at 288.2, 303.2 and 313.2 K, and for pressures up to the critical point. The interaction parameters for the Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) equations of state (EOS) that best fit the experimental results are also given.

A simplified CEOS/ AE mixing rule and its applications for vapor–liquid and liquid–liquid equilibrium predictions

The new CEOS/ A E mixing rule recently developed by Twu et al. [Fluid Phase Equilib. 158–160 (1999) 271] is simplified and tested for high-pressure vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) predictions. This mixing rule has some significant features such as: (1) it is density dependent, (2) it is based on no reference-pressure, and (3) it automatically reduces to van der Waals mixing rule for normal mixtures. The mixing rule is used with any G E activity coefficient model such as NRTL, UNIQUAC, and UNIFAC. This approach can employ the available binary interaction parameters from those activity coefficient models without requiring any additional parameters or causing any thermodynamic inconsistency. It extends the predictive capability of the cubic type equation of state (CEOS) to highly nonideal mixtures, which have traditionally been handled using an activity coefficient approach. This work has tested various binary VLE/LLE systems including nonpolar, polar, and associating compounds. Overall, the accuracy of the mixing rule with a CEOS (with a modified alpha-function for each component) is comparable with that of the activity coefficient approach. For LLE, the mixing rule can predict the three different types of phase diagrams (with UCST, LCST, or both). This work also shows that the CEOS/ A E mixing rule can be applied to high-pressure systems for which the activity coefficient models have limited success.

Measurements and correlation of high-pressure VLE of binary CO 2–alcohol systems (methanol, ethanol, 2-methoxyethanol and 2-ethoxyethanol)

High-pressure vapor–liquid equilibrium (VLE) data were measured for binary CO 2–alcohol systems (e.g. methanol, ethanol, 2-methoxyethanol, and 2-ethoxyethanol) at various isotherms (313.15–345.15 K). The quantitative VLE data and mixture critical conditions were measured using a new design for a circulation VLE system. The measure data were correlated by the classical Peng–Robinson and the multi-fluid nonrandom lattice fluid hydrogen-bonding (MF-NLF-HB) equation of state. The MF-NLF-HB model was formulated previously by the present authors based on the proton donor–acceptor principle to the hydrogen-bonding interaction in CO 2–alcohol systems. For the measured and calculated data of CO 2–alcohol systems, the relative accuracy of the data was discussed.

High pressure vapor-liquid equilibria and critical loci for the HFC125-HFC134a system

We measured vapor-liquid equilibria (VLE) ranging from 303.75 to 363.15 K and the critical locus for the system of pentafluoroethane (HFC125)-1,1,1,2-tetrafluoroethane (HFC134a). The critical locus exhibited type I behavior by van Konynenberg and Sccot. Correlating the VLE data with an extended BWR equation of state, we found the optimum binary interaction parameter for this system 1.0081 and estimated coefficients of performance (C.O.P.) as a mixture refrigerant. As a result of the correlation, we found that the HFC125-HFC134a system is a potential alternative refrigerant when mole fraction of HFC125 is lower than 0.6. Calculations showed a 4.9% saving energy in the cycle compared with chlorodifluoromethane (HCFC22), for a composition of 30 mole percent HFC125.

Equation of state associated with activity coefficient models to predict low and high pressure vapor–liquid equilibria

A simple and thermodynamically consistent method is presented to establish an equation of state for mixtures by using activity coefficient model parameters. All current solution models such as NRTL, van Laar, UNIFAC, or any other thermodynamic model can be used. The main feature of the method presented is that only a single scaling factor value determined at a given reference temperature is required to predict the vapor–liquid equilibria in a wide range of temperature and pressure. The performance of the method is tested on the prediction of the vapor–liquid equilibria at low, moderate, and high pressures for six binary systems (methanol−benzene, acetone−water, methanol−acetone, methanol−water, ethanol−water, and 2-propanol−water) and a ternary system (acetone−water−methanol). For comparison, vapor–liquid equilibrium calculations were carried out with the Wong and Sandler method by using the PRSV equation of state associated with the van Laar and scaling factors. On the whole, it is found that at high pressures both methods give similar predictions but at low pressures the proposed method gives sometimes better results than that of Wong and Sandler method.

Evaluation of vapor–liquid equilibrium of ethane binary systems using UNIQUAC-based mixing rules and its extension to multicomponent systems

In order to investigate the ability and accuracy of the UNIQUAC-based SRK EOS for prediction of high-pressure vapor–liquid equilibrium (VLE) the UNIQUAC parameter for 19 ethane binary systems have been determined. The missing binary interaction parameters are reported for PSRK, MHV1, MHV2, and LCVM mixing rules. These parameters were determined using the VLE experimental data reported in literature. The percentage average relative pressure error for 19 C 2H 6 binary systems is 1.93, 1.99, 2.21, and 2.03 using PSRK, MHV1, MHV2, and LCVM mixing rules, respectively. The regressed binary interaction parameters then, without any further modification, were applied to six multicomponent systems over a wide range of temperature covering more than 300 data points. The calculated percentage average relative pressure error for six multicomponent systems is 3.47, 3.75, 5.57, and 4.51 for PSRK, MHV1, MHV2, and LCVM mixing rules, respectively. Based on the results obtained in this study, it is concluded that the PSRK/UNIQUAC model has reasonable accuracy for VLE calculations and gives the most accurate results among the four mixing rules tested.

Modeling high-pressure vapor–liquid equilibrium of limonene, linalool and carbon dioxide systems

The research reported in this study is focused on modeling high-pressure phase behavior for CO 2–limonene and CO 2–linalool. A modified Peng–Robinson equation of state was applied to calculate vapor–liquid equilibrium using five different mixing rules obtained by incorporating activity coefficient models. The methodologies proposed by Heidemann–Kokal, Wong–Sandler and LCVM were used coupled with NRTL, UNIQUAC and UNIFAC models. A comparative analysis of the generated models was done for the binary systems and the best model was chosen to describe phase behavior of the system CO 2–limonene–linalool. An isothermal flash calculation was applied to investigate selectivity and yield simultaneously for this ternary system in order to understand better the process parameters governing supercritical CO 2 deterpenation of citrus peel oil. The results showed that to obtain good separation between limonene and linalool at 50°C and pressures from 80 to 90 bar a high CO 2/oil ratio is needed. As this ratio decreases, the process can be operated at 60 and 70°C over the same pressure range with equivalent performance.

High-pressure vapor–liquid equilibrium of binary systems with R236fa

Within the European Union Joule project aimed at the substitution of R114 in high temperature heat pumps with chlorine-free, environmentally benign fluids, R236fa has been chosen as one of the components of mixtures to consider as alternative fluids for R114 (1,2-dichlorotetrafluoroethane). The results of VLE measurements performed at our laboratory on mixtures including R236fa are summarized and discussed for the systems R600a (isobutane)+R236fa (1,1,1,3,3,3-hexafluoropropane) at 303 K, RE170 (dimethyl ether)+R236fa at 303 and 323 K, R134a (1,1,1,2-tetrafluorethane)+R236fa at 283 and 303 K, R32 (difluoromethane)+R236fa and R125 (pentafluoroethane)+R236fa, both at 303 and 323 K. All data were correlated by means of the CSD EOS. Generally small deviations between experimental and calculated vapor compositions confirm the thermodynamic consistency of the experimental results and the model used for data reduction. An extensive discussion of the deviations from Raoult's law is performed through analysis of the excess Gibbs energy. All systems formed by HFCs show a very small g E, with small deviation from Raoult's law. A much higher g E is shown by the systems R600a+R236fa, with a positive deviation from Raoult's law, and RE170+R236fa, with a negative deviation clearly coming from the hydrogen bonding.

High-Pressure Vapor−Liquid and Solid−Gas Equilibria Using a Peng−Robinson Group Contribution Method

In this paper, the new excess Gibbs energy mixing rule, which coupled with the consistent form with the quadratic composition dependence of the second virial coefficient and the excess Gibbs energy ( ) at standard zero pressure, has been developed. This proposed mixing rule, combining a Peng−Robinson equation of state with the analytical solutions of groups (ASOG) group contribution method, provide a Peng−Robinson group contribution method (PRASOG). The PRASOG model has predicted the high-pressure vapor−liquid equilibria (VLE) for binary systems containing alcohols, acetone, and water using the available ASOG group pair parameters determined at low pressure with good accuracy. The ASOG parameters have also been shown for 31 group pairs relating to two gas groups, CO2 and CH4, which indicate potential for global warming, using binary experimental high-pressure VLE data in the temperature range 200−600 K. High-pressure VLE have then been correlated for 56 binary systems containing carbon dioxide and/or meth...

Statistical regression of binary vapor–liquid equilibrium data for ternary phase equilibrium predictions

High-pressure vapor–liquid equilibrium data of more than 50 binary systems were correlated by a DDLC (density-dependent local-composition) model incorporated into the Soave–Redlich–Kwong equation of state. The Error-Propagation-Law Method based on the maximum likelihood principle and the simple least-squares method were applied to data reduction. Fitting accuracies of the DDLC model by statistical regression were found better than those obtained by the least-squares as well as those of the SRK equation of state by both methods. However, no improvements were obtained for the original SRK equation by the statistical method. Further, vapor–liquid equilibrium behaviors of eight ternary systems were predicted by utilizing the binary interaction parameters of both models obtained from experimental data of the constituent binaries by both statistical and conventional methods, respectively. Results showed that better prediction accuracies were obtained for the DDLC model by statistical regression. Similarly, no improvements were found for the SRK equation of state by statistical regression. In addition, the superiority of the statistical regression over the conventional method was demonstrated by various simulated data.

Development and extension of PSRK/UNIQUAC model to methane and nitrogen gases

Two successful procedures for matching the equation of state (EOS) and the excess Gibbs energy model at zero pressure belong to Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 60 (1990) 213] and Holderbaum-Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilibria, 70 (1991) 251]. These procedures lead to volume independent mixing rules for the mixture parameter a. Michelsen proposed the MHV1 and MHV2 mixing rules and Holderbaum-Gmehling proposed the PSRK mixing rule. Keshtkar et al. [A. Keshtkar, F. Jalali, M. Moshfegian, Fluid Phase Equilibria, 140 (1997) 107] demonstrated the utility of these mixing rules together with UNIFAC and UNIQUAC models for the prediction of high-pressure vapor-liquid equilibrium (VLE) of CO 2-binary systems. Also, they showed that the PSRK/UNIQUAC model gives better VLE results than other models. In this paper, we develop and extend the above model to methane and nitrogen gases. For this purpose, it is required that the missing interaction parameters of model are fitted with experimental VLE data. The VLE calculations show that good agreement between calculated results and experimental data can be produced by using the obtained parameters.

Prediction of vapor–liquid equilibria in non-polymer and polymer solutions using an ASOG-based equation of state (PRASOG)

An ASOG-based equation of state called PRASOG (Peng–Robinson ASOG) has been developed to predict vapor–liquid equilibria in non-polymer and polymer solutions. It makes use of the zero-pressure G E mixing rule consistent with the second virial coefficient condition for calculating the mixture parameters in Peng–Robinson EOS and predicts the G E using ASOG method. The first object of this paper is to predict low-pressure vapor–liquid equilibria (VLE) using PRASOG for 37 binary systems containing alcohols, hydrocarbons, ketones, esters, ethers, aromatic compounds and water. The PRASOG model has been then used to predict high-pressure VLE for ammonia-containing systems. In order to apply PRASOG to polymer solutions, PRASOG-FV has been proposed by calculating G E from ASOG-FV and VLE in polyisobutylene solutions have been then predicted.