Modeling Vapor Liquid Equilibrium Research Articles

Modeling vapor–liquid equilibrium and liquid–liquid extraction of deep eutectic solvents and ionic liquids using perturbed‐chain statistical associating fluid theory equation of state. Part II

AbstractThis study aims to use perturbed‐chain statistical associating fluid theory (PC‐SAFT) to describe the phase behavior of systems containing deep eutectic solvents (DESs) and ionic liquids (ILs). The DESs are based on tetrabutylammonium chloride and tetrabutylammonium bromide as hydrogen bond acceptors, and levulinic acid and diethylene glycol as hydrogen bond donors in the mole ratio of 1:2 and 1:4, respectively. Predictions of phase equilibria by PC‐SAFT were compared with the results of COnductor like Screening MOdel for Real Solvents (COSMO‐RS) and non‐random two‐liquid (NRTL). In this work, low viscosity ether‐ and pyridinium‐based ILs [EnPy][NTf2] and [CmPy][NTf2] were used for vapor–liquid equilibrium systems, while 1‐(2‐methoxyethyl)‐1‐methylpyrrolidinium bis(trifluoromethylsulfonyl)‐amide and 1‐propyl‐3‐methylimidazolium bis{trifluoromethylsulfonyl}imide with n‐heptane + thiophene and n‐hexane + ethylbenzene were used in the liquid–liquid extraction, respectively. In the last part, the phase behavior of the mixtures of perfluoroalkylalkanes with their linear alkane counterparts was studied and compared with the SAFT‐Mie pair potential.

Experimental and modeling vapor-liquid equilibria: Separation of Bi from Sn by vacuum distillation

The vapor-liquid equilibria (VLE) for SnBi binary alloy at 5 Pa were carried out at distillation temperatures in the range of 1150 K–1550 K under vacuum condition. The experimental results indicate that Bi can be satisfactorily removed from crude Sn, the content of tin in liquid phase reaching more than 99.99 wt% at a temperature higher than 1300 K. The thermodynamic consistency of the experimental data was checked by Van Ness method. The Wilson equation is used to predicate VLE data. The results show good agreement with the experimental data, indicating that VLE phase diagram is feasible and practical for the process of vacuum distillation of alloys.

Modeling vapor liquid equilibrium of ionic liquids + gas binary systems at high pressure with cubic equations of state

Ionic liquids (IL) have been described as novel environmentally benign solvents because of their remarkable characteristics. Numerous applications of these solvents continue to grow at an exponential rate. In this work, high pressure vapor liquid equilibria for 17 different IL + gas binary systems were modeled at different temperatures with Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state, combined with the van der Waals mixing rule with two binary interaction parameters (vdW-2). The experimental data were taken from the literature. The optimum binary interaction parameters were estimated by minimization of an objective function based on the average absolute relative deviation of liquid and vapor phases, using the modified Simplex algorithm. The solubilities of all gases studied in this work decrease as the temperature increases and increase with increasing pressure. The correlated results were highly satisfactory, with average absolute relative deviations of 2.10% and 2.25% for PR-vdW-2 and SRK-vdW-2, respectively.

On the capabilities and limitations of harmony search for parameter estimation in vapor–liquid equilibrium modeling

The modeling of vapor–liquid equilibrium data using local composition models is an interesting and challenging global optimization problem in the context of chemical engineering and applied thermodynamics. Until now, several deterministic and stochastic global optimization strategies have been used for modeling vapor–liquid equilibrium (VLE) data. Stochastic optimization methods may offer several advantages for solving global optimization problems and, until now, some meta-heuristics have been tested for modeling phase equilibrium data. However, these optimization strategies usually show a robust performance but, in some challenging problems, they may fail to locate the global optimum. In particular, Harmony Search (HS) is a direct-search method with attractive characteristics for its use in phase equilibrium modeling and calculations. However, to the best of our knowledge, this stochastic optimization strategy has not been used to perform this type of thermodynamic calculations. This study introduces the HS method for solving the non-linear parameter estimation problem involved in the modeling of VLE data. Specifically, the performance of this meta-heuristic has been tested and analyzed using several sets of binary VLE data with local composition models and both the classical approach of the least squares regression and the error-in-variable formulation. Results of this study are used to identify the capabilities and limitations of HS for VLE data modeling. In summary, HS is a promising meta-heuristic for processing these phase equilibrium data using the classical least square formulation and may offer a better performance than those obtained using current stochastic methods such as Genetic Algorithm or Particle Swarm Optimization. However, the reliability of the traditional HS is poor for VLE parameter estimation using the error-in-variable formulation. Finally, this paper discusses and analyzes alternatives to improve the performance of HS in VLE data modeling especially for the error-in-variable approach. Results indicate that the HS variants called the Improved Harmony Search and the Global-Best Harmony Search offer a better performance for solving EIV parameter estimation problems.

Modeling vapor–liquid equilibrium of various binary mixtures with a statistically based equation of state

The present study is a continuation of previous work (F. Yousefi, J. Moghadasi, M. M. Papari, A. Campo, Ind. Eng. Chem. Res. 48 (2009) 5079–5084) related to the assessment of the ability of the Tao-Mason (TM) equation of state (EOS) in predicting thermodynamic properties of fluid mixtures. In our previous study, we extended the TM EOS to predict pressure–volume–temperature–composition of fluid mixtures. The present paper aims to model vapor–liquid equilibria of some binary mixtures of ionic liquids, refrigerants, hydrocarbons, and monatomic fluids. In this study, the Sheikh-Papari-Boushehri (SPB) correlations have been employed to predict temperature-dependent parameters appeared in the EOS. The novelty of the present work is the application of Tao-Mason (TM) EOS to fluid phase equilibria of mixtures. The outcomes of the computations are compared with the experimental data. Our results demonstrate that the TM EOS can properly model phase equilibria of fluid mixtures with acceptable accuracies.

Integrated Differential Evolution for Global Optimization and Its Performance for Modeling Vapor–Liquid Equilibrium Data

Parameter estimation in thermodynamic models has been of great interest in chemical engineering because of its complex nature, including nonlinearity, flat objective function in the neighborhood of the global optimum, badly scaled model, and nondifferential term(s) in the equations. In this article, a stochastic global optimization algorithm called integrated differential evolution (IDE) is introduced to solve the parameter estimation problems for modeling vapor–liquid equilibrium (VLE) data. In IDE, the choice of mutation strategy and associated parameters are adapted according to the learning experience from previous generations. The tabu list used in IDE can avoid revisiting the same area and avoid unnecessary function evaluations. A novel and effective stopping criterion based on the number of rejected points during the generation of a trial vector is tested and compared with other criteria. Furthermore, IDE uses a local optimizer after the global search to find the optimum accurately and efficiently. The performance of IDE for benchmark functions and VLE modeling is compared with that of other stochastic algorithms such as DE, DE with tabu list, particle swarm optimization, simulated annealing, and the deterministic algorithm Branch and Reduce Optimization Navigator (BARON). IDE is shown to be better than or comparable to these algorithms for parameter estimation in modeling VLE data.

Prediction of vapor–liquid equilibrium data of the system MTBE + methanol + ethanol by PRSV2 EOS

The Stryjek and Vera (1986) [9] modification of Peng–Robinson (PRSV2) equation of state has been applied for modeling vapor–liquid equilibrium of the systems MTBE + methanol, MTBE + ethanol and methanol + ethanol. Binary interaction parameters for mixing rules have been estimated by using experimental data at the atmospheric pressure. The calculated binary interaction parameters were used for predicting azeotropic behavior at high pressure and also for isobaric equilibrium points which showed an excellent agreement with experimental data. In addition, estimated binary interaction parameters for binary systems were used for ternary system (MTBE + methanol + ethanol). The predictions deviated only slightly from the experimental data. The results show PRSV2 can be used for VLE prediction of polar systems.

Novel bare-bones particle swarm optimization and its performance for modeling vapor–liquid equilibrium data

Parameter estimation in models plays a significant role in developing mathematical models which are used for understanding and analyzing physical, chemical and biological systems. Parameter estimation problems for vapor–liquid equilibrium (VLE) data modeling are very challenging due to the high non-linearity of thermodynamic models. Recently, stochastic global optimizations and their applications to these problems have attracted greater interest. Of the many stochastic global optimization methods, Bare-bones particle swarm optimization (BBPSO) is attractive since it has no parameters to be tuned by the user. In this study, modifications are introduced to the original BBPSO using mutation and crossover operators of differential evolution algorithm to update certain particles in the population. The performance of the resulting algorithm is tested on 10 benchmark functions and applied to 16 VLE problems. The performance of the proposed BBPSO for VLE modeling is compared with that of other stochastic algorithms, namely, differential evolution (DE), DE with tabu list, genetic algorithm and simulated annealing in order to identify their relative strengths for VLE data modeling. The proposed BBPSO is shown to be better than or comparable to the other stochastic global optimization algorithms tested for parameter estimation in modeling VLE data.

Activity Coefficient Models to Describe Vapor-Liquid Equilibrium in Ternary Hydro-Alcoholic Solutions

In this study, three semipredictive activity coefficient models: Wilson, non-random-two liquid model (NRTL), and universal quasi-chemical model (UNIQUAC), have been used for modeling vapor-liquid equilibrium properties of ternary mixtures that include substances found in alcoholic distillation processes of wine and musts. In particular, vapor-liquid equilibrium in ternary mixtures containing water + ethanol + congener has been modeled using parameters obtained from binary and ternary mixture data. The congeners are substances that although present in very low concentrations, of the order of part per million, are important enological parameters. The results given by these different models have been compared with literature data and conclusions about the accuracy of the models studied are drawn, recommending the best models for correlating and predicting phase equilibrium properties of this type of mixtures.

Solubility measurement and modeling for the system propane–water from 277.62 to 368.16 K

In this communication, a total of 61 new experimental data on the solubility of propane in water are reported over a wide temperature range (i.e., 277.62–368.16 K) up to 3.915 MPa (i.e., liquid water–vapor region). A static-analytic apparatus taking advantage of a pneumatic capillary sampler is used for fluid sampling. The Valderrama modification of the Patel–Teja equation of state combining with non-density dependent mixing rules is used for modeling vapor–liquid equilibrium. The new solubility data generated in this work are used for adjusting the binary interaction parameters between propane and water. The experimental data generated in this work are compared to literature data and to the calculations through the thermodynamic model tuned on our experimental data. In order to further evaluate the performance of the thermodynamic model, a comparison is made between the predicted water content data and the experimental data reported in the literature. The predictions are in good agreement with the independent experimental data, demonstrating the reliability of the thermodynamic approach used in this work.

Application of peng-Robinson equation to high-pressure aqueous systems containing gases and sodium chloride

A novel approach is proposed for modeling vapor-liquid equilibria in systems containing aqueous NaCl and supercritical gases. The Peng-Robinson equation of state is used for all species, with the salt treated as a hypothetical liquid component. To correctly model the highly non-ideal liquid solution, a two-fluid model is used for the mixing rules in the equation of state. Effective pure-component parameters are reported for NaCl as well as binary interaction parameters for all possible binaries. Representation of high-pressure phase equilibria data show good agreement with experimental data. The principal advantage of this approach is the ability to treat high pressure systems containing non-volatile salts, while maintaining the simplicity of a cubic equation of state.