Description Of Vapor-liquid Equilibrium Research Articles

Multi-criteria optimization for parametrizing excess Gibbs energy models

Thermodynamic models contain parameters which are adjusted to experimental data. Usually, optimal descriptions of different data sets require different parameters. Multi-criteria optimization (MCO) is an appropriate way to obtain a compromise. This is demonstrated here for Gibbs excess energy (GE) models. As an example, the NRTL model is applied to the three binary systems (containing water, 2-propanol, and 1-pentanol). For each system, different objectives are considered (description of vapor-liquid equilibrium, liquid-liquid equilibrium, and excess enthalpies). The resulting MCO problems are solved using an adaptive numerical algorithm. It yields the Pareto front, which gives a comprehensive overview of how well the given model can describe the given conflicting data. From the Pareto front, a solution that is particularly favorable for a given application can be selected in an instructed way. The examples from the present work demonstrate the benefits of the MCO approach for parametrizing GE -models.

Extractive Distillation of Acetone – Methanol Mixture using 1-Ethyl-3-methylimidazolium Trifluoromethanesulfonate

Acetone and methanol are organic solvents widely used in industry. Acetone with methanol forms a homogeneous minimum-boiling azeotrope which is not separable by conventional distillation processes. A common method for its separation is the extractive distillation in the presence of a selective solvent (such as water). In this paper, the use of an ionic liquid (1-ethyl-3-methylimidazolium trifluoro methanesulfonate [Emim][triflate]) for acetone–methanol separation by extractive distillation was designed. The aim of the design calculation was to obtain acetone with the purity of 99.5 mol % and methanol with the purity of above 99.0 mol %. Calculations were carried out in a proprietary program constructed in Matlab® by solving a set of material balances at individual theoretical stages of the distillation column combined with the vapor–liquid equilibrium (VLE) of the ternary system acetone–methanol–[Emim][triflate]. For the description of VLE of the above mentioned system, the NRTL equation was used. Several optimization cycles were done resulting in optimal parameters of the extractive distillation column (number of theoretical stages, solvent consumption, reflux ratio and position of the feed stage) in regard to the required purity of products (acetone and methanol). Regeneration of ionic liquid was provided by evaporation at the low pressure of 20 kPa. The heat and cooling consumption duties of the designed separation process were analyzed. Regeneration of the ionic liquid is energy-demanding compared to the separation of acetone–methanol in an extractive distillation column. The heat consumption is only 11 % of the heat used up by the whole separation process.

Genetic algorithm for multi-parameter estimation in sorption and phase equilibria problems

ABSTRACTThe techniques of applying single and multi-objective optimization (MOO) for single/multiple parameters estimation in sorption and phase equilibria calculations were demonstrated, and it was shown that non-dominated sorting genetic algorithm with jumping genes adaptation is a useful tool for standard nonlinear regressions. Simultaneous description of vapor liquid equilibrium (VLE) and the heat of mixing (excess enthalpy) are considered a complex task in applied thermodynamics. MOO problem for simultaneous VLE and excess enthalpy prediction was formulated by (1) transforming multi-objectives into an aggregated/single scalar objective function, and (2) formulating independent objectives and solving simultaneously. It was shown that GA leads to an entire set of equally good optimal solutions known as Pareto-optimal fronts. However, simultaneous solution of MOO problem produced a wide range Pareto-optimal solution than that of the weighted sum approach. Pareto-optimal solutions are important process knowledge from which a decision-maker can opt for any set based on the applications/requirements.

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Vapor-Liquid equilibrium (VLE) data involving alcohols and hydrocarbons are relevant to the gas and oil industry. Under certain circumstances, for instance, in the determination of the distribution of components between phases in equilibrium, and physical properties of the fluids in reservoirs, the predictions from the available models for hydrocarbon systems in the presence of flow-assurance additives, such as alcohols, are, at times, insufficient. This study used the Conductor-like Screening Model-Segment Activity Coefficient (COSMO-SAC) to predict liquid phase activity coefficients for the description of VLE of seven binary systems containing alcohols and hydrocarbons, at low and high pressures (10-2500kPa), and under temperatures ranging from 298-400K. The COSMO SAC has a relatively simple mathematical form and can be easily incorporated into a process simulation software. COSMO-SAC model predictions in this work showed average absolute relative deviation (AARD) values ranging from 5.0% to 13.8%.

Vapor−Liquid Equilibrium Measurements and Modeling of the Propyl Mercaptan + Methane + Water System

In this work, vapor−liquid equilibrium (VLE) measurements of propyl mercaptan (PM) in pure water were performed at three different temperatures, (303, 323, and 365) K, with a pressure variation from (1 to 8) MPa. The total system pressure was maintained by CH4. The inlet mole fraction of propyl mercaptan in all experiments was the same, around 4.5·10−4 in the liquid phase. The objective was to provide experimental VLE data points of the propyl mercaptan + methane + water system for modeling since there is a lack of available data. These data will allow the industrial modeling of sulfur emission. The thermodynamic model used for the description of VLE is the extended UNIQUAC model. The model parameters are valid in the temperature range similar to the measured data and a pressure range up to 8 MPa.

Extended Flexibility for GE Models and Simultaneous Description of Vapor−Liquid Equilibrium and Liquid−Liquid Equilibrium Using a Nonlinear Transformation of the Concentration Dependence

A method to increase the flexibility of the composition dependence of G E models or equations of state is proposed. The formalism is based on a nonlinear transformation of the concentration space and can be applied to any mixture model without re-deriving the model equations. Any number of additional binary parameters can be introduced, which show nearly no intercorrelation with the original model parameters. The reason is that the additional parameters only effect the form but not the size and symmetry of, for example, G E . The mathematical formalism for the introduction into G E models was derived and applied to the UNIQUAC model. The modified model (FlexQUAC) was then used to regress a large number of vapor-liquid equilibrium (VLE) data sets (approximately 4000), whereby significant improvements were observed for systems with medium to large positive deviation from Raoult's law. As a result of the very small intercorrelation with the original model parameters it was assumed that the additional parameters have no negative effect on the prediction of multicomponent behavior from binary data. This was verified for 13 carefully selected systems. The motivation for this development was not primarily the improvement of the regression capability but the simultaneous description of VLE and liquid-liquid equilibrium (LLE) data. Typically models such as NRTL or UNIQUAC predict immiscible regions that are way too large from VLE data or VLE separation factors that are too low from LLE. This shortcoming of the original models is corrected by the concentration space transformation. Examples for the simultaneous description of VLE and LLE for binary and ternary systems are presented and compared to the corresponding results of the UNIQUAC equation.

Effects of potential models in the vapor–liquid equilibria and adsorption of simple gases on graphitized thermal carbon black

In this paper, we investigate the effects of various potential models in the description of vapor–liquid equilibria (VLE) and adsorption of simple gases on highly graphitized thermal carbon black. It is found that some potential models proposed in the literature are not suitable for the description of VLE (saturated gas and liquid densities and the vapor pressure with temperature). Simple gases, such as neon, argon, krypton, xenon, nitrogen, and methane are studied in this paper. To describe the isotherms on graphitized thermal carbon black correctly, the surface mediation damping factor introduced in our recent publication should be used to calculate correctly the fluid–fluid interaction energy between particles close to the surface. It is found that the damping constant for the noble gases family is linearly dependent on the polarizability, suggesting that the electric field of the graphite surface has a direct induction effect on the induced dipole of these molecules. As a result of this polarization by the graphite surface, the fluid–fluid interaction energy is reduced whenever two particles are near the surface. In the case of methane, we found that the damping constant is less than that of a noble gas having the similar polarizability, while in the case of nitrogen the damping factor is much greater and this could most likely be due to the quadrupolar nature of nitrogen.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: a computer simulation study.

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

Vapor−Liquid Equilibria at 453.25 K and Excess Enthalpies at 363.15 K and 413.15 K for Mixtures of Benzene, Toluene, Phenol, Benzaldehyde, and Benzyl Alcohol with Benzyl Benzoate

Isothermal P−x data at 453.25 K and excess enthalpies at 363.15 K and 413.15 K are presented for binary systems of benzyl benzoate together with benzene, toluene, phenol, benzaldehyde, and benzyl alcohol. As pointed out previously (Nienhaus, B.; Limbeck, U.; Bolts, R.; de Haan, A. B.; Niemann, S. H.; Gmehling, J. J. Chem. Eng. Data 1998, 43, 941−948), information about the real behavior of systems including these components is very important, especially for the production of phenol by toluene oxidation. In addition, these data will be used for the introduction of a new aromatic ester group (AC−COO−) into modified UNIFAC (Dortmund), which is part of the revision, extension, and further development of this group contribution method. The vapor−liquid equilibrium (VLE) data of four systems were measured using a static apparatus. The corresponding experimental excess enthalpy (HE) data were determined with the help of an isothermal flow calorimeter. For the simultaneous description of VLE and HE data the NRTL ...

Vapor−Liquid Equilibria at 413.65 K and Excess Enthalpies at 323.15, 363.15, and 413.15 K for Mixtures of Benzene, Toluene, Phenol, and Benzaldehyde

Isothermal P, x data at 413.65 K, excess enthalpies at 323.15, 363.15, and 413.15 K, and azeotropic data are presented for binary systems containing benzaldehyde, benzene, toluene, and phenol. Reliable information about the real behavior of systems including these components is very important for various chemical processes, e.g., for the production of phenol by toluene oxidation. Furthermore, these data will be used for the revision, extension, and further development of the group contribution method modified UNIFAC (Dortmund). The vapor−liquid equilibrium (VLE) data of four systems were measured using a static apparatus. In the case of the system benzaldehyde + phenol, azeotropic data were determined by distillation. For all systems, the corresponding experimental excess enthalpy (HE) data were determined with the help of an isothermal flow calorimeter. For the simultaneous description of VLE and HE data, the NRTL model was used.