Prediction Of Vapor-liquid Equilibria Research Articles

Simulation on vapor-liquid equilibrium of CO2-[emim][Tf2N] in flow state and depressurization of its refrigeration cycle based on Aspen Plus

To investigate the depressurization mechanism of the CO 2 vapor compression refrigeration cycle with an ionic liquid loop, a vapor-liquid equilibrium (VLE) model of CO 2 -[emim][Tf 2 N] in the flow state was established based on Aspen Plus, and the prediction of VLE in the supercritical state was carried out. Furthermore, the effects of CO 2 inlet pressure, absorber temperature, CO 2 inlet mole fraction and CO 2 inlet flow rate on the depressurization amplitude of absorber were analyzed through the absorption-desorption process simulation. The results showed that with the increase of CO 2 inlet pressure in the supercritical state, the depressurization amplitude increased but its growth rate slowed down, which indicated that the effect of pressure as a driving term of mass transfer decreased in the supercritical state. The depressurization amplitude decreased with the increase of absorber temperature, and decreased rapidly with the increase of CO 2 inlet mole fraction. In this sense, adding an auxiliary desorber at the absorber inlet is beneficial to the system depressurization. Due to the limited absorption capacity of quantitative [emim][Tf 2 N] in the absorber, with the continuous increase of CO 2 inlet flow rate, the depressurization amplitude first dropped sharply, then flattened, and later dropped rapidly. Because the CO 2 flow rate in an actual system is proportional to the system cooling capacity, the proper mass flow ratio of CO 2 -[emim][Tf 2 N] should be selected to reconcile the cooling capacity and depressurization amplitude.

New modified PC-SAFT pure component parameters for accurate VLE and critical phenomena description

The theory of Perturbed Chain Statistical Associating Fluid (PC-SAFT) is largely applied in many industrial fields. It requires three parameters: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By convention, they are determined by fitting vapor pressure and liquid density data. However, the shortage behind these parameters adopted by their respective authors is that they give excessive values of critical temperatures and critical pressures, which are crucial to forecasting vapor-liquid critical pressure and composition of the mixture at high pressures and temperatures.In this paper, a new approach is proposed to evaluate PC-SAFT parameters of different substances from diverse chemical families. Good fits of saturation pressure and vapor densities values of 94 pure substances are obtained, with an overall AARD of 0.89% and 1.50% respectively.The proposed method requires as input the critical pressure (Pc), the critical temperature (Tc), and the acentric factor (ω). By using these parameters, PC-SAFT estimates with accuracy the critical properties of pure compounds as well as the successful prediction of vapor-liquid equilibria for many non-associating binary systems at critical regions including mixtures containing ammonia, comparing with other literature values. But the limitation of this method is reflected in underestimated liquid densities.

Vapor–Liquid Equilibrium Prediction of Refrigerant Mixtures with Peng–Robinson Equation of State and Binary Interaction Parameters Calculated Through Group Contribution Model

Vapor–liquid equilibrium (VLE) properties of refrigerant mixtures are essential to the analysis of thermodynamic cycle performance. The accurate value of binary interaction parameter (kij) for classical Van der Waals (VDW) mixing rules is highly significant for the VLE prediction of mixtures. Therefore, in this contribution, a theoretical correlation for kij is derived as a function of the activity coefficients, which are obtained from the group contribution model UNIFAC. So that, the widely applied Peng–Robinson equation of state with the VDW mixing rule can be predictable for any refrigerant mixtures, according to the existing group contribution values. 18 alternative refrigerant mixtures and two GE models, namely MHV1 and WS are used to exhibit the capacities and limitations of the proposed VDW. The calculated results show that the developed VDW can correlate the VLE experimental data well in most cases. Compared with the MHV1 and WS, the proposed model has better VLE prediction, especially for HFCs + HFCs/HFOs mixtures. Thereafter, VLE of 6 refrigerant mixtures are obtained by GC-VTPR. The comparison shows that the accuracy of VDW model is comparable with that of GC-VTPR. Furthermore, mixture densities at different temperatures and pressures are predicted by the developed VDW and GC-VTPR. Results show that GC-VTPR has better density prediction than VDW and the largest deviation of VDW between predicted results and experimental data is 7.04% for R125 + R143a.

Quantum effect on adsorption of fluids in slit pores: A DFT study

In this paper, the Wigner-Kirkwood quantum theory and the Weeks-Chandler-Andersen (WCA) effective diameter method in Classical DFT are employed to account for the effects of quantum corrections on the Helmholtz free energy of bulk and confined fluids. Initially, experimental data are exploited toward accurate prediction of pressure-volume isotherms and vapor-liquid equilibrium in bulk fluids. In the second part, the effects of quantum correction on the structure and thermodynamic properties of fluids confined in slit pores are investigated. Our results show that quantum effects may come into account by considering the effective size of the particles and also intermolecular interaction which both of them have direct effects on the density distribution of molecules in the slit pore. Furthermore, the excess adsorption of fluids at a fixed bulk density is shown to increase with quantum effect, but this trend is reversed with increasing wall fluid interaction because of the entropy and energy effects. Also, it is found that the excess adsorption and interfacial tension of the fluid against the solid surface of fluids exhibit oscillatory behaviors with maximum and minimum values for half integer and integer values of pore width. This oscillatory behavior disappears at high values of pore width with increasing quantum effect. Another finding of the present study indicates that the interfacial tensions of the fluid against the solid surface for a classical fluid are negative but quantum effect increases it and shifts its sign to positive. Finally, it is shown that the locus of phase transition is shifted toward higher bulk densities as a result of increasing quantum effect.

Isobaric vapor-liquid equilibrium of a ternary system of ethyl acetate + propyl acetate + dimethyl sulfoxide and binary systems of ethyl acetate + dimethyl sulfoxide and propyl acetate + dimethyl sulfoxide at 101.3 kPa

Isobaric vapor-liquid equilibrium data were measured for three systems, namely, ethyl acetate + dimethyl sulfoxide, propyl acetate + dimethyl sulfoxide and ethyl acetate + propyl acetate + dimethyl sulfoxide at 101.3 kPa in this work. The experimental data were checked by the Van Ness (point-to-point test) and Herington (integral test) methods. The binary systems’ vapor-liquid equilibrium data tested by experiments were fitted well with the NRTL, UNIQUAC and Wilson models. The binary interaction parameters regressed by the three models and experimental data were accepted to predict vapor liquid equilibrium data of a ternary system. The maximum absolute deviations and mean absolute deviations between the experimental and thermodynamic model data were within a reasonable range, indicating that corrected binary interaction parameters can be used to accurately predict vapor-liquid equilibrium data of the ternary system.

Vapor liquid equilibrium prediction of methanol–ionic liquid systems using UNIFAC model to select alternative working fluids of absorption cycle

AbstractThe purpose of this paper is to study the working fluids in absorption cycle containing methanol (CH3OH) as the refrigerant and the imidazolium ionic liquid (IL) as the absorbent. The UNIFAC model was implemented to correlate the published experimental vapor liquid equilibrium data of CH3OH–IL working fluids and 14 new group interaction parameters between CH3OH and ILs were obtained. Method reliability and applicability were evaluated by calculating the vapor pressures of five CH3OH–IL working fluids. The ILs contained 1‐methyl‐3‐methylimidazolium dimethylphosphate ([Dmim][DMP]), 1‐ethyl‐3‐methylimidazolium ethyl sulfate ([Emim][ES]), 1‐ethyl‐3‐methylimidazolium diethylphosphate ([Emim][DEP]), 1‐butyl‐3‐methylimidazolium dibutylphosphate ([Bmim][DBP]), and 1‐ethyl‐3‐ethylimidazolium diethylphosphate ([Eeim][DEP]). The average absolute relative deviations for the vapor pressures between the calculated results and the experimental data were 0.91%, 1.67%, 0.66%, 0.75%, and 2.1%, respectively. Then, the CH3OH–IL systems without experimental data were predicted. Comparisons of the vapor pressure and excess Gibbs function of the studied CH3OH–IL systems, CH3OH‐[Hmim][DEP] (1‐hexyl‐3‐methylimidazolium diethylphosphate) system, as an alternative working fluid, was found to have potential to improve the absorption cycle performance upon more research work.

Thermodynamic Analysis of n-Hexane-Ethanol Binary Mixtures Using the Kirkwood-Buff Theory.

A complete thermodynamic analysis of mixtures consisting of molecules with complex chemical constitution can be rather demanding. The Kirkwood-Buff theory of solutions allows the estimation of thermodynamic properties, which cannot be directly extracted from atomistic simulations, such as the Gibbs energy of mixing (Δmix G). In this work, we perform molecular dynamics simulations of n-hexane-ethanol binary mixtures in the liquid state under two temperature-pressure conditions and at various mole fractions. On the basis of the recently published methodology of Galata [ Fluid Phase Equilib. 2018 , 470 , 25 - 37 ] , we first calculate the Kirkwood-Buff integrals in the isothermal-isobaric ( NpT) ensemble, identifying how system size affects their estimation. We then extract the activity coefficients, excess Gibbs energy, excess enthalpy, and excess entropy for the n-hexane-ethanol binary mixtures we simulate. We employ two approaches for quantifying composition fluctuations: one based on counting molecular centers of mass and a second one based on counting molecular segments. Results from the two approaches are practically indistinguishable. We compare our results against predictions of vapor-liquid equilibria obtained in a previous simulation work using the same force field, as well as with experimental data, and find very good agreement. In addition, we develop a simple methodology to identify the hydrogen bonds between ethanol molecules and analyze their effects on mixing properties.

A United Chemical Thermodynamic Model: COSMO-UNIFAC

A united chemical thermodynamic model, that is, the COSMO-UNIFAC model, was first proposed to predict the phase equilibrium of multicomponent systems in which the UNIFAC model parameters are missing. This model combines the advantages of the UNIFAC model (accurate prediction) and the COSMO-based models (a priori prediction). The predicted vapor–liquid equilibrium results by the COSMO-UNIFAC model were compared with experimental data from the literature and this work, confirming that it can provide a moderate quantitative prediction even if the UNIFAC model parameters are missing.

Experimental and predicted vapor–liquid equilibrium for binary systems with diethanolamine, m-cresol and p-cresol at 20.0 kPa

Isobaric vapour–liquid equilibrium (VLE) data for two binary systems of p-Cresol (PC) + diethanolamine (DEA) and m-Cresol (MC) + DEA were measured at 20.0 kPa. The Herington area method was used to check the binary VLE data, and the results showed good thermodynamic consistency. Meanwhile, the Wilson, NRTL, UNIQUAC models and the chemistry theory proposed by Dolezalek were used to correlate the VLE data. The binary energy interaction parameters for activity models, and reaction equilibrium constants for chemistry theory were obtained. With help of the parameters obtained in this work, the NRTL model was used to predict the VLE data of the two binary systems at the pressure of 8.33 kPa. The predictive results were compared with the literature’s data. At same time, the excess Gibbs free energy for the two binary systems, and infinite dilution activity coefficients for MC and PC in DEA were estimated. The calculated results showed that the DEA had slightly stronger interaction with PC than MC.

Experimental Isobaric Vapor Liquid Equilibrium for Binary Systems Diethylene Glycol Dibenzoate + Diethylene Glycol, Diethylene Glycol Dibenzoate + Octyl Benzoate, and Ternary System Diethylene Glycol Dibenzoate + Diethylene Glycol + Octyl Benzoate at 1.0152 kPa

Diethylene glycol dibenzoate (DEDB) is nowadays considered as one of the most promising environment-friendly plasticizers. Isobaric vapor–liquid equilibrium (VLE) data were measured for the binary systems diethylene glycol dibenzoate (DEDB) (1) + diethylene glycol (2), DEDB (1) + octyl benzoate (2) and ternary system DEDB (1) + diethylene glycol (2) + octyl benzoate (3) at 1.0152 kPa using a modified Othmer still, which enriched the basic data for DEDB. The UNIFAC model, Wilson model, and NRTL model were used to predict the VLE data of the binary and ternary systems. The comparison reveals that on average the most accurate VLE predictions are obtained with the NRTL model.

Extension of the F-SAC model to ionic liquids

In this work, the F-SAC model was extended to describe ionic liquids (IL). The proposed model was tested with cations of the 1-alkyl-3-methylimidazolium family (extended to 1-butyl, 1-hexyl and 1-octyl by group contribution) and six different anions. Only 25 new IL parameters were estimated based on infinite dilution activity coefficient (IDAC) data. The non-IL group parameters were retrieved from previous works, not related to IL. The obtained parameters resulted in a good agreement for 1332 IDAC points of alkanes, alkenes, cycloalkanes, cycloalkenes, aromatics, ethers, ketones, and water diluted in IL, with an absolute average deviation of 0.160 for the IDAC logarithm and R2 of 0.980. Prediction of vapor-liquid equilibria as well as liquid-liquid equilibria of binary and ternary mixtures also showed a good agreement with experimental data. Comparison with excess enthalpy data showed a good temperature dependence prediction. When compared to UNIFAC (Do), F-SAC presented similar results, but with a much smaller number of parameters needed (Unifac (Do) currently contains 163 non-zero binary parameters to describe a subset of the mixtures studied in this work).

Ammonia/ionic liquid based double-effect vapor absorption refrigeration cycles driven by waste heat for cooling in fishing vessels

To use high-temperature waste heat generated by diesel engines for onboard refrigeration of fishing vessels, an ammonia-based double-effect vapor absorption refrigeration cycle is proposed. Non-volatile ionic liquids are applied as absorbents in the double-effect absorption system. In comparison to systems using ammonia/water fluid, the complexity of the system can be reduced by preventing the use of rectification sections. In this study, a multi-scale method is implemented to study the proposed system, including molecular simulations (the Monte Carlo method) for computing vapor-liquid equilibrium properties at high temperatures and pressures, thermodynamic modeling of the double-effect absorption cycles, and system evaluations by considering practical integration. The Monte Carlo simulations provide reasonable vapor-liquid equilibrium predictions. 1-butyl-3-methylimidazolium tetrafluoroborate is found to be the best performing candidate among the investigated commercialized ionic liquids. In the proposed cycle, the best working fluid achieves a coefficient of performance of 1.1 at a cooling temperature of −5 °C, which is slightly higher than that obtained with generator-absorber cycles. Integrated with the exhaust gas from diesel engines, the cooling capacity of the system is sufficient to operate two refrigeration seawater plants for most of the engine operating modes in high-latitude areas. Thereby, the carbon emission of onboard refrigeration of the considered fishing vessel could be reduced by 1633.5 tons per year compared to the current practice. Diagrams of vapor pressures and enthalpies of the studied working fluids are provided as appendices.

Predicting vapor liquid equilibria using density functional theory: A case study of argon.

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

Experimental and Predicted Vapor–Liquid Equilibrium for Diisopropanolamine with m-Cresol and 2,6-Dimethylphenol at 20.0 kPa

Measurements of isobaric vapor–liquid equilibrium (VLE) results for binary systems of m-cresol (MC) + diisopropanolamine (DIPA) and 2,6-dimethylphenol (DMP) + DIPA and the ternary system of MC + DMP + DIPA were conducted at the pressure of 20.0 kPa. The binary VLE experimental data showed that DIPA had stronger interaction with MC than DMP. The ternary system experimental VLE data showed that DIPA could improve the relative volatility of DMP to MC. The binary experimental data were checked by using Herington area and point test methods, and the checked results were thermodynamically consistent. Meanwhile, the VLE data were correlated by Wilson, nonrandom two-liquid, and universal quasichemical models, and the binary energy interaction parameters for these models were obtained. These activity coefficient models were used to predict the ternary system VLE data. The predictive results suggested that the Wilson model had the best prediction.

New models for the binary interaction parameters of nitrogen–alkanes mixtures based on the cubic equations of state

ABSTRACTIn this study, the goal was to derive a new purely predictive model to obtain binary interaction parameters based on intermolecular theories. The Lorentz–Berthelot and Halgren HHG molecular combining rules were coupled with the vdw1 mixing rule to derive the new equations for binary interaction parameters. These equations were used with the PR and ER EoSs to calculate the vapor–liquid equilibria of 14 binary mixtures of nitrogen with either methane, ethane, propane, iso-butane, n-butane, iso-pentane, n-pentane, n-hexane, n-heptane, n-octane, n-nonae, n-decane, n-dodecane, or n-tetradecane over wide ranges of temperature and pressure. To increase the accuracy for all of the investigated systems, we have additionally suggested a new correlative mode for the proposed equations. For some of the systems, the proposed predictive equations enhance the accuracy of vapor–liquid equilibria predictions up to three times in comparison to the case where binary interaction parameters are set to zero.

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.

Genetic programming based models for prediction of vapor-liquid equilibrium

The design, operation, and control of chemical separation processes heavily rely on the knowledge of the vapor-liquid equilibrium (VLE). Often, conducting experiments to gain an insight into the separation behavior becomes tedious and expensive. Thus, standard thermodynamic models are used in the VLE prediction. Sometimes, exclusively data-driven models are also used in VLE prediction although this method too possesses drawbacks such as a trial and error approach in specifying the data-fitting function. For overcoming these difficulties, this paper employs a machine learning (ML) formalism namely “genetic programming (GP)” possessing certain attractive features for the VLE prediction. Specifically, three case studies have been performed wherein GP-based models have been developed using experimental data, for predicting the vapor phase composition of a ternary, and a group of non–ideal binary systems. The inputs to models consists of three pure component attributes (acentric factor, critical temperature, and critical pressure), and as many intensive thermodynamic parameters (liquid phase composition, pressure, and temperature). A comparison of the VLE prediction and generalization performance of the GP-based models with the corresponding standard thermodynamic models reveals that the former class of models possess either superior or closely comparable performance vis-a-vis thermodynamic models. Noteworthy features of this study are: (i) a single GP-based model can predict VLE of a group of binary systems, and (ii) applicability of a GP-based model trained on an alcohol-acetate series data for its higher homolog. The VLE modeling approach exemplified here can be gainfully extended to other ternary and non-ideal binary systems, and for designing corresponding experiments in different pressure and temperature ranges.

Prediction of vapor-liquid equilibrium in highly asymmetric paraffinic systems with new modified EOS-GE model

A new modified EOS-GE model is developed for the highly asymmetric paraffinic systems, where the volume translated Peng-Robinson EOS is adopted coupled with the LCVM mixing rule. In the new modified EOS-GE model, the original UNIFAC is replaced by a newly established UNIFAC where the nonlinear calculation of the segment fractions of molecules in γC (the combinatorial activity coefficient) is introduced to modify the traditional assumption that “all groups are isotropic in solution”. A total of 956 vapor-liquid experimental bubble points in highly asymmetric paraffinic systems including binary systems, ternary systems, quaternary systems and multiple systems are used to test the new developed EOS-GE model. Results show that the original UNIFAC and the improved UNIFAC both perform well if the molefractions of light components (CH4 or C2H6) are low; however, with the increase of the light components, the improved UNIFAC is remarkably superior to the original UNIFAC.

Prediction of Vapor–Liquid Equilibria for Pb–Pd and Pb–Pt Alloys Using Ab Initio Methods in Vacuum Distillation

The vapor–liquid equilibrium (VLE) phase diagrams of Pb–Pd and Pb–Pt alloy systems in vacuum distillation were obtained based only on pure-component properties and the structures of the atoms. The interaction energies between pairs of atoms were calculated from ab initio methods and were used as the input energy parameters for the Wilson equation. The calculated activity data of the components, using energy parameters which were obtained by ab initio methods, are in good agreement with the experimental data. It is revealed that a cluster size of eight atoms, optimized using the NVT ensemble at 300 K, a time step of 1 femtosecond, and the simulation time 10 ps gives a good representation of the liquid phase systems. This approach can be used to obtain accurate VLE predictions for alloy systems in vacuum distillation. The VLE phase diagram has a significant advantage in guiding experiment and industrial production in vacuum metallurgy.

High-fidelity simulation of drop collision and vapor–liquid equilibrium of van der Waals fluids

The availability of a method to accurately predict the interaction of fuel drops and vapor–liquid equilibrium is crucial to the development of a predictive spray combustion model. The objective of this paper is to present such a method. A numerical method, based on the smoothed particle hydrodynamics (SPH), was coupled with a cubic equation of state for simulating the fuel drop dynamics and liquid–vapor distributions at various temperatures in the present study. SPH is a Lagrangian particle-based method, which is useful to simulate the dynamics of fluids with large deformations without the need for a transport equation to track the interface. The present study, furthermore, coupled SPH with van der Waals equation of state to simulate the phenomena of liquid oscillation, drop collisions at high velocity and characteristics of vapor–liquid equilibrium. This approach was found to offer the convenience of using a single set of equations, without the need for submodels, to predict drop breakup or vaporization. A hyperbolic spline kernel function was employed to eliminate the tensile instability that often has been reported in the literature. The numerical method presented here was found to successfully model the merging, stretching separation, fragmentation, and generation of secondary droplets in high-velocity collisions. In predicting vapor–liquid equilibrium, a variable-smoothing-length function was implemented to better facilitate the evaluation of vapor density at low temperatures. Finally, the results of this study indicate that, as the critical temperature was approached, no clear distinction was observed between the liquid and gas phases.