Prediction Of VLE Research Articles

Application of CP-PC-SAFT and PC-SAFT for Simultaneous Prediction of LLE and High-Pressure VLE with Universal k12 Values in Systems of Gases and n-Alkanes with N-Methyl-2-pyrrolidone and Some Substituted Aromatic Compounds

Application of CP-PC-SAFT and PC-SAFT for Simultaneous Prediction of LLE and High-Pressure VLE with Universal <i>k</i>₁₂ Values in Systems of Gases and <i>n</i>-Alkanes with <i>N</i>-Methyl-2-pyrrolidone and Some Substituted Aromatic Compounds

Open access, thermodynamically consistent, electrolyte NRTL model for piperazine, AMP, water, CO2 systems on Aspen Plus

This study developed a comprehensive, open-access, thermodynamically consistent, validated vapour-liquid equilibrium model for CO2 absorption into aqueous solutions of piperazine (PZ) activated 2-amino-2-methyl-1-propanol (AMP) on Aspen Plus. This solves a two-decade-old problem of inconsistent specification of PZ, and lacking AMP/PZ, thermodynamic models on Aspen Plus, supporting robust process modelling of AMP/PZ-based CO2 capture systems, considered the contemporary benchmark. The model coverage is wide: total amine concentrations from 30 wt% to 50 wt%, AMP/PZ mole ratios from 0.46 to 23.1, CO2 loadings from 0.04 to 1.07 mol CO2/mol amine, and temperatures from 20 °C to 160 °C. The significance lies in the model’s innovative treatment of the zwitterion PZH+CO2–, leading to accurate VLE predictions and closed charge balances. Absolute average relative deviations (AARD) are 16.6 % to 22.3 % for CO2 partial pressure predictions and 6.3 % to 7.7 % for absorption heats. Gibbs-Helmholz and flash calculated absorption heats consistently compare within 1.5 % to 7.0 %, signalling the model’s thermodynamic consistency.

The integrative approach of learning chemical engineering thermodynamics by using simulation-based exercises

The active learning integrative approach of simulation-based exercises along with the core course would help undergraduate students with more engaged learning. The present study describes the simulation approach using an open-source process simulator with the help of three simulation-based exercises. The first one exemplifies the importance of the selection of an appropriate fluid package. The second exercise presented in the study shows the effect of using optimized and default values of binary interaction parameters on VLE prediction of alcohol-ester systems. The small interactive simulation-based problems with expected outcomes were presented in the third exercise which makes the learning more engaging and interesting. The current study highlights an integrative approach to inculcating critical thinking and self-learning abilities using small simulation-based exercises while learning chemical engineering thermodynamics. Finally, a survey with closed- and open-ended questions was used to gather the opinions of students on the presented exercises. A short communication is needed that sheds light on the integrative approach of learning process simulation complementing the thermodynamic theory learning.

Predictions of thermodynamic properties and phase equilibria of refrigerant systems with COSMO approaches

The knowledge of the phase equilibrium of refrigerant mixtures is crucial for the optimization of the production processes of refrigerant molecules, and the design of energetic systems (heat pumps, Organic Rankine Cycles, …). In this work, different predictive thermodynamic models (COSMO-RS and COSMO-SAC-dsp) have been used to determine the phase behavior of mixtures of refrigerants involving alkanes, fluorinated and chlorinated compounds. The COSMO-RS model leads to rather satisfactory predictions of the vapor-liquid equilibria of mixtures and is able to capture the azeotropic behavior for most systems. However, the original COSMO-SAC model as well as the COSMO-SAC 2010 version lead to unsatisfactory predictions of VLE for these systems, as they are unable to predict the azeotropic behavior in alkane + refrigerants. By combining COSMO-SAC with a dispersion term (COSMO-SAC dsp model) and readjusting the universal parameter for the F atom, it is possible to get very satisfactory predictions of similar accuracy as COSMO-RS. In order to predict the phase behavior at high pressure, the COSMO-SAC-dsp model can be combined with the Peng-Robinson equation of state and the MHV1 mixing rule. Excellent predictions of relative volatilities can be obtained with this approach over wide temperature and pressure ranges. COSMO calculation can also be used to predict saturated liquid densities, vaporization enthalpy and boiling points of pure refrigerants.

Experimental measurement and modelling of vapor-liquid equilibrium for 3,3,3- Trifluoropropene (R1243zf) and trans-1,3,3,3-Tetrafluoropropene (R1234ze(E)) binary system

• Experimental measurement of VLE data for R1243zf + R1234ze(E) by a static analytical method. • The R1243zf + R1234ze(E) system is a zeotropic system within 283.15 to 323.14 K. • Experimental data show good agreement with the predicted results of PR-MC-vdW and PR-MC-MHV2 models. The environmental performance becomes the critical factor of the selection of refrigerant. 3,3,3-trifluoropropene (R1243zf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) are environmental friendly candidates to replace R134a. Whereas, in the consideration of environmental factor, safety, and energetic efficiency at the same time, none of the pure refrigerants has been proved to be a suitable solution. Mixed refrigerants provide an approach to this problem because the characteristics of refrigerant blends can be optimized for particular applications in the way pure component refrigerant alone cannot be. The purpose of this work is to explore an R1243zf/R1234ze(E) blend which can be possibly used as a long-term alternative to replace hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs). We report the measurements of saturated vapor pressures of R1234ze(E) and R1243zf ranging from 273.17 to 353.13 K, and isothermal vapor-liquid equilibrium of R1243zf + R1234ze(E) systems from 283.15 to 323.14 K. The measurements are performed by static-analytic type apparatus coupled with two electromagnetic capillary samplers (ROLSI®, patent of Armines). The experimental data are correlated by the Peng-Robinson (PR) equation of state (EoS) associated with Mathias-Copeman (MC) alpha function and classical mixing rules. For the comparison of conventional mixing rules and excess free energy ( G E ) mixing rules models, classic van der Waals one fluid mixing rules and modified Huron-Vidal second-order (MHV2) mixing rules are employed respectively to the correlation of experimental VLE data. The modeling results are in good agreement with the measured data, while the PRMC-MHV2 model exhibits better performance in VLE prediction.

Prediction of Vapour Liquid Equilibria for Binary Azeotropic Systems using Activity Coefficient Models

Distillation operations are inevitable in chemical and petrochemical process industries. Design of distillation equipment requires knowledge of precise vapor-liquid equilibrium data. Due to the complexity and expenses incurred to obtain the VLE data experimentally for those systems for which the data are not available, solution thermodynamics and phase equilibria serve as an important tool in theoretical VLE prediction. In the current investigation five binary azeotropes namely Acetone-water, Acetone-methanol, Ethanol-water, Ethanol-benzene, and Methanol-water are taken for study. The theoretical prediction of VLE for these systems were computed using activity coefficient models namely NRTL, UNIQUAC, UNIFAC and modified form of Florry - Huggins equations (SRS and TCRS). The parameters for the five systems of four models viz. NRTL, UNIQUAC, SRS and TCRS were computed using Newton Raphson technique. UNIFAC model was adopted using Analytical solution of group contribution (ASOG) method. The performance of these models are tested using thermodynamic consistency test and validation from experimental VLE from literature. It was seen that the Acetone - Water system follows TCRS model, Acetone - Methanol and Ethanol - Water and Methanol - Water systems follow UNIFAC model, whereas SRS model suits for the Ethanol - Benzene system with highest accuracies.

Measurements by using an automatic pressure control and predictions of isobaric VLE at 1.5 MPa for binary mixtures of methyl acetate, ethyl acetate, 1–propanol and 1–butanol

The experimental data of vapor–liquid equilibrium for the binary systems methyl acetate+1–propanol, methyl acetate+1–butanol and ethyl acetate+1–propanol at 1.5MPa has been obtained, using an ebulliometer made of stainless steel. This equipment works through the Cottrell pump effect, so that the liquid and vapor phases are recirculated. The isobaric data T–x–y are informed and analyzed with respect to the literature data. The evolution of the azeotropic point with the pressure in the binary system of ethyl acetate+1–propanol is included. The thermodynamic consistency of the systems was verified by employing the Peng–Robinson equation of state in different forms and using the φ–φ approach.

Influence of binary ionic liquid mixtures of [BMIM][Cl] and [BMIM][BF4] on isobaric vapor-liquid equilibrium of acetonitrile + water at atmospheric pressure

The effects of ionic liquid mixtures on the phase behavior of azeotropic mixture of acetonitrile + water were presented through the experimental determinations of isobaric vapor-liquid equilibrium for acetonitrile + water + 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]) and acetonitrile + water + 1-butyl-3-methylimidazolium chloride ([Bmim][Cl]) + [BMIM][BF4] at atmospheric pressure (101.3 kPa). The mole ratios of [BMIM][Cl] to [BMIM][BF4] in the mixing ILs were fixed at 2:1, 1:1 and 1:2, respectively. The results showed that [BMIM][BF4] was ineffective in breaking the azeotropy of acetonitrile and water, which whereas could be broken when [BMIM][Cl] reached a certain concentration in the mixing ILs. VLE data of ternary and quaternary mixtures were satisfactorily correlated and predicted with NRTL model and COSMO-SAC could give a reasonable prediction of VLE for the investigated mixtures. Additionally, the analysis of interactions among different molecules showed that the interactions between [BMIM][Cl] and water are strong while ones between [BMIM][BF4] and water weak.

Comparison of SAFT-VR-Mie and CP-PC-SAFT in predicting phase behavior of associating systems III. Aliphatic hydrocarbons - 1-propanol, 1-butanol and 1-pentanol

This study compares the predictions of CP-PC-SAFT and SAFT-VR-Mie for binary systems of aliphatic hydrocarbons and the C3-C5 1-alkanols. Systems of carbon monoxide and hydrogen sulfide are considered as well. In all the cases zero values of the binary adjustable parameters have been implemented. Thanks to the superior flexibility achieved by fitting 6 pure compound parameters, SAFT-VR-Mie excellently represent various thermodynamic properties of the considered 1-alkanols. Since CP-PC-SAFT fits these data with only 2 adjustable parameters, its pertinent performance is less accurate, but remains reasonable good. At the same time, unlike SAFT-VR-Mie, CP-PC-SAFT rigorously obeys of the pure compound Tc and Pc, which allows accurate predictions of critical loci and VLE in the symmetric systems. Moreover, in exception of LLE in the systems of ethane and ethene, CP-PC-SAFT truthfully predicts critical data and the high pressure VLE in the asymmetric systems. SAFT-VR-Mie estimates these data in a less accurate manner, excepting the VLE of the C4-isomers and n-pentane systems. It the latter cases the results of both models are comparable. At the same time, SAFT-VR-Mie often yields more accurate results for the low-pressure VLE. Besides that, the predictions of CP-PC-SAFT for LLE in 1-alkanol – [C1MIM][NTF2] and – [C2MIM][NTF2] ionic liquid systems are presented. Despite the simplified approach to ILs, this model truthfully predicts the UCST data in 1-alkanol – [C1MIM][NTF2] and – [C2MIM][NTF2] systems, overestimating however the concentrations of ILs in both equilibria phases.

Comparison of Cubic-Plus-Association and Soave-Redlich-Kwong equations of state for prediction of vapor-liquid equilibrium of Fischer-Tropsch reaction mixture

Predictions of vapor liquid equilibrium for Fischer-Tropsch mixtures were compared using the classical Soave-Redlich-Kwong (SRK) and cubic-plus-association (CPA) equations of state. The performance of the two equations of state was evaluated based on comparison with results from eight sets of experimental runs in which different process conditions (pressure, reactants feed ratio, space velocity) were used. Flash calculations were used to determine the phase split at defined process conditions, whereas the phase equilibrium was defined utilizing the concept of equal fugacities in the vapor and the liquid phase for all components. A total of 75 components were considered in the reaction mixture: CO, H2, H2O, CO2, C1-C57 paraffins and C2-C15 olefins. All calculations were performed in MATLAB. The results showed that both equations of state had similar performance regarding the hydrocarbons, whereas CPA gave better results with inorganic components and SRK with prediction of the composition of the liquid phase. Computational time for CPA was substantially (100 times with the CPU used) higher than that for SRK. Overall, the use of CPA did not improve VLE prediction for FTS systems significantly enough to be recommended for use in FTS reactor models.

On the mixing rules matter: The VLE predictions for binary systems

Mixing rules are used to extend the range of applicability of both equations of state and excess Gibbs energy models. The equations of state are limited by the molecules complexity, whilst the excess Gibbs energy constraint is the range of temperature and pressure. Mixing rules allow the coupling of both types of thermodynamics models to overcome such limitations. In this work, the analysis of the performance of 5 excess Gibbs energy models using the Peng-Robinson equation of state and two of its variants with 3 different mixing rules – VDW1, HVOS, and WS. Great accuracy of the UNIFAC and UNIFAC(Do) models, especially when using the VDW1 mixing rule to couple with either PRSV or PRSV2, was obtained. The F-SAC model has provided reliable results as well. In addition, evaluations over the performance of the excess Gibbs energy, the equations of state, and the mixing rules were made separately, in order to better analyze their results. The COSMO-SAC model was greatly affected by the HVOS mixing rule, leading to very high objective function values.

Polar (s)PC-SAFT: Modelling of polar structural isomers and identification of the systematic nature of regression issues

The systematic nature of regression problems in the polar SAFT framework is identified in this work. This is achieved by considering parameter regression and VLE predictions for structural isomers of medium length linear ketones, esters and ethers. The inability to generate a unique polar parameter set by what we define as the standard regression approach (SRP) is a frequently reported problem in the literature. These problems are attributed to the similarity of saturation properties between the polar component and those of a nonpolar equivalent. There is thus an inability to distinguish between dispersion and polar contributions to component behaviour during regression. This is systematically demonstrated by the consideration of isomers, where a systematic deterioration of prediction strength is in evidence as the distinction between the properties of polar component and the nonpolar analogue diminishes with successive isomers. The fixed polar parameter (FPP) approach formalised in this work offers the best means of combatting these problems and yielding predictive parameter sets. Predictions based on this approach are consistently superior to conventional regression approaches, whether using the Jog and Chapman (JC) or Gross and Vrabec (GV) polar terms. Finally, the identical treatment of both these terms provides a balanced comparison of their performance and points towards a superior predictive capacity for the GV polar term.

Effective Critical Constants for Helium for Use in Equations of State for Natural Gas Mixtures

Most of the world’s helium supply is obtained by the cryogenic distillation of natural gas. Modeling the distillation conditions requires equations of state capable of predicting vapor–liquid equilibria over wide ranges of conditions. Equations of state, including cubic equations and multiparameter Helmholtz models, depend on the critical properties of pure substances for predicting various properties of multicomponent fluid mixtures. Predictions for helium are problematic as its critical point (5.195 K, 0.2275 MPa) is influenced strongly by quantum effects; large, empirical interaction parameters tend to be used in equations of state to compensate for these effects. Prausnitz and co-workers proposed an alternative approach using effective critical constants for quantum gases but demonstrated it for only three helium-containing binary mixtures. Here, we demonstrate that the use of an effective critical point at (11.73 K, 0.568 MPa) for helium substantially improves the prediction of VLE by the Peng–Robinson equation of state for 15 binary and 2 ternary mixtures, including the major components of natural gas. This effective critical point for helium was selected from a critical analysis of pTxy data for the (methane + helium) binary. The effective critical constants for helium are compatible with an acentric factor near zero, as expected for a small spherical molecule and similar to the acentric factors of heavy noble gases. The possibility of applying this approach to address recognized limitations of the GERG-2008 equation of state is discussed.

The NRTL-PRA group contribution EoS for the simultaneous prediction of LLE, VLE and hE of hydrocarbon mixtures with associating compounds

The goal of this study is to propose a modification of the NRTL-PR EoS for the prediction of phase equilibria and excess enthalpies in mixtures containing methanol with hydrocarbons; indeed, with these systems, the original equation is confronted to many difficulties arising from the simultaneous prediction of liquid-liquid equilibria together with vapor-liquid and enthalpy data. For this purpose, an additional term is included in the EoS excess Gibbs energy, gEoSE, of the Peng-Robinson equation to account for the self-association of methanol. The resulting NRTL-PRA EoS is successfully used for the prediction of both liquid-liquid and vapor-liquid equilibria, as well as excess enthalpies, in mixtures of methanol with hydrocarbons, light gases and associating compounds. Results are comparable to those obtained with other predictive EoS (VTPR and SAFT), but with the main advantage to predict all thermodynamic properties with a simple cubic equation.

Simultaneous correlation of infinite dilution activity coefficient, vapor–liquid, and liquid–liquid equilibrium data with F-SAC

In this work, the recently proposed Functional-Segment Activity Coefficient (F-SAC) model is revised and extended in order to simultaneously represent infinite dilution activity coefficient (IDAC), vapor–liquid (VLE), and liquid–liquid (LLE) equilibrium data. For this investigation, systems involving aromatics, alkanes, cycloalkanes, alkenes and n-Formylmorpholine were selected for the tests. The behavior of these mixtures vary from nearly ideal to partially miscible. A new parameter per group was introduced in order to better represent LLE data in wide temperature ranges. The revised model was calibrated with experimental IDAC and LLE (binary and ternary systems) data. F-SAC correlation results and predictions of VLE experiments were compared with different UNIFAC parametrizations available in the literature. For the systems tested, the proposed approach showed to be more general; there were good IDAC and LLE correlations as well as VLE predictions, all with a single parameter set.

Application of artificial neural network for vapor liquid equilibrium calculation of ternary system including ionic liquid: Water, ethanol and 1-butyl-3-methylimidazolium acetate

A feed forward three-layer artificial neural network (ANN) model was developed for VLE prediction of ternary systems including ionic liquid (IL) (water+ethanol+1-butyl-3- methyl-imidazolium acetate), in a relatively wide range of IL mass fractions up to 0.8, with the mole fractions of ethanol on IL-free basis fixed separately at 0.1, 0.2, 0.4, 0.6, 0.8, and 0.98. The output results of the ANN were the mole fraction of ethanol in vapor phase and the equilibrium temperature. The validity of the model was evaluated through a test data set, which were not employed in the training case of the network. The performance of the ANN model for estimating the mole fraction and temperature in the ternary system including IL was compared with the non-random-two-liquid (NRTL) and electrolyte non-random-two-liquid (eNRTL) models. The results of this comparison show that the ANN model has a superior performance in predicting the VLE of ternary systems including ionic liquid.

Prediction of mutual solubility and low-pressure VLE using high-precision correlation lines

Binary liquid–liquid equilibrium (LLE) data are correlated using thermodynamic consistency (TC) lines. Of the 283 binaries investigated, 257 have correlation errors less than 3%, providing an average of 0.52%. The average correlation error of the 283 binaries was 2.2%. The TC lines can satisfactorily predict solubilities from near the lower to the upper critical solution temperatures. Furthermore, the TC lines determined from the low-pressure P, x and T, x data can satisfactorily predict the VLE relationships.

Simulation study on biodiesel production by reactive distillation with methanol at high pressure and temperature: Impact on costs and pollutant emissions

Recently, a two-step biodiesel production process which uses short-chain alcohols at supercritical conditions has been proposed. In addition, literature reports suggest that the COSMO-SAC thermodynamic model is a suitable alternative for the prediction of VLE for supercritical methanol/methyl esters mixtures. Thus, in this work a simulation study of the two-step supercritical method for the production of biodiesel is performed by using the COSMO-SAC model. Further, alternative system configurations for biodiesel production based on reactive distillation are proposed and their total emissions are compared to those corresponding to the conventional catalytic method. The study demonstrates the benefits of using reactive distillation for the esterification step and discusses the environmental impact of the supercritical production process. It has been found that the intensified alternatives reduce the emissions considerably and, through the reuse of the excess methanol, the emissions level of the supercritical process can be compared to those of the catalytic method.

Influence of Gas Impurities on Thermodynamics of Amine Solutions. 1. Aromatics

New parameters for improving the Electrolyte-NRTL model have been regressed for acidic gas-MDEA aqueous solution systems containing aromatics. Values of binary interaction parameters for liquid phase activity coefficients are estimated from regressions of experimental data. Aspen Plus has been used for regressions and thermodynamic modeling. The focus of the work is to have better predictions of VLE of aromatic compounds in amine systems for acidic gases purification.

Influence of Gas Impurities on Thermodynamics of Amine Solutions. 2. Mercaptans

New parameters for improving the Electrolyte-NRTL model have been regressed for acidic gas-MDEA aqueous solution systems containing mercaptans. Values of binary interaction parameters for liquid phase activity coefficients are estimated from regressions of experimental data. Aspen Plus has been used for regressions and thermodynamic modeling. The focus of the work is to have better predictions of VLE of mercaptans in amine solutions for acidic gases purification.