Vapor-liquid Equilibrium Model Research Articles

A New PC-SAFT Model for Pure Water, Water–Hydrocarbons, and Water–Oxygenates Systems and Subsequent Modeling of VLE, VLLE, and LLE

Accurate analytic thermodynamic modeling of water and its mixtures with hydrocarbon and oxygenates is difficult even with new and advanced equations of state such as the perturbed-chain statistical associating fluid theory (PC-SAFT). Several attempts have been made in the past by various authors to solve this issue. However, current models generally fail to describe simultaneously and accurately pure water properties (especially its liquid density) and liquid–liquid equilibria for mixtures involving water, hydrocarbons, and oxygenates. In the current work, this problem is dealt with by modification in the fundamental structure of the model. It was established that the temperature dependent diameter d(T) does not behave in the same way for water as it inscribed in the original model. Hence, a modification was proposed for d(T) of water in order to correctly represent the phase behavior of pure water and its mixtures with hydrocarbons and oxygenates. The deviations in saturated liquid densities and vapor pressure for pure water were reduced to 0.6% and 2.2%, respectively, in a large temperature range. The results for liquid–liquid equilibrium (LLE), vapor–liquid equilibrium (VLE) and vapor–liquid–liquid equilibrium (VLLE) of various water–hydrocarbons and oxygenates show the accuracy of this new model and its predictive capability when coupled with a group contribution approach. For certain oxygenated mixtures such as water with aldehydes, ketones, ethers, and esters a new contribution to the Helmholtz energy, known as the “non-additive hard sphere” contribution, was used. The cross-interaction parameters obtained for mixtures were validated qualitatively by calculating octanol/water partition coefficients and the Gibbs free energy of hydrogen bonding (ΔGHB). Results are found in good agreement with experimental data.

Design of protonation constant measurement apparatus for carbon dioxide capturing solvents

Global warming phenomenon has led to world climate change caused by high concentrations of greenhouse gases (GHG), e.g. carbon dioxide (CO2), in the atmosphere. Carbon dioxide is produced in large amount from coal-fired power plants, iron and steel production, cement production, chemical and petrochemical manufacturing, natural gas purification, and transportation. Carbon dioxide emissions seem to rise from year to year; some efforts to reduce the emissions are, therefore, required. Amine-based absorption could be deployed for post-combustion capture. Some parameters, e.g. mass transfer coefficients and chemical equilibrium constants, are required for a vapor-liquid equilibrium modeling. Protonation constant (pKa), as one of those parameters, could then be measured experimentally. Therefore, an experimental setup to measure pKa of CO2 capturing solvents was designed and validated by measuring the pKa of acetic acid at 30 to 70 °C by a potentiometric titration method. The set up was also used to measure the pKa of MEA at 27 °C. Based on the validation results and due to low vapor pressure of CO2 capturing solvents in general, e.g. alkanolamines, the setup could therefore be used for measuring pKa of the CO2 capturing solvents at temperatures up to 70 °C.

Modeling the effect of piperazine on CO2 loading in MDEA/PZ mixture

The equilibrium of CO2 solubility and species concentration data for the absorption of CO2 in the aqueous solutions of Methyl-di-ethanolamine (MDEA), Piperazine (PZ) and their mixture (MDEA+PZ) were analyzed using Matlab software. A thermodynamic model was developed to predict the vapor liquid equilibrium of CO2 in aqueous mixtures of MDEA/PZ. The electrolyte-nonrandom two-liquid (e-NRTL) model was used to build the vapor-liquid equilibrium model, which defines equilibrium behavior of the solution. This model was applied to correlate the species concentration in the solutions of MDEA, PZ and their mixtures using default interaction parameters reported in the literature. It was observed that this model gave a good estimation of CO2 loadings over a wide range of operating conditions for both single and mixed amine solutions. The model has been used to estimate the species concentrations and CO2 solubility in aqueous DEA/PZ [1]. The application of this model is new to this system, i.e. of CO2-MDEA-PZ-H2O. In this work, the model was further extended to predict the effect of piperazine on CO2 loading for carbonated aqueous solutions of MDEA/PZ systems. The addition of PZ to MDEA as an activator increased the solubility of CO2 under low and high range of CO2 partial pressures and temperatures. The species concentrations, activity coefficients, and pH of the CO2 loaded solutions were studied, and the model predicts amine volatility as well. The model was validated using the experimental data generated from our previous work and data available in the open literature. The results of the current model are in an acceptable degree of agreement with the experimental data of CO2 solubility reported in previous work for this system.

An experimental investigation on the solubility of methane in 1-octanol and n-dodecane at ambient temperatures

The synthetic method is used for the determination of the liquid phase solubility of methane in 1-octanol at three temperatures (273.25, 283.15, and 293.2) K and of methane in n-dodecane at 273.1 K at pressures up to about 10 MPa. The new gas solubility data is applied to evaluate the molality scale based Henry's constant of methane in those solvents: (4.31, 4.67, and 4.81 ± 0.05) MPa in 1-octanol and (2.75 ± 0.04) MPa in n-dodecane at the given temperatures, respectively. The experimental technique provides as well the density of the gas-saturated liquid phase and thus allows for evaluation of the partial molar volume of methane at infinite dilution in the solvent: (47, 49, and 49 ± 5) cm3/mol in 1-octanol and (45 ± 5) cm3/mol in n-dodecane, respectively. The experimental results are compared with the limited data from the open literature. At the investigated temperatures, the vapour phase can be treated as pure methane, and the extended Henry's law suffices to accurately correlate the new gas solubility data. However, that vapour-liquid equilibrium model is here expanded allowing to accurately predict the small vapour phase solubility of the solvent in compressed methane which is demonstrated by comparison with experimental data from the literature.

Prediction of VLE for aqueous blended amines using VLE models of single amines

The possibility of the vapor-liquid equilibrium (VLE) prediction of aqueous blended amines using Kent-Eisenberg (KE) VLE models of single amines has been investigated in this study. The VLE data of five different types of single amine and seven types of aqueous blended amine as mixtures of the selected single amines were collected first. The VLE of the single amines was fit to the KE models, and the VLE of the aqueous blended amines was predicted using the KE models of single amines without introducing any interaction terms between the amines. As a result, it was found that the VLE of the aqueous blended amines could be satisfactorily predicted using only the VLE models of single amines. Finally, VLE prediction ability as a function of temperature and the possible uses of the proposed method in the development of new aqueous blended amines were discussed.

Experimental Measurement and Modeling of Vapor–Liquid Equilibrium for the Ternary System Water + 1-Propanol + Glycerol

Vapor–liquid equilibrium (VLE) data were reported for the ternary system water + 1-propanol + glycerol at 100 kPa. The NRTL equation was used for the modeling of ternary VLE. Binary parameters of water + glycerol were fixed as the same for water + ethanol + glycerol and were taken from the literature. The ternary VLE data, together with literature results of binary VLE data and infinite dilution activity coefficients for water +1-propanol, were used for the modeling. To extend the glycerol composition range and the temperature range, infinite dilution activity coefficients of 1-propanol in glycerol were measured in a temperature range of 313.15 to 393.15 K, and were used in the modeling. The correlation provided good agreement for all the source data. It is shown that the infinite dilution activity coefficients provide key information for reliable correlation in a wide composition range. With the addition of glycerol, the azeotrope of water + 1-propanol can be removed at a glycerol mole fraction of 0.398,...

Determination of vapor—liquid equilibrium diagrams of multicomponent systems

AbstractA method for the determination of vapor–liquid phase diagram structure of five-component systems based on the analysis of types and Poincare indexes of singular points of the geometric scan and full structure of the concentration simplex is proposed. Validity of the proposed method was demonstrated by vapor–liquid equilibrium modeling in five-component mixtures: ethanol + water + toluene + butanol + chlorbenzene and acetone + chloroform + ethanol + cyclohexane + water.

Predicting phase equilibrium of a ternary feed to the hydroiodic acid section of SI thermochemical cycle

This work presents a comparative study in predicting the vapor–liquid equilibrium (VLE) properties of a ternary feed, consisting of HI, H2O and I2, to the hydroiodic acid section of SI (sulfur-iodine) thermochemical cycle. Three binary interaction parameters sets are proposed for an activity-based NRTL (non-random two liquid) model and two equation of state models, namely SRK (Soave–Redlich–Kwong) and PR (Peng–Robinson). A comparative performance of these three VLE models is evaluated based on their single parameters set by using the available experimental data points.

Separation of Azeotropic Mixture Using Multi-stage Ultrasound-Assisted Flash Distillation

Abstract A mathematical model for an ultrasound-assisted vapor liquid equilibrium (VLE) system developed in Aspen Custom Modeler is exported to Aspen Plus flowsheeting environment to form a block in the software library to represent a single stage flash separation unit. The block is then arranged in series to mimic an ultrasonically intensified distillation process. As a case study, an ethanol/ethyl acetate separation process is examined. The results show that a 99 mol% ethyl acetate recovery is established when a series of 27 flash VLE devices are used. The system is also evaluated for other minimum boiling azeotropic mixtures, and consistent results are obtained, thus revealing the potentials of ultrasound-assisted system as an alternative strategy for azeotropic mixture separations.

Accurate Modeling of Evaporation and Enthalpy of Vapor Phase in CO2 Absorption by Amine Based Solution

The effect of enthalpy of liquid and vapor phases for the CO2 absorption process in mono-ethanolamine (MEA) solution is one of the important factors involved in CO2 absorption processes. This phenomenon is more prominent at the bottom of the column for countercurrent operations resulting in corrosion, erosion, and loss in amine, mostly at high enthalpy of liquid. The absorption column temperature increases during the CO2 absorption process, due to exothermic absorption of CO2 in amine solution. This rise in temperature increases water evaporation. These water vapors condense back to the liquid phase when they come in direct contact with cold amine solution coming from the top of the column. The Kent-Eisenberg vapor-liquid equilibrium model used is accurate with less than 3% error. A loss of MEA and water in the vapor phase is studied in this research. It is revealed that only 0.001 mole% MEA and 3 mole% water leave the absorption column with flue gases at 298 K. This loss in amine solution is quite low and acceptable for industrial processes.

Catalytic and non catalytic solvent regeneration during absorption-based CO2 capture with single and blended reactive amine solvents

Molecular potential energy surface (PES) diagrams of the deprotonation of a protonated amine (AmineH+) were used in combination with ion speciation plots of the vapour liquid equilibrium (VLE) model to provide a better understanding of the reasons for the drastic reduction of energy required for CO2 stripping from some amine solutions under certain operating conditions. Experiments for CO2 stripping were performed using single and blended amines (namely, MEA, MEA–MDEA, MEA–DEAB (4-(diethylamine)-2-butanol)) with and without solid acid catalysts (Al2O3 or HZSM-5) at 90–95°C. The heat duty to regenerate 5M MEA without any catalyst was the baseline taken as 100%. The results showed that the CO2 stripping performance in terms of heat duty decreased in the order: MEA–DEAB with HZSM-5 (38%)>MEA–DEAB with γ-Al2O3 (40%)>MEA–DEAB with no catalyst (51%)>MEA with HZSM-5 (65%)>MEA with γ-Al2O3 (73%)>MEA–MDEA with γ-Al2O3/no catalyst (74%), all relative to MEA with no catalyst (100%). The results further show that the addition of MDEA or DEAB (as tertiary amines) in a blended solvent provided R3N and HCO3−, which split and thus decreased the free energy gaps. On the other hand, even though MDEA is intrinsically less basic as per the energy diagram, DEAB generated a lot more HCO3− resulting in a tremendously lower heat duty. γ-Al2O3 (Lewis acid) was more effective in the CO2 lean region by duplicating the role of HCO3−, which is negligible in the CO2 lean region, whereas HZSM-5 (Brϕnsted acid) is effective throughout the loading range by donating protons. The implication is that the use of solid acid catalysts could result in stripper size and heat duty reductions during solvent regeneration.

Improving Batch Reactive Distillation Processes with Off-Cut

Methods for improving the operation of batch reactive distillation with off-cut are presented and discussed. Although off-cut can improve the operation of batch reactive distillation, its usefulness is limited in some cases due to the relative volatility ranking of reactants and products. In these cases, performance can be improved by using a middle vessel column or by using an excess of one reactant. These methods are demonstrated with case studies of three processes with realistic reaction kinetics and vapor–liquid equilibrium models: hydrolysis of methyl lactate, esterification of formic acid, and production of 1,1-dimethoxyethane. Batch capacity can be improved on average 41.9% if the appropriate method is employed.

Temperature Peak Analysis and Its Effect on Absorption Column for CO2 Capture Process at Different Operating Conditions

Abstract The role of temperature is important in CO2 capture processes. Unfortunately, detailed analysis on the temperature profile of the absorption column is scarce in the literature. Important factors like CO2 capture capacity and corrosion rate directly depend on temperature of the column. Many side reactions such as solvent degradation, formation of stable salts, corrosion and reduction in CO2 capture are prominent at a higher temperature. This study reports a broad study on the temperature profile for CO2 capture process based on a detailed mathematical model, Kent–Eisenberg vapor–liquid equilibrium (VLE) model. This model is quite accurate in calculating CO2 capture for any specific operating condition. Results produced from Kent–Eisenberg VLE model are consistent with experimental data. This study reports temperature profiles of an absorption column for different operating conditions. Moreover, it was found that CO2 absorption is more effective at low and ambient temperatures than at high temperature confirmed by a peak temperature in all cases and in the lower section of the column, which is attributed to exothermic CO2 absorption in monoethanolamine. This temperature variation of the column will be helpful in designing CO2 capture plants.

Hybrid swarm optimization for vapor–liquid equilibrium modeling

A hybrid algorithm based on particle swarm optimization and ant colony optimization was used to describe the vapor–liquid equilibrium of complex mixtures. The proposed PSO+ACO algorithm is tested on several benchmark functions from the usual literature. Firstly, nine binary vapor–liquid phase systems containing supercritical fluids and ionic liquids were evaluated for optimizing the equation of state method. Next, twenty binary vapor–liquid phase systems were described using two activity coefficient models optimized by the hybrid algorithm. The results of vapor–liquid equilibrium modeling were compared with the Levenberg–Marquardt algorithm, and show that the application of PSO+ACO algorithm on thermodynamic models such as equation of state methods and activity coefficient models, is crucial, and that the hybrid PSO+ACO algorithm is a good tool to optimize the interaction parameters to describe the vapor–liquid equilibrium of several systems.

Modeling of vapor-liquid equilibrium for binary polypropylene glycol/solvent solutions using cubic equation of state models: optimization and comparison of CEoS models

Abstract The cubic equation of state (CEoS) is a powerful method for calculation of the vapor-liquid equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, VLE calculations of polypropylene glycol (polypropylene oxide) [PPG(PPO)]/solvent solutions were carried out. In this approach, eight models containing Peng-Robinson-Stryjek-Vera (PRSV) and Soave-Redlich-Kwong (SRK) CEoS separately combined with four mixing rules, namely van der Waals one-fluid mixing rule with one adjustable parameter (vdW1), van der Waals one-fluid mixing rule with two adjustable parameters (vdW2), Wong-Sandler (WS), and Zhong-Masuoka (ZM) were applied to calculations of bubble point pressure. For a better correlation, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations (%AAD) between computed results and experimental bubble point pressure data were calculated and presented. Although the capability of two CEoS had a good agreement with experimental data and illustrated the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

A simple thermo-physical model for vapor–liquid equilibrium of the reactive HIx (HI–H2O–I2–H2) system

Thermodynamic phase equilibrium of the reactive HIx system encountered in the sulfur-iodine (SI) cycle has been identified as a basic research need for the hydrogen economy. In this communication, a simple NRTL (nonrandom two-liquid)-based vapor–liquid equilibrium (VLE) model is devised for the HIx system considering the HI decomposition reaction in the gas phase only. We propose a new set of NRTL binary interaction parameters as well as a new expression for the HI decomposition chemical equilibrium constant as a function of temperature. This simple VLE model with the use of only one set of NRTL binary parameters is capable of reproducing the Larousse et al. (Int. J. Hydrogen Energy 34 (2009) 3258–3266) experimental data for a wide range of pressures (1–24bar) and HI concentrations beyond the azeotrope.

Evaluation of Cubic, SAFT, and PC-SAFT Equations of State for the Vapor–Liquid Equilibrium Modeling of CO2 Mixtures with Other Gases

Accurate thermodynamic models for phase equilibria calculations of carbon dioxide mixtures with other gases are of high importance for the safe and economic design of carbon capture and storage (CCS) technologies. In this work, we assess the capability of Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR) cubic equations of state (EoS), as well as Statistical Associating Fluid Theory (SAFT) and Perturbed-Chain SAFT (PC-SAFT) in modeling vapor–liquid equilibria for binary mixtures of CO2 with CH4, N2, O2, SO2, Ar, and H2S, and for the ternary mixture CO2–N2–O2. Liquid density calculations for some of these mixtures are also performed. Experimental data available are used to assess the accuracy of the models. Two different expressions are used for the calculation of parameter α in PR EoS. PC-SAFT is, on average, more accurate than cubic EoS and SAFT when no binary interaction parameter is used. However, when a binary interaction parameter fitted to the experimental data is used, model correla...

Thermodynamic Model for Vapor-Liquid Phase Equilibrium in an Exerted Magnetic Field

Many researchers have shown a great deal of interest in the effects that magnetic fields have when applied in chemical reactions, crystallization, magnetic separation of materials, magnetic levitation, materials processing, and wastewater treatment. However, surprisingly little research has been done on the effects of magnetic fields on the vapor-liquid equilibrium and the thermodynamic model for vapor-liquid phase equilibrium. The influence of magnetic fields on vapor-liquid equilibrium of binary heterogeneous azeotrope was investigated with ethanol-water in this paper. It was found that the vapor-liquid equilibrium of an ethanol-water system is influenced by the external magnetic field, but that the azeotropic point of the ethanol-water system is not changed by the magnetic field when the magnetic intensity reaches 0.8 T. Rather, the exerted magnetic field reduces the equilibrium temperature and shortens the distance between T-x curve and T-y curve in T-x-y diagram of the vapor-liquid equilibrium of the ethanol-water system. A thermodynamic model for vapor-liquid phase equilibrium in the exerted magnetic field was derived theoretically, based on the fundamental thermodynamic theory. The results show that the logarithm value of the ratio of the composition of the certain component in a magnetic field to that without the magnetic field is proportional to the magnetic susceptibility of the solution, and to the square of magnetic field intensity. This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

13C NMR Spectroscopy of a Novel Amine Species in the DEAB–CO2–H2O system: VLE Model

In the present work, ion speciation studies in solutions of the novel amine 4-(diethylamine)-2-butanol (DEAB), at various CO2 loadings (0–0.8 mol of CO2/mol of amine) and amine concentrations (0.52–1.97 M), were determined by 13C nuclear magnetic resonance (NMR) spectroscopy. In addition, the dissociation constant K of DEABH+ was determined at 24.5, 35, and 45 °C using a pH meter. The ion speciation plot, which contains various sets of concentrations of DEAB, protonated DEAB, bicarbonate, and carbonate, was successfully generated. Because DEAB is a novel solvent, this is the first time that the ion speciation plots of the DEAB–CO2–H2O system have been developed. It is also the first time that the 13C NMR calibration technique was applied to develop the vapor–liquid equilibrium (VLE) model for an amine–CO2–H2O system. The results obtained from the present work can be a great help for the further analysis of the DEAB VLE model, as well as CO2 absorption and kinetics studies. Furthermore, it was found that t...

CO2 capture into aqueous solutions of 3-methylaminopropylamine activated dimethyl-monoethanolamine

In this work, experimental data and a simplified vapor-liquid equilibrium (VLE) model for the absorption of CO2 into aqueous solutions of 3-methylaminopropylamine (N-methyl-1,3-propane diamine – MAPA) and dimethyl-monoethanolamine (2-dimethylaminoethanol – DMMEA) are reported. The chemicals were selected based on kinetic, energy and environmental properties for post-combustion CO2 capture. The effect of the DMMEA/MAPA ratio and the total concentration level of amine were studied. Based on the results of preliminary semi-quantitative tests (screening) the best amine ratios were determined. Two amine concentrations were selected for the VLE study. The result of both the screening and the VLE measurements are compared to the generally used 5M (30 mass %) monoethanolamine (MEA) solution. The presented systems seem to be better performing than 5M MEA, and have significantly higher cyclic capacity combined with moderate impact on the environment.