Vapor-liquid Equilibrium Calculations Research Articles

Erratum to: Thermodynamic modeling of vapor–liquid equilibrium for binary polyethylene glycol/solvent solutions using cubic equations of state: optimization and comparison of CEoS models

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium 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, vapor–liquid equilibrium calculations of Polyethylene glycol(Polyethylene oxide)/solvent solutions were carried out. In this approach eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely one-parameter van der Waals one-fluid, two-parameter van der Waals one-fluid (vdW2), Wong–Sandler, and Zhong–Masuoka were applied to calculations of bubble point pressure. For the better prediction, 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 between predicted results and experimental bubble point pressure data were calculated and presented. Although the capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

Optimum synthesis of solvent-based post-combustion CO2 capture flowsheets through a generalized modeling framework

A generalized framework for the optimal design of post-combustion CO2 capture processes based on a systemic and flexible equilibrium separation model that employs orthogonal collocation on finite elements techniques is proposed. Within this context, a column section of adaptive separation capability and functionality serves as the fundamental structural block for the identification of efficient separation schemes. Separation column sections in combination with heat transfer blocks, as well as stream splitters and mixers enable the generation and evaluation of alternative flowsheet configurations within a nonlinear optimization program. The main objectives for the flowsheet evaluation involve separation and thermal efficiency that eventually impact the economics of the overall process. Vapor–liquid equilibrium calculations are performed using statistical associating fluid theory for potentials of variable range (Mac Dowell et al., Ind Eng Chem Res 49:1883–1899, 2010). The proposed design framework is used for the optimal design of five alternative flowsheet configurations for the separation of CO2 from a flue gas stream using a 30 % weight monoethanolamine aqueous solution. These flowsheets illustrate the various connection patterns between the process units and indicate suitable distribution of process-driving forces through which the overall efficiency can be drastically enhanced.

Molecular-level simulation of bubble and dew points of fluid mixtures and application to refrigerant cycle design

Molecular simulation is an increasingly important and useful tool in the design of devices based on many types of chemical phenomena. Such methods for the simulation of all types of vapour–liquid equilibrium (VLE) are particularly important, because they potentially permit their direct application to the design of refrigeration processes. Several molecular simulation methods exist for the calculation of VLE in the cases of flash calculations and bubble-point calculations for fluid mixtures. However, implementations for other VLE problems such as dew-points remain challenging. We present an algorithm for the calculation of all four types of these VLE phenomena in binary mixtures. We illustrate it for a 30 mass% R32/R134a binary refrigerant mixture by means of example dew- and bubble-point problems, in addition to the calculation of P–h and T–h diagrams. We also demonstrate its application to the simulation of a vapour compression refrigeration cycle involving the refrigerant mixture.

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.

Considering the dispersive interactions in the COSMO-SAC model for more accurate predictions of fluid phase behavior

A term to consider the contribution of the dispersive interactions to the non-ideality of mixtures is introduced into the COSMO-SAC model on the basis of molecular simulation data from classical model force fields. This dispersion term is a one-constant Margules equation, where the constant is determined from the molecular dispersion parameter of the components. Furthermore, an atomic contribution method is proposed to calculate the dispersion parameter for a given molecule. For binary systems containing molecules consisting of C, H, N, O, F and Cl atoms, a total of 13 global parameters is introduced with the COSMO-SAC-dsp model. These parameters are obtained from regression to a large training set of binary vapor–liquid equilibrium (VLE) data from experiment. The overall deviations for VLE calculations on this training set are reduced by 25% in terms of the vapor pressure and 12% in terms of the vapor phase mole fraction. This dispersion term can provide a significant improvement for infinite dilution activity coefficient predictions, where the accuracy was increased by around 33%.

Development and analysis of the Original UNIFAC-CI model for prediction of vapor–liquid and solid–liquid equilibria

In this work, we present a further development and analysis of the Original UNIFAC-CI models for the prediction of vapor–liquid equilibrium (VLE) and solid–liquid equilibrium (SLE) for a wide range of mixtures. Three sets of atom interaction parameters (AIPs) have been regressed. For the first two sets, only VLE experimental data were used in parameter estimation. In the first set, no weighting factors were used for each of the VLE data in the objective function when regressing the AIPs. However, for the second set, the AIPs have been regressed using the so-called QVLE quality factors obtained for each of the VLE data from a quality assessment algorithm (consistency tests) as weighting factors in the objective functions. For the third set of parameters, SLE and VLE data were used in the regression of AIPs. The result of the correlations in terms of deviations errors and predictions using these three sets of regressed parameters are presented, compared and discussed. The significance of adding the QVLE values and SLE systems in the regression of the AIPs are also highlighted. UNIFAC is a model that can be in principle used for both VLE and SLE (as well as other types of phase behavior) calculations. The range of applicability of the predictive UNIFAC-CI is investigated and it is shown to what extent the Original UNIFAC-CI model can successfully predict SLE especially when the needed parameters are missing.

Modelling CO2 –Water Thermodynamics Using SPUNG Equation of State (EoS) Concept with Various Reference Fluids

Due to the continuous increase of CO2 emission to environment, the Carbon Capture and Storage (CCS) processes gained a very high importance in the last decades. One common CO2 impurity during various CCS processes is water. Therefore, the calculation of CO–water thermodynamic properties is a vital issue. This work preliminary investigates the accuracy of the extended corresponding states equation of state SPUNG using various reference fluids for the density and vapour liquid equilibrium (VLE) calculations of the CO2 - water system. The evaluation is done by comparing the numerical prediction with experimental data. The study is conducted at different mixture concentrations, and covering a broad range of conditions. The study is conducted using N2, O2, C1, C2, C3, and C4 as reference fluids. The results show an impact on density prediction. On the other hand, the VLE calculations exhibited very low sensitivity to varying reference fluids.

An Experimental Calculation of Asphaltene Critical Properties in Crude Oil Reservoir Systems

High-molecular-weight hydrocarbons and asphaltenes are important constituents of petroleum and can cause problems related to crystallization and deposition of asphaltene. This article introduces an extension of the cubic equation of state (Peng-Robinson EOS) to describe asphaltene–toluene mixture vapor–liquid equilibria (VLE) and characterize pure asphaltene, and the critical properties of asphaltene were adjusted. Experimental data were used to examine the proposed procedure in an Iranian crude oil reservoir. We determined the critical properties of asphaltene for this EOS using a two-phase vapor–liquid equilibrium calculation. The test results showed that the proposed procedure is adequate for predicting asphaltene precipitation data.

Vapor–Liquid Equilibria in the Low-Temperature Fischer–Tropsch Synthesis

The design and the performances of reactors for the low-temperature Fischer–Tropsch synthesis may be strongly affected by the presence of a liquid phase creating a boundary layer around the catalyst pellets and filling their pores. Accordingly, it is of the utmost importance to be able to compute the yield of liquid products formed during the reaction. In this paper, such a problem has been faced through the joint use of a detailed mechanistic kinetic model, able to predict the product yields as a function of the process conditions, and of a nonideal isothermal and isobaric vapor–liquid equilibrium calculation. It has been found that when a representative cobalt-based catalyst is operated at the typical low-temperature Fischer–Tropsch synthesis process conditions, more than 99 mol % of the hydrocarbon products are in the vapor phase. In particular, C20– species are almost entirely vapor, C31+ species are almost entirely liquid, while C21–C30 species are split between the two phases. The precise prediction...

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 minimum miscibility pressure in oil reservoirs using a modified SAFT equation of state

In a miscible gas flooding to heavy oil reservoirs, multiple-contact miscibility between injected gas and reservoir oil can be achieved at pressure greater than a minimum value that is referred to Minimum Miscibility Pressure (MMP). This research includes two parts: first, modification of simplified SAFT (mSSAFT) equation of state is derived to describe vapor-liquid equilibrium calculations and second, prediction of MMP according to forward multiple contact model is done. With respect to objective function, adjustable parameters of SSAFT and mSSAFT were obtained for 21 pure compounds. Comparison of AAD% of the results of mSSAFT, SSAFT and PR EOSs in predicting vapor pressure, liquid density and enthalpy shows that mSSAFT is the most accurate of all. Also, accuracy of these three EOSs for various mixtures has been verified, and the results confirm the reliability of mSSAFT EOS. At last, AAD% of MMP prediction by mentioned EOSs (mSSAFT is 2.20%, SSAFT is 3.25% and PR is 4.13%) proves that Statistical EOSs are more reliable than cubic EOS in modeling MMP.

Vapor-Liquid Equilibrium Calculation of Multi-Components System with Estimation of Pre-Heat Temperature

Vapor-Liquid Equilibrium Calculation of Multi-Components System with Estimation of Pre-Heat Temperature

Solids Modelling and Capture Simulation of Piperazine in Potassium Solvents

Piperazine is an amine which is used both as an activator or promoter, but also as active component in CO2 capture solvents. High concentrations are being formulated to draw benefit of the PZ properties. This results in a risk of precipitation of PZ and other solid phases during capture. It could be a benefit to the capture process, but it could also result in unforeseen situations of potential hazardous operation, clogging, equipment failure etc.Security of the PZ process needs to be in focus. Flow assurance requires additional attention, especially due to the precipitation phenomenon. This entails all parts of the streams, but also during formulation and transport of the solvent.In this work the extended UNIQUAC thermodynamic model is presented with the addition of piperazine (PZ or PIPH2) in combination with the potassium ion of mixtures with CO2 in equilibration with KOH-KHCO3-K2CO3. Phase boundaries are laid out which shows the concentration regions of solid formation. A special focus will be given to the boundary where precipitations occur.The model is a generic. It builds on consistent parameters of the extended UNIQUAC model previously published. It allows for accurate vapor liquid equilibrium (VLE) calculation, heat capacity determination, and similar thermodynamic properties. It especially allows for determination of solid liquid equilibria (SLE) and heat of absorption/heat of desorption which are core variables in the determination of energy requirements for CO2 capture. In this work the typical phase behavior will be shown for the PZ solvent with potassium (K2CO3/KHCO3) for CO2 capture. Conclusions are given on a solvent compositions resulting in low heat requirements using the predictive nature of the extended UNIQUAC model. Concentration of a PZ/K2CO3 solvent is suggested with a heat of absorption/desorption of 40kJ/mol.

Calculating the product yields and the vapor–liquid equilibrium in the low-temperature Fischer–Tropsch synthesis

The ultimate goal of this paper is the assessment of the yield of liquid hydrocarbons formed in the low-temperature Fischer–Tropsch synthesis over a representative cobalt-based catalyst at relevant process conditions. To achieve this goal, a set of steady-state Fischer–Tropsch runs has been carried out in a lab-scale reactor loaded with a 20wt.% Co/Al2O3 catalyst, investigating the effects of the main process conditions (temperature, H2/CO inlet ratio, content of inert gas in the feed, syngas space velocity) on the reactants conversion and on the C1–C50 product selectivity. Then, a CO conversion kinetic model and a product distribution model have been developed and have been jointly adopted to describe the product yields in the reactor as a function of the process conditions. Product yields have been finally used as input for an isothermal and isobaric non-ideal vapor–liquid equilibrium calculation. It has been found that, at the typical low-temperature Fischer–Tropsch synthesis process conditions, more than 95mol.% of the C1–C30 hydrocarbons, that in general represent more than 99mol.% of the hydrocarbon products, are in the vapor phase.

A Modified van der Waals Mixture Theory for Associating Fluids: Application to Ternary Aqueous Mixtures

In this study a simple and general chemical association theory is introduced. The concept of infinite equilibrium model is re-examined and true mole fractions of associated species are calculated. The theory is applied to derive the distribution function of associated species. As a severe test the application of presented theory to the van der Waals mixture model is introduced in order to perform Vapor-Liquid Equilibrium (VLE) calculations of aqueous ternary mixtures. The calculations are shown to be consistently improving the prediction over the non-associating case. Also, well known empirical models of NRTL and UNIQUAC are applied on the studied systems and their results are compared with proposed model.

A simple, reliable and fast algorithm for the simulation of multicomponent distillation columns

This work has developed a simple, reliable and fast algorithm for the simulation of multicomponent distillation columns, where any equilibrium stage can accept a feed-stream and/or a vapor-side-stream and/or liquid-side-stream. The new scheme considers internal molar overflows and constant relative volatilities to avoid the need of heat balances and vapor–liquid equilibrium calculations. The solution scheme is founded on a Newton-based formulation in block algebra, which relies in a simple, reliable and fast algorithm. Although the proposed calculation scheme can be classified as an approximate method, it is very useful when accurate phase equilibrium and enthalpy data are lacking. Numerical experimentations show good agreement with the results obtained with well-known rigorous simulation approaches.

Isobaric Vapor–Liquid Equilibrium of the Mixture of Methyl Palmitate and Methyl Stearate at 0.1 kPa, 1 kPa, 5 kPa, and 10 kPa

Isobaric vapor–liquid equilibrium (VLE) data of the mixture of methyl palmitate and methyl stearate at 0.1 kPa, 1 kPa, 5 kPa, and 10 kPa were measured with a modified Othmer still. Methyl palmitate and methyl stearate were the major components of the biodiesel. The experimental results were correlated with Wilson and nonrandom two-liquid (NRTL) activity coefficient models and were compared with a group contribution model (UNIFAC). The binary interaction parameters of the Wilson and NRTL models were fitted into the experimental data which were obtained at different pressures. The UNIFAC model did not predict the VLE for methyl palmitate and methyl stearate at reduced pressures well. The Wilson and NRTL models could well correlate with the experimental data at 1 kPa, 5 kPa, and 10 kPa. However, for the lower pressure 0.1 kPa, the Wilson model and NRTL model had worse correlatations with our experimental data than the higher pressures. These models could develop VLE calculations of the mixtures and provide guidelines for the separation of components by vacuum distillation.

Application of the kinetic Monte Carlo method in the microscopic description of argon adsorption on graphite

We present an application of kinetic Monte Carlo (kMC) in the canonical ensemble to a calculation of vapour liquid equilibrium and to describe the adsorption of argon on a flat graphite surface and in a slit-like graphitic pore. Simulations at 77 and 87.3 K accurately describe the experimental data. The kMC method is simple to implement and, unlike conventional Monte Carlo, no rejection trials are necessary. The only move is a uniform sampling of the volume space, which makes the determination of the chemical potential straightforward using real particles in the simulation, in the same spirit as the Widom inverse potential distribution. This avoids the need to freeze the real particles before the trial insertion of test particles as is necessary in other methods, such as the Widom method and its variants.

Modeling CO2 Solubility in Aqueous N-methyldiethanolamine Solution by Electrolyte Modified Peng–Robinson Plus Association Equation of State

In the present work, the electrolyte equation of state proposed by Huttenhuis et al. [Fluid Phase Equilibria2008, 264, 99–112] is improved to describe the solubility of carbon dioxide in aqueous solutions of N-methyldiethanolamine (MDEA) in wide ranges of concentration, pressure, temperature, and acid gas loading. The molecular part of the equation is based on the modified Peng–Robinson Plus Association equation of state (mPR-CPA EoS) proposed by Zoghi et al. [J. Pet. Sci. Eng.2011, 78, 109–118]. To account for the presence of ions, three contributions are added to the mPR-CPA EoS to describe short-range interactions, long-range interactions, and the Born term. The same EoS is used for both vapor and liquid phases. A consistent database including 567 experimental data points is utilized in this study. In the first step of modeling the parameters of the EoS have been tuned by regression to the vapor pressure and saturated liquid density experimental data for associating pure components (i.e., water and MDEA). In the next step, the vapor–liquid equilibrium calculations were carried out for adjusting the molecular binary interaction parameters. These parameters are optimized for binary subsystems including H2O–CO2, CO2–MDEA, and H2O–MDEA. Finally, the binary interaction parameters between ionic and molecular species are tuned via the simultaneous vapor–liquid and chemical reaction equilibrium calculations. The results show that the proposed model is able to improve the precision of prediction of the solubility of CO2 in aqueous MDEA solution by more than 6.7% in comparison with that of Huttenhuis et al. [Fluid Phase Equilibria2008, 264, 99–112] in a wide range of pressures, temperatures, acid gas loadings, and aqueous MDEA concentrations.

Predicting the vapor–liquid equilibrium of hydrocarbon binary mixtures and polymer solutions using predetermined pure component parameters

In our previous work, a new close-packed lattice model was developed for multi-component system of chain fluids with taking the chain length dependence from Monte-Carlo (MC) simulation results into account. In this work, we further extend this model to describe pressure, volume and temperature (PVT) properties, such as vapor–liquid equilibrium (VLE). To consider the effect of pressure on the phase behavior, the volume change effect is taken into account by introducing holes into the incompressible lattice model with two mixing steps. The corresponding new lattice fluid equation of state (LF-EoS) is applied to predict the thermodynamic properties of pure and binary mixtures of hydrocarbons as well as pure polymer solutions. The results of the proposed model are compared to other predictive approaches based on VLE calculations using predetermined pure model parameters without further adjustment. Thermodynamic properties predicted using the method developed in this work are consistent with the experimental data.