Vapor-liquid Equilibrium Calculations Research Articles

Solvent effects on high-pressure hydrogen gas generation by dehydrogenation of formic acid using ruthenium complexes

High-pressure H2 was produced by the selective dehydrogenation of formic acid (DFA) using ruthenium complexes at mild temperatures in various organic solvents and water. Among the solvents studied, 1,4-dioxane was the best candidate for this reaction to generate high gas pressure of 20 MPa at 80 °C using the Ru complex having a dearomatized pyridine-based pincer PN3P* ligand. This complex shows reusability for the high-pressure DFA in 1,4-dioxiane while maintaining the catalytic performance, however, deactivation occurred in other solvents. In dimethyl sulfoxide, its decomposition products may cause catalytic deactivation. The gas pressure generated in 1,4-dioxane was lower than that in water due to the high dissolution of 1,4-dioxane into CO2 according the vapor-liquid equilibrium calculations. The role of solvent is crucial since it affected the catalytic performance and also the generated gas pressure (H2 and CO2) from FA.

Accelerating and stabilizing the vapor-liquid equilibrium (VLE) calculation in compositional simulation of unconventional reservoirs using deep learning based flash calculation

The flash calculation with large capillary pressure often turns out to be time-consuming and unstable. Consequently, the compositional simulation of unconventional oil/gas reservoirs, where large capillary pressure exists on the vapor-liquid phase interface due to the narrow pore channel, becomes a challenge to traditional reservoir simulation techniques. In this work, we try to resolve this issue by combining deep learning technology with reservoir simulation. We have developed a compositional simulator that is accelerated and stabilized by stochastically-trained proxy flash calculation.We first randomly generated 300,000 data samples from a standalone physical flash calculator. We have constructed a two-step neural network, in which the first step is the classify the phase condition of the system and the second step is to predict the concentration distribution among the determined phases. Each network consists of four hidden layers in between the input layer and the output layer. The network is trained by Stochastic Gradient Descent (SGD) method with 100 epochs.With given temperature, pressure, feed concentration pore radius, the trained network predicts the phases and concentration distribution in the system with very low computational cost. Our results show that the accuracy of the network is above 97% in the metric of mean absolute percentage error. The predicted result is used as the initial guess of the flash calculation module in the reservoir simulator. With the implementation of the deep learning based flash calculation module, the speed of the simulator has been effectively increased and the stability (in the manner of the ratio of convergence) has been improved as well.

Vapor-liquid (azeotropic systems) and liquid-liquid equilibrium calculations using UNIFAC and NRTL-SAC activity coefficient models

The aim of present study was to investigate some of the most important maximum and minimum azeotrope boiling temperature systems using UNIFAC and NRTL-SAC models as the predictive models. Also, the predictive power of UNIFAC, UNIFAC-LLE and NRTL-SAC models were compared in liquid-liquid equilibrium calculations. For maximum azeotrope temperature systems, except for formic acid-water, the UNIFAC model had higher degree of accuracy than the NRTL-SAC model. The NRTL-SAC model could not appropriately predict the maximum azeotrope temperature systems, in particular for acetone-chloroform, chloroform-methyl acetate, and chloroform-diethyl amine systems. For these systems, the NRTL-SAC model gave a minimum azeotrope temperature. For the examined minimum azeotrope boiling temperature systems, the results of both models were in consistent with the experimental data, but in most cases, the results of the UNIFAC model were in good agreement with the experimental data. On the other hand, as the pressure deviated from 101.3 kPa, the deviation of both models increased. In the case of ternary VLE systems under study, UNIFAC model indicated better results than NRTL-SAC model. Totally, in most VLE systems, UNIFAC was much better than NRTL-SAC and we preferred UNIFAC model as a good candidate for VLE calculations of the studied systems. Based on the overall deviation of models for LLE calculations at all temperatures, the best representation of the system was in the following order: UNIFAC-LLE > UNIFAC > NRTL-SAC. There would appear to be a major difficulty in selecting one thermodynamic model as the best, as the choice might be system-dependent.

Salts Effect on Isobaric Vapor–Liquid Equilibrium for the Azeotropic Mixture 2-Propanol + Water

Vapor–liquid equilibrium (VLE) data for the systems 2-propanol + water + calcium chloride, 2-propanol + water + magnesium chloride, 2-propanol + water + calcium nitrate, and 2-propanol + water + magnesium nitrate were measured at the pressure of 101.3 kPa. Experimental data of all ternary systems passed the thermodynamic consistency test by modified McDermott–Ellis method. Then, the effects of salts on the vapor phase mole fraction of 2-propanol and the relative volatility of 2-propanol to water were analyzed. Results show that the azeotropic point of the system 2-propanol and water can be removed with addition of the salts, and the salting-out effects follow the order calcium nitrate > calcium chloride > magnesium nitrate > magnesium chloride. Furthermore, the LIQUAC model was adopted to correlate the VLE experimental data of the systems. The comparative results of the average relative deviation (Δz̅) and the corresponding standard deviations (σ) between the experimental and calculated values indicate that LIQUAC model is suitable for the VLE calculation for the systems of 2-propanol + water + salts.

Numerical and experimental study on keyhole and melt flow dynamics during laser welding of aluminium alloys under subatmospheric pressures

Porosity defects was highly related to the keyhole and melt flow dynamic during laser welding process. In this paper, a novel 3D numerical model was developed to describe the keyhole dynamic and melt flow behaviors during laser welding of 5A06 aluminium alloy under subatmospheric pressures. The effect of ambient pressure on laser welding process was taken into consideration by optimizing the boiling point of aluminium alloy and recoil pressure of evaporated metallic vapor jets based on vapor–liquid equilibria calculation and Wilson equation. A moving hybrid heat source model was employed to describe the laser energy distribution under subatmospheric pressures. Numerical results indicated that a wider and deeper keyhole with less humps was produced under subatmospheric pressure comparing with that of atmospheric pressure. The vortices in the rear keyhole wall became unapparent or even disappeared with the decrease of ambient pressures. The melt flow velocity on the keyhole wall was larger under a lower pressure. A smaller difference between boiling point and melting point was produced and this led to the formation of a thinner keyhole wall and improved the stability of molten pool. Larger recoil pressure produced under subatmospheric pressure was responsible for the weakened vortices and enhanced melt flow velocity. Bigger keyhole opening size, larger melt flow velocity, thinner keyhole and the weakened vortices all resulted into the reduction of porosity defects during laser welding of aluminium alloys. Based on the simulation results, the plasma distribution, weld formation and porosity defects had been demonstrated. The compared results showed that the simulation results exhibited good agreements with the experimental ones.

Performance analyses on four configurations of natural gas liquefaction process operating with mixed refrigerants and a rectifying column

Natural gas (NG) fields of low pressure and small reserve are usually located remotely and dispersedly in China, for which pipeline transport in gaseous state is not economic. As a result, liquefying natural gas with small-scale liquefiers is a more preferable choice. In this paper, four configurations of natural gas liquefaction process (NGLP) operating with mixed refrigerants (MRs) and a rectifying column were proposed. The mixture was composed of R728, R50, R1150, R290 and R600a. In the rectifying column, the volatile and less volatile components of the MR were better separated, and the entrained lubricating oil of the compressor was trapped, thus avoiding blockage in the low temperature section. Simulations were conducted for these configurations using modified PT equation and Virial mixing rule in vapor-liquid equilibrium (VLE) calculation of MR. The influences of operating pressures, refrigerant composition and process configuration on system performance indicators, such as specific power consumption (SPC) and discharge temperature, were detailly investigated. It was found by simulation that SPC first decreases and then increases with the decrease of suction pressure in all configurations, while the minimum is achieved at around 250 kPa. The simulation results also suggested keeping the molar fraction of R600a the highest among the components, and increasing the molar fractions of R50 and R728 as much as possible provided that the compressor discharge temperature does not exceed the limit. Preliminary experiments have been conducted to compare the performances of four configurations under specified MR composition and NG flow rate.

Investigation of gas sweetening by nanofluid in isothermal tower with consideration of thermodynamic equilibrium; experimentally and theoretically

The hydrogen sulfide is a basic contaminant which is exited to atmosphere from chemical factories. The study focuses on initialization of Stefan-Maxwell equations to calculate the hydrogen sulfide removal molar flux by nanofluid in an absorption process. The sweetening process is done in a packed bed tower, isothermally. The aluminum oxide nanofluid as solvent in the role of the liquid phase is considered as a non-ideal solution. The activity coefficient for the vapor-liquid equilibrium calculation is based on molar transfer equations is proposed. No ideality within vapor phase is considered based on the modified state equation of Virial. The hydrogen sulfide removal molar flux is based on two cases of film theorem and KGa calculation are investigated in this paper. Results show increasing percentage of mass transfer coefficient for increasing of solvent flow rate from 2 m3/h to 3 m3/h is 71.2%. The theoretical values of hydrogen sulfide molar flux which is based on film theorem using Fick’s diffusion factor shows much deviation with experimental hydrogen sulfide molar flux. Also, H2S removal molar flux based on KGa is calculated in this research. Finally, the performance of absorber is modelled by ANN. The value of RMSE and R in this theoretical model is 0.2979 and 0.9537, respectively.

Adsorption Thicknesses of Confined Pure and Mixing Fluids in Nanopores.

In this paper, adsorption thicknesses of confined pure and mixing fluids in nanopores are quantitatively determined and their influential factors are specifically evaluated. First, a new analytical formulation is developed thermodynamically to calculate the adsorption thicknesses. Second, a new generalized equation of state (EOS), which considers the confinement effect-induced phenomena, is developed analytically for calculating the thermodynamic confined fluid phase behavior. Third, the modified model based on the generalized EOS and coupled with the parachor model is applied to calculate the vapor-liquid equilibrium (VLE) and fluid adsorptions for the pure CO2, alkanes of C1-C10, and two mixtures of CO2-C10H22 and CH4-C10H22 in nanopores. Finally, the following five important factors are studied to evaluate their effects on the adsorption thickness: temperature, pressure, pore radius, wall-effect distance, and feed gas-to-liquid ratio (FGLR). The proposed modified EOS is found to be accurate for the VLE and adsorption isotherm calculations. The adsorption thicknesses of confined pure or mixing alkanes are increased with the increasing carbon number but decreased with the temperature increase. For the alkanes of C1-C10, the degree of temperature effect is strengthened with the carbon number increase. Moreover, the adsorption thicknesses are significantly decreased with the pore radius increase until rp = 50 nm, after which they have slight changes or are even constant at any pore radii. On the other hand, the wall-effect distance (δp) increase causes the adsorption thickness to be linearly increased at δp/ rp ≥ 0.02. In addition, the effects of the FGLR and pressure on the adsorption thicknesses at the nanoscale are found to be negligible.

Modeling of CO2 solubility in aqueous alkanolamine solutions with an extended UMR-PRU model

The phase and chemical equilibria in aqueous alkanolamine solutions containing CO2 is examined in this work. The alkanolamines considered are monoethanolamine (MEA), methyldiethanolamine (MDEA), as well as blends of these two amines. For the vapor-liquid equilibrium calculations, the UMR-PRU model has been extended by incorporating the extended UNIQUAC activity coefficient model to account for the long range electrostatic interactions. The parameters of the UMR-PRU model are either taken from the literature, when available, or determined in this work through fitting vapor-liquid equilibrium experimental data. Very satisfactory results are obtained in all cases examined, which are similar or better than those obtained by other models proposed in the literature, indicating that the UMR-PRU model is able to accurately describe the phase and chemical equilibria in aqueous solutions of alkanolamines and carbon dioxide.

VAPOR-LIQUID EQUILIBRIUM CALCULATION FOR SIMULATION OF BIOETHANOL CONCENTRATION FROM SUGARCANE

ABSTRACT The robustness of the simulation of bioethanol concentration from sugarcane faces two major challenges: the presence of several minor components and the nonlinear behavior of vapor-liquid equilibrium (VLE) calculations. This work assesses the effect of simplifications to overcome these difficulties. From a set of seventeen substances, methanol, n-propanol, isobutanol, 2-methyl-1-butanol and 3-methyl-1-butanol were selected through the examination of the influence of each minor component on vapor-liquid equilibrium calculations of ethanol-water-third component systems. The selection procedure was based on Txy diagrams built using the modified Raoult's law. The influence of the ratio between the vapor phase fugacity coefficients and of the Poynting correction factor were verified. The accuracy of four correlations for vapor pressure was evaluated, and two functional-group activity coefficient models were scrutinized: the recent Functional-Segment Activity Coefficient (F-SAC) and the UNIFAC-Do model.

Predicting phase equilibrium for polymer solutions using COSMO-SAC

With the aim of predicting mixture behavior based on information of pure components only, COSMO-based models have emerged as a promising alternative. Several works in the literature are available attesting the good performance of COSMO-RS variants in several different applications. However, the extension of COSMO calculations for polymers and other macromolecules was not extensively explored. In this work, a new procedure to evaluate the parameters of the polymers repeating unit for COSMO-based models is proposed. The idea of a large polymer molecule consisting of many repeating units is employed, however, a more comprehensive analysis using oligomers of different sizes is suggested. The COSMO-SAC model with parameters from the literature was used to test the new methodology. Infinite dilution activity coefficient (IDAC) and vapor-liquid equilibrium (VLE) calculations with homopolymer and copolymer systems were performed to verify the predictive capability of the approach. The good results obtained showed the adequacy of the proposed methodology to represent IDAC and VLE data of solvent-polymer and -copylymer systems.

Vapor–Liquid Equilibrium Measurements for 2,3,3,3-Tetrafluoroprop-1-ene + Butane at Temperatures from 283.15 to 323.15 K

Vapor–liquid equilibrium (VLE) property measurements for 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) + butane (HC-600) were carried out. The range of temperature is from 283.15 to 323.15 K, and the corresponding range of pressure is from 0.148 to 1.30 MPa. The experimental uncertainties in pressure, temperature, and mole fraction are estimated within 3.5 kPa, 5 mK, and 0.003, respectively. Peng–Robinson (PR) equation of state coupling with Wong–Sandler (WS) mixing rule and van der Waals (vdW) mixing rule were used to correlate the experimental VLE data of HFO-1234yf/HC-600. Both of the two models reproduce the VLE property of HFO-1234yf/HC-600 with high accuracy, and PR–WS-NRTL model gave slightly more accurate VLE calculations. Azeotropic behavior was found at high mole fraction of HFO-1234yf.

Vapor Liquid Equilibria for Acetic Acid–Acetaldehyde–Crotonaldehyde System: Gibbs Ensemble Molecular Simulation for Pure Components and Binary Systems and NRTL Model Prediction for Ternary System

The vapor–liquid equilibrium (VLE) for the system acetic acid, acetaldehyde, and crotonaldehyde was investigated by combining the Gibbs ensemble Monte Carlo (GEMC) method and activity coefficient models prediction. The VLE of above pure components and their binary systems were first studied using GEMC method. Based on the strong association characteristics of acetic acid, the revised TraPPE-UA-D force field was developed with quantum chemistry methods for the VLE calculation of the acetic acid system. The original and mixed TraPPE-UA force field was introduced for the VLE calculation of the acetaldehyde and crotonaldehyde system, respectively. The results showed that the predictions agreed fairly well with the average relative deviations of the saturated densities smaller than 4.60%. Moreover, the binary VLE diagram was calculated using the above force fields. The simulation results of the mole composition were in good agreement with the experimental values, which verified the high simulation accuracy of ...

Reliable Flash Calculations: Part 2. Process Flowsheeting with Nonsmooth Models and Generalized Derivatives

This article presents new methods for robustly simulating process flowsheets containing nondifferentiable models, using recent advances in exact sensitivity analysis for nonsmooth functions. Among other benefits, this allows flowsheeting problems to be equipped with newly developed nonsmooth inside-out algorithms for nonideal vapor–liquid equilibrium calculations that converge reliability, even when the phase regime at the results of these calculations is unknown a priori. Furthermore, process models for inherently nonsmooth unit operations may be seamlessly integrated into process flowsheets, so long as computationally relevant generalized derivative information is computed correctly and communicated to the flowsheet convergence algorithm. These techniques may be used in either sequential-modular simulations or simulations in which the most challenging modules are solved using tailored external procedures, while the remaining flowsheet equations are solved simultaneously. This new nonsmooth flowsheeting ...

Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A

We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component subcritical two-phase states via a homogeneous mixture approach. Well-resolved LES results for the Spray A benchmark case of the Engine Combustion Network (ECN) and three additional operating conditions are found to agree very well with available experimental data. We also address well-known numerical challenges of trans- and supercritical fluid mixing and compare a fully conservative formulation to a quasi-conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi-conservative formulation on typical LES grids.

Modelling the thermodynamics of air-component mixtures (N2, O2 and Ar): Comparison and performance analysis of available models

With a view to finding which of the available equations of state is the most suitable for the representation of the thermodynamics of mixtures containing nitrogen, oxygen and argon, this paper mainly intends to address the comparison of the performance of the - already optimized - GERG-2008, Bender and Peng-Robinson (PR) Equations of State (EoS) in the calculation of Vapour-Liquid Equilibrium (VLE) and volumetric properties of N2-O2-Ar mixtures. The comparison between experimental measurements collected in the literature and model calculations has led to conclude about the overall superiority of GERG-2008. It is also shown that the Peng-Robinson EoS leads to comparable results in VLE calculations and that the use of Bender EoS should be avoided as it leads, despite its complex multiparameter formulation, to very inaccurate results in the calculation of VLE properties of the binary Ar-O2 and of volumetric properties. For completeness, the paper also shows the poor accuracy of the PR EoS in calculating VLE properties when zero-kij are selected. Moreover, the paper evaluates the impact of deviations on densities, calculated with the different equations of state, on the computation of transport properties (thermal conductivity, viscosity), in turns determined by means of correlations which are typically applied. Liquid thermal conductivity is highly affected by errors on liquid density calculations while the liquid viscosity is independent of density. Differently, errors on vapour thermal conductivity and dynamic viscosity are lower than those observed on vapour density.

Transferability of cross-interaction pair potentials: Vapor-liquid phase equilibria of n-alkane/nitrogen mixtures using the TAMie force field

The van der Waals contribution of force fields designed for calculating phase equilibria and thermodynamic properties are usually adjusted to experimental data of pure components. Using these force fields for mixtures by applying combining rules for the cross-wise interaction potentials does not always lead to satisfactory results. This study considers the cross-wise van der Waals energy parameters εαβ among individual pairs of (united-)atom groups as adjustable (but subsequently transferable) parameters. The cross-energy parameters are simultaneously adjusted to an experimental training set of several mixtures. An analytic equation of state, the Perturbed-Chain Polar Statistical Associating Fluid Theory (PCP-SAFT), is used for ensuring very swift convergence of the optimization procedure. As an example, we consider the phase equilibria of n-alkane/nitrogen mixtures. The cross-energy parameters (-CH3 to N and -CH2- to N) are adjusted to three mixtures as the training set. We explore the transferability of the so-obtained force field for varying temperatures and for mixtures that were not considered in the training set. Phase equilibria of nine n-alkane/nitrogen mixtures (each at various temperatures) are determined using Monte Carlo simulations in the grand canonical ensemble. Results for vapor-liquid equilibrium calculations show very good agreement with experimental data.

The determination of the Henry’s Coefficient of reactive gases – An example of CO2 in aqueous solutions of monoethanolamine (MEA)

The Henry’s Coefficient of CO2 is a fundamental property, it quantifies the equilibrium between the partial pressure of CO2 in the gas phase and the concentration of dissolved free CO2 in the liquid phase. This value is critical for simulation and may lead to improvements in the process of post combustion capture of CO2. However, because of its reactive nature, CO2 reacts in amine solutions and forms multiple carbon-containing species, so that the free CO2 concentration is very small and difficult to determine. The “N2O analogy” has been used to estimate the physical solubility of CO2 based on the assumption that the two gases behave similarly in water and amine solutions. In the current study, a direct way is proposed for the determination of the Henry’s Coefficient of CO2 in MEA solutions. The method only requires vapor-liquid equilibrium (VLE) measurements of the MEA-CO2-H2O system; and all equilibrium/protonation constants for all solution reactions are sourced from the open literature while activity coefficients for all ionic species were estimated using the Davis equation. The free CO2 concentration in solution can be computed using the total MEA concentration, total CO2 concentration and temperature, which allows the determination of the Henry’s Coefficient from the CO2 partial pressure. A 10-parameter polynomial is used to approximate the Henry’s Coefficient as a function of the total MEA concentration, total CO2 concentration and temperature. VLE calculations were performed using the liquid-phase equilibrium calculations and the polynomial function calculating the Henry’s Coefficient, and the results show the VLE calculations are adequate to describe the VLE data.

Application of artificial neural networks and genetic programming in vapor–liquid equilibrium of C1 to C7 alkane binary mixtures

In this study, the capacity of artificial neural networks (ANNs) and genetic programming (GP) in making possible, fast and reliable predictions of equilibrium compositions of alkane binary mixtures is investigated. A data set comprising 847 data points was gathered and used in both training the proposed ANN and generating the closed-form expressions of the GP procedure. The results obtained demonstrate the relative precision of the proposed ANN, while, on the other hand, exhibit that the GP model, although less precise, affords high CPU time efficiency and simplicity. Concisely, the proposed models can serve the purpose of being close first estimates for more thermodynamically rigorous vapor–liquid equilibrium calculation procedures and do obviate the necessity for the availability of a large set of experimental binary interaction coefficients. Mean absolute errors of 0.0100 and 0.0404 for liquid compositions and of 0.0054 and 0.0254 for vapor-phase mole fractions, for the proposed ANN and GP models, respectively, are a testament to the reliability of the proposed models.

Modeling of Asphaltene Precipitation in Calculation of Minimum Miscibility Pressure

An algorithm has been developed to investigate the effect of asphaltene precipitation on calculation of minimum miscibility pressure (MMP), which is one of the key design parameters of any gas injection projects. In fact, this algorithm is the extension of procedure suggested by Jaubert et al. for prediction of MMP whatever the displacement mechanism. The vapor–liquid equilibrium calculation and then liquid–liquid equilibrium calculation are required to be taken account to estimate the amount of asphaltene precipitation. The association equation of state (AEOS) has been applied to determine the phase behavior of asphaltene. The algorithm has been used for the MMP prediction of Weyburn reservoir oil in which the precipitation of asphaltene has been reported. The results show good agreement with those experimental data obtained by slim tube, and improved by 7.6% and 5.3% on average compared to Jaubert’s algorithm and Ahmadi’s approach, respectively.