Vapor-liquid Equilibrium Calculations Research Articles

Simulation research on absorption refrigeration system based on NH3-H2O-LiBr vapor-liquid equilibrium calculation model

In order to investigate the NH3+H2O+LiBr (lithium bromide) absorption refrigeration cycle process and to simulate it accurately, a vapor-liquid equilibrium calculation model was proposed to obtain thermodynamic characteristic data of the ternary mixtures. The calculation of parameters of liquid phase is based on Wilson?s equation and non-random two liquid equation. The vapor phase, assumed to consist of NH3 and H2O only, is described by The Redlich-Kwong Equation of State. The data of the equilibrium vapor pressure and the NH3 concentration in liquid phase calculated by this model was compared with the experimental data, the difference is between 0.5% to 9.6% within the temperature range from 303 K to 425 K. The COP obtained by the simulation matches with that obtained by experiment and the absolute deviation is less than 0.02. Therefore, this calculation model can be used for simulation to extend the temperature range and pressure range of the system, so as to determine the design parameters of the absorption refrigeration system. The simulation results indicates that under different working conditions, the optimal generator temperature and concentration of adding LiBr can be selected, to which the theoretical explanations were given in this paper.

Calculation of thermodynamic properties of mixtures in two-phase equilibrium

Thermodynamic properties of mixtures in vapor-liquid equilibrium (VLE) were studied. Thermodynamic properties of the methane-ethane mixtures in VLE were calculated with highly accurate Helmholtz free energy equation of state GERG-2008, simplified GERG-2008 and common cubic PR equation of state (EOS). Results show that GERG-2008 has high accuracy in VLE calculations. However, simplified GERG-2008 and PR-EOS both work unsatisfactorily in VLE calculations.

Thermodynamic Property Calculation in Vapor-Liquid Equilibrium for Multicomponent Mixtures using Highly Accurate Helmholtz Free Energy Equation of State

Thermodynamic properties of multicomponent mixtures in phase equilibrium were studied. The tangent plane criterion was used for stability analysis, and the Gibbs energy minimization was employed for phase equilibrium calculation when the successive substitution didn't converge. Thermodynamic properties of a 12-component natural gas mixture in vapor-liquid equilibrium were calculated with highly accurate Helmholtz free energy equation of state GERG--2008, simplified GERG--2008 and common cubic Peng --- Robinson (PR) equation of state. Results show that in vapor-liquid equilibrium, GERG--2008 has high accuracy and works better than simplified GERG--2008 and PR-equation of state. Simplified GERG--2008 and PR-equation of state both work unsatisfactorily in vapor-liquid equilibrium calculation, especially near the saturation zone. The deviation function in GERG--2008 can significantly affect the accuracy of GERG--2008 when calculating thermodynamic properties of mixtures in vapor-liquid equilibrium

Calculation of vapor-liquid equilibrium of binary precious metal alloys using modified molecular interaction volume model

In this work, the activities and activity coefficients of binary precious metal alloys (Ag-Pb, Ag-Sb, Ag-Bi, Au-Pb, Pd-Pb, Pt-Pb and Cu-Pb) were predicted using molecular interaction volume model (MIVM), modified MIVM (M-MIVM), Wilson equation and nonrandom two-liquid (NRTL) model. The average standard deviation and average relative deviations of these models were also calculated. The results show that the prediction deviations of the M-MIVM were smallest among the four thermodynamic models, indicating that the M-MIVM is reliable. On this premise, the separation coefficient and vapor-liquid equilibrium (VLE) data of Ag-Pb, Au-Pb, Pd-Pb and Pt-Pb were calculated based on the M-MIVM. The results show that the separation coefficients were much larger than one, indicating that these alloys can be easily separated by vacuum distillation. There is good agreement between the predicted and experiment VLE data, indicating that M-MIVM is reliable for the VLE calculation in vacuum distillation. The VLE phase diagrams procured in this work can afford theoretical guidance for experimental design and industrial production in vacuum distillation.

Isobaric vapor–liquid equilibria and distillation process design for separating ketones in biomass pyrolysis oil

Biomass pyrolysis oil is a renewable resource and some of compounds (such as ketones, phenols and furans) in biomass pyrolysis oil are very useful compounds that can be used as raw materials for production of fine chemicals. Vapor-liquid equilibrium (VLE) data are critical and fundamental for designing distillation separation process. The VLE experiment and calculation of ketone-related binary systems (2-butanone + cyclopentanone, 2,3-butanedione + cyclopentanone) at atmospheric pressure are studied in this work. Binary interaction parameters of activity coefficient models (NRTL, Wilson and UNIQUAC) are obtained by correlating VLE experimental data. The new group CH2COCH2 is defined and the new group interaction parameters are presented and used to predict VLE data by UNIFAC-DMD model. The distillation separation process of ketones is designed and simulated based on VLE results. This work will provide theoretical basis and technical guidance for industrial separation process of biomass pyrolysis oil.

Laboratory‐scale liquefiers for natural gas: A design and assessment study

AbstractExact knowledge of natural gas composition is essential in custody transfer to determine the energy content of the delivery. However, for liquefied natural gas (LNG), a reliable composition determination is difficult. Here, we describe the design of a laboratory‐scale reference liquefier that enables the validation and calibration of optical spectroscopy sensors by providing them with a sample of metrologically traceable composition. Hence, it is crucial to avoid fractionation of the sample during liquefaction. This is realized by supercritical liquefaction of a reference gas mixture in conjunction with a special vapor–liquid‐equilibrium (VLE) cell. As this is a demanding high‐pressure application, low‐pressure condensation as liquefaction method was also assessed. Through experimental investigations and VLE calculations, preservation of the composition of the produced liquid sample during condensation was studied. We conclude that under optimized conditions, validation, and calibration measurements of optical sensors can be performed on condensed liquids, which, however, needs further confirmation.

Preferential cavitation and friction-induced heating of multi-component Diesel fuel surrogates up to 450MPa

The present work investigates the formation and development of cavitation of a multicomponent Diesel fuel surrogate discharging from a high-pressure fuel injector operating in the range of injection pressures from 60MPa to 450MPa. The compressible form of the Navier-Stokes equations is numerically solved with a density-based solver employing the homogeneous mixture model for accounting the presence of liquid and vapour phases, while turbulence is resolved using a Large Eddy Simulation approximation. Simulations are performed on a tapered heavy-duty Diesel engine injector at a nominal fully-open needle valve lift of 350μm. To account for the effect of extreme fuel pressurisation, two approaches have been followed: (i) a barotropic evolution of density as function of pressure, where thermal effects are not considered and (ii) the inclusion of wall friction-induced and pressurisation thermal effects by solving the energy conservation equation. The PC-SAFT equation of state is utilised to derive thermodynamic property tables for an eight-component surrogate based on a grade no.2 Diesel emissions-certification fuel as function of pressure, temperature, and fuel vapour volume fraction. Moreover, the preferential cavitation of the fuel components within the injector's hole is predicted by Vapour-Liquid Equilibrium calculations; lighter fuel components are found to cavitate to a greater extent than heavier ones. Results indicate a significant increase of temperature with increasing pressures due to friction-induced heating, leading to a significant increase in the mean vapour pressure of the fuel and an increase of the mass of fuel cavitating, but at the same time to an unprecedented decrease of cavitation volume inside the fuel injector with increasing injection pressure. This has been attributed to the shift of the pressure drop from the feed to the back pressure inside the injection hole orifice as fuel discharges; as injection pressure increases, so does the pressure inside the orifice, confining the location of cavitation formation to a smaller volume attached to the upper part of orifice, thus restricting cavitation growth.

Vapour-liquid equilibrium for mixed-solvent - strong electrolytes mixtures with EoS/GE models

In this work, the ϕ-ϕ approach is used to describe the behaviour of vapour-liquid equilibrium of mixed-solvent electrolyte solutions by means of EoS/GE type models. The approach in this article consists in the inclusion of activity coefficient information in the Peng-Robinson equation of state through three different mixing rules: Heidemann-Kokal (HK), LCVM (Linear Combination of Vidal and Michelsen) and Wong-Sandler (WS). The significance of the inclusion of an electrostatic term, from the Debye-Hückel Theory, is also evaluated. An extensive database, containing 57 mixed-solvent-strong electrolyte solutions, is revisited and a parameter estimation strategy proper to be applied in large data sets is proposed. As result, it is shown that this type of model is very successful in the vapour-liquid equilibrium calculations for salt concentrations up to 13 molal, and that the electrostatic term has little significance in this application when the UNIQUAC parameters are re-adjusted.

Surrogate modelling of VLE: Integrating machine learning with thermodynamic constraints

An easy-to-implement methodology to develop accurate, fast and thermodynamically consistent surrogate machine learning (ML) models for multicomponent phase equilibria is proposed. The methodology is successfully applied to predict the vapour-liquid equilibrium (VLE) behavior of a mixture containing CO2, monoethanolamine (MEA), and water (H2O). The accuracy of the surrogate model predictions of VLE for this system is found to be satisfactory as the results provide an average absolute relative difference of 0.50% compared to the estimates obtained with a rigorous thermodynamic model (eNRTL + Peng-Robinson).It is further demonstrated that the integration of Gibbs phase rule and physical constraints into the development of the ML models is necessary, as it ensures that the models comply with fundamental thermodynamic relationships.Finally, it is shown that the speed of ML based surrogate models can be ~10 times faster than interpolation methods and ~1000 times faster than rigorous VLE calculations.

Application of ePC_SAFT-MB EoS in prediction of VLE for CO2+MDEA+H2O ternary and H2O+MDEA+CO2-CH4 quaternary mixtures

The present study aims to implement an electrolyte EoS developed in our previous work [A. Raeispour Shirazi, M. N. Lotfollahi, Fluid Phase Equilib., 502 (2019) 112289] to model the vapor-liquid equilibria (VLE) of CO2 solubility in aqueous N-methyldiethanolamine (MDEA) solution (CO2+MDEA+H2O ternary mixture) as well as H2O+MDEA+CO2-CH4 quaternary mixture. The proposed electrolyte PC-SAFT+MSA+Born equation of state ((ePC_SAFT-MB) consists of PC-SAFT equation of state, the mean spherical approximation (MSA) term and the Born term. First, an appropriate association scheme for water is specified via performing VLE calculations for H2O-CO2 binary mixture and without any adjustment in binary interaction parameter (BIP). By determining the proper association scheme for water (4C), the BIPs of H2O-CO2, MDEA-CH4 and CH4-H2O binary mixtures are adjusted with binary VLE experimental data. In what follows, the nonelectrolyte PC-SAFT EoS is applied considering the obtained BIPs to predict 162 selected data points of bubble pressure for H2O-MDEA-CO2 ternary system in a wide range of temperature (298-413 K), MDEA concentration (18.7-48.8 wt.%) and CO2 loading (0.0001-1.5). The average absolute relative deviation (AAD%) for the calculation results is obtained 25.9%. In order to consider the ions interactions in the solution and to improve the precision of calculations, Born and MSA contributions are added to PC-SAFT EoS. By adjusting two BIPs (kMDEAH+−−CO2and kMDEAH+−HCO3−) and without any readjustment of other BIPs, the AAD% is obtained 15.3%. Finally, the obtained BIPs between the molecular and ionic species for proposed ePC_SAFT-MB EoS are employed to predict the VLE of H2O-MDEA-CO2-CH4 quaternary mixture without any readjustment in BIPs. For this case, the AAD% of 28.05% indicates the reliability of proposed ePC_SAFT-MB EoS for the prediction of H2O-MDEA-CO2-CH4 quaternary VLE results.

Coupling of Fischer-Tropsch reaction kinetics, enhanced vapor–liquid flash calculation and residence time distribution modeling for time-dependent product determination in load-flexible plants

Fischer-Tropsch synthesis may be a solution for converting volatile renewable energies into storable liquid fuel. Microstructured reactors have been proven to cope with varying operation conditions and are able to adapt to fluctuations in this circumstance. In this regard, a suitable kinetic model for chemical synthesis is essential for the prediction of reactor and catalyst behavior. The assessment and description of the reactor and plant response during dynamic operation must also be considered to develop a control system for varying operating conditions. In this work, a time-resolved model for the description of relevant processes inside a pilot scale microstructured Fischer-Tropsch reactor and the associated test rig including the product condensation stages is presented. A residence time distribution model describes flow and mixing behavior for all system components. Time and temperature-dependent product concentration in the product traps is determined by vapor–liquid-equilibrium calculation. Phase equilibria models with ideal and real phase behavior assumptions are compared. A micro-kinetic model was adapted with good agreement to a variety of experimental data. When coupled, the overall model is able to predict time-resolved product characteristics based on process conditions and feed only. This mathematical description may be of use for decentralized plants in the future.

Phase-Behavior Modeling of Hydrocarbon Fluids in Nanopores Using PR-EOS Coupled with a Modified Young-Laplace Equation.

The effect of capillary pressure on the vapor–liquid two-phase equilibrium calculation has been extensively studied for the past two decades. However, the calculation accuracy is often weakened by the false assumptions and inherent flaws present in the modeling process. In this work, a modified Young–Laplace equation proposed by Tan and Piri [Tan, S.; Piri, M. Equation-of-State Modeling of Confined-Fluid Phase Equilibria in Nanopores. Fluid Phase Equilibr. 2015,393, 48–63.] is coupled with volume-translated Peng–Robinson equation of state to study the effect of capillary pressure on the two-phase equilibrium calculation in confined nanopores. In order to successfully apply the modified Young–Laplace equation during the vapor–liquid equilibrium calculation process, this study models the tuning parameter λ in the modified Young–Laplace equation (as proposed by Tan and Piri for perturbed-chain statistical associating fluid theory equation of state) for several pure hydrocarbons and their mixtures by matching experimental data collected from the literature. The tuning parameter λ can be expressed as a unique function for each pure substance or mixture. It is found that the tuning parameter λ shows a quadratic polynomial relationship with temperature, and the value of λ is always less than one. The λ can become negative under certain circumstances, which adjusts the capillary pressure to a lower value. It increases with an increasing pore radius; this is different from the results obtained by Tan and Piri which showed that the tuning parameter λ decreases with an increasing pore radius. The above rules apply to the tuning parameter λ obtained for both pure substances and mixtures. Using the two-phase equilibrium calculation coupled with the modified Young–Laplace equation, the calculated vapor pressures for pure substances and two-phase boundaries for mixtures match very well with the experimental data. Implementation of the modified Young–Laplace equation greatly improves the accuracy of the two-phase equilibrium calculation considering the capillarity effect. Such a modeling strategy could be integrated into a reservoir simulator to conduct more accurate flow simulations for tight/shale reservoirs.

Vapor-liquid equilibrium calculations at specified composition, density and temperature with the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state

In this study, the PC-SAFT equation of state is used for vapor-liquid equilibrium calculations using as independent variables the mixture composition, density and temperature. The method is based on unconstrained minimisation of the Helmholtz Free energy via a combination of the successive substitution iteration and Newton-Raphson minimisation methods with line-search; the positive definiteness of the Hessian is guaranteed by a modified Cholesky decomposition. The algorithm consists of two stages; initially, the mixture is assumed to be a single-phase and its stability is assessed; in case of being found unstable, a second stage of phase splitting (flash) takes place, in which the pressure of the fluid and compositions of both the liquid and vapor phases are calculated. The reliability of two different methods presented in the existing literature, (i) using mole numbers and (ii) using the logarithm of the equilibrium constants as iterative variables, is evaluated in terms of both iterations and computational time needed to reach convergence, for seven test cases. These include both single and multicomponent Diesel fuel surrogates, known to give incomplete density information when using pressure and temperature as independent variables. Results show that iterating with the logarithm of the equilibrium constants also reproduces this issue, while it requires a smaller number of iterations than using with mole numbers as independent variables. However, the total computational time needed for the latter case is vastly inferior. Pressure and vapor volume fraction fields are discussed for a range of temperatures and densities, apart from the number of iterations needed during the flash calculation stage. A performance comparison is obtained against the Peng-Robinson equation of state, showing similar number of iterations required but a computational time increasing with the number of components. While for a single component PC-SAFT needs around 3 times more CPU time, for 4 components it is 6 times and for a mixture of 8 components it increases up to 14 times. Finally, the method is demonstrated to converge unconditionally for all conditions tested.

Modeling of H2S, CO2 + H2S, and CH4 + CO2 Solubilities in Aqueous Monoethanolamine and Methyldiethanolamine Solutions

The extended UMR-PRU (eUMR-PRU) model is used in this work to describe the solubilities of H2S and mixed acid gases (H2S + CO2) in aqueous monoethanolamine (MEA) and methyldiethanolamine (MDEA) solutions. Moreover, the effect of methane on the solubility of CO2 in aqueous MDEA solutions is examined. For the chemical equilibrium description, the equations of the mole fraction-based equilibrium constants are solved simultaneously with mass balance and electroneutrality equations. For the vapor–liquid equilibrium calculations, the eUMR-PRU model is applied after the determination of the missing interaction parameters. The eUMR-PRU model is compared to other widely used models, namely, the Kent–Eisenberg model and the electrolyte NRTL model. It is shown that the eUMR-PRU results are in satisfactory agreement with the experimental data and similar to those obtained by other models.

Comparison of MOSCED (NRTL) model results with regular correlative and predictive models based on vapor-liquid equilibrium calculations for azeotropic systems

The Modified Separation of Cohesive Energy Density (MOSCED) model is an attractive and accurate engineering tool for process design and modeling. MOSCED is able to make qualitative as well as precise quantitative predictions of principal molecular-level interactions. However, the capability of this model in predicting Vapor-Liquid Equilibrium (VLE) of different azeotropic systems has not yet been fully assessed, when compared with the conventional methods. In this study, the ability of MOSCED model to predict the binary interaction parameters of NRTL model has been evaluated by comparing the obtained isobaric phase diagrams of the experimental sets of data for 11 binary isobaric systems. In order to better evaluate the performance of MOSCED model, the same calculations were performed via correlative (Wilson and NRTL) and predictive (UNIFAC) models. The values of statistical parameters have demonstrated acceptable predictions for the studied systems. Overall, the MOSCED model has provided an Average Absolute Relative Deviation(s) (AARD %) of 0.1978% and 4.3239% for temperature and K-value, respectively; which illustrate excellent performance of this model in spite of no dependence on experimental data, which is a big advantage over other methods.

Change in hydrocarbon composition in rock samples as a function of time: A thermodynamic evaporation model

Recent pyrolysis analytical methods such as Shale Play (Romero-Sarmiento et al. 2016), HAWK-PAM (Maende et al., 2017) and Incremental S1 (Beti et al., 2018) enable improved understanding of the quantity and quality of free petroleum present in rock samples. However, it is well established that the evaporation losses restrict the ability of an experiment to accurately quantify and qualify free petroleum in rock sample (Michael et al., 2013; Jiang et al., 2016; Li et al. 2020). This article presents a thermodynamic model to explain the change in hydrocarbons composition of rock samples residing in a laboratory as a function of time. The model involves multicomponent residue curves and vapor-liquid equilibrium calculations. The changes in hydrocarbon composition predicted using models were compared with experimental data obtained from thermal desorption-gas chromatography (TD-GC) analysis of rock samples. High correlation coefficients are observed between predicted compositions and the experimental data inferring a good model fidelity. Relatively higher deviations were also observed between experimental data and predicted composition with time. The proposed model is useful in complementing the experimental results and enhancing the fundamental understanding of hydrocarbon loss from rock samples. This model also has the potential to eliminate multiple experiments to estimate the compositions after hours of sample collections.

Thermodynamic modeling for the carbonate system K-HCO3-CO3 in alkanolamine solutions: An extended application for CO2 scrubbing

The K2CO3 slurry-based, CO2 absorption technology in amines involves in-depth analysis of chemical equilibrium for all three phases. However, the reported studies regarding solubility and thermodynamics modeling of the solid-liquid system: K-CO3-HCO3 in alkanolamine solutions are limited. We first performed vapor-liquid equilibrium calculation to study the absorption profile of CO2 in monoethanolamine (MEA) /diethanolamine (DEA) solutions using OLI Studio Stream Analyzer, results were in good agreement with literature data. We further applied the dissolution method to measure the solubility of K2CO3 and KHCO3 in the aqueous alkanolamine solution from 283 to 353 K, P = 0.1 MPa. A chemical model was developed for the purpose of conducting thermodynamic analysis by the regression of solubility data via the mixed-solvent-electrolyte, activity coefficient model. The relative deviations are within 5% for each solid-liquid system after reparameterization. Tuning the newly-regressed parameters allowed for a better prediction of solubility, they also come vital in evaluating the absorption performance of CO2 in quaternary systems, which are made available to aid in process modeling.

Complex multicomponent real-fluid thermodynamic model for high-pressure Diesel fuel injection

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) has been coupled with Vapor-Liquid Equilibrium (VLE) calculations in a density-based solver of the Navier-Stokes equations to perform multicomponent two-phase simulations of Diesel injections at high-pressure conditions. This molecular-based EoS requires three empirically determined but well-known parameters to model the properties of a specific component, and thus, there is no need for extensive model calibration, as is typically the case when the NIST (REFPROP) library is utilised. PC-SAFT can handle flexibly the thermodynamic properties of multi-component mixtures for which the NIST (REFPROP) library supports only limited component combinations. Moreover, complex hydrocarbon mixtures can be modelled as a single pseudo-component knowing its number averaged molecular weight (MW) and hydrogen-to-carbon (HN/CN) ratio. Published molecular dynamic simulations have been utilised to demonstrate that the developed algorithm properly captures the VLE interface at high-pressure conditions. Several advection test cases and shock tube problems were performed to validate the numerical framework using analytical and exact solutions. Additionally, two-dimensional simulations of n-dodecane and Diesel injections into nitrogen are included to demonstrate the multidimensional, multispecies and multiphase capability of the numerical framework.

Five-Lump Mild Thermal Cracking Reaction Model of Crude Oils and Bitumen with VLE Calculations

Thermal cracking involves the breakdown of large hydrocarbons to smaller hydrocarbons via the scission of carbon–carbon, carbon–nitrogen, and carbon–sulfur bonds. Mild thermal cracking reactions occur between 350 and 450 °C and primarily in the liquid phase. A reaction model implementing vapor–liquid equilibrium (VLE) calculations was developed in this work to better represent the reacting system–the liquid phase. The resulting model can be used to determine reaction kinetics in experimental systems that have a VLE component, which would normally make it inadequate for reaction kinetics determination. A mild thermal cracking experimental program was conducted with three crude assays: Hardisty (MBL), Albian heavy synthetic (AHS), and Christina Lake diluted bitumen (CDB). The experiments were conducted in a pilot-scale semibatch vertical reactor with a sweeping nitrogen gas blanket in the head space. The three crude oils were reacted at mild conditions: 350, 400, 425, and 450 °C at 1.24 MPa(a). The reaction...

Study on Particle Swarm Optimization Variant and Simulated Annealing in Vapor Liquid Equilibrium Calculation

Phase equilibrium calculation plays a major rule in optimization of separation process in chemical processing. Phase equilibrium calculation is still very challenging due to highly nonlinear and non-convex of mathematical models. Recently, stochastic optimization method has been widely used to solve those problems. One of the promising stochastic methods is Particle Swarm Optimization (PSO) due to its simplicity and robustness. This study presents the capability of particle swarm optimization for correlating isothermal vapor liquid equilibrium data of water with methanol and ethanol system by optimizing Wilson, Non-Random Two Liquids (NRTL), and Universal Quasi Chemical (UNIQUAC) activity coefficient model and also presents the comparison with bare-bones PSO (BBPSO) and simulated annealing (SA). Those three optimization methods were successfully tested and validated to model vapor liquid equilibrium calculation and were successfully applied to correlate vapor liquid equilibrium data for those types of systems with deviation less than 2%. In addition, BBPSO shows a consistency result and faster convergence among those three optimization methods. Keywords: Phase equilibrium, stochastic method, particle swarm optimization, simulated annealing and activity coefficient model