Liquid Equilibrium Calculations Research Articles

A modified simplified SAFT EOS for VLE study of associating fluids

AbstractIn this study, the simplified version of statistical associating fluid theory (SAFT) equation of state (EOS) developed by Fu and Sandler is modified by replacing the dispersion term of this EOS with the Haghtalab–Mazloumi equation. This new SAFT‐based EOS has three adjustable parameters for non‐associating compounds and five adjustable parameters for associating compounds. The adjustable parameters of the new EOS are obtained by simultaneously fitting vapour pressures and liquid densities of pure substances. The new EOS shows better results in correlating vapour pressure and saturated liquid densities than SSAFT EOS for a selection of non‐associating and associating substances. Then, by using proper mixing rules, the new EOS is extended for mixtures. Both self‐associating and cross associating binary mixtures are used to test the capability of the new EOS in vapour–liquid equilibrium (VLE) calculations, and the results demonstrate good accuracy of the new EOS.

A Numerical Study of Vapor–Liquid Equilibrium in Binary Refrigerant Mixtures Based on 2,3,3,3-Tetrafluoroprop-1-ene

The binary refrigerant mixtures containing 2,3,3,3-Tetrafluoroprop-1-ene are considered as excellent substitutes for traditional refrigerants. Weak hydrogen bonds exist in hydrofluorocarbons and hydrofluoroolefins. However, for several recently published binary refrigerant mixtures, there is no Vapor–Liquid Equilibrium calculation study considering hydrogen-bonding associations. This work presents a calculation work of the saturated properties of nine pure refrigerants using the Cubic-Plus-Association Equation of State, considering the hydrogen-bonding association in refrigerant fluids. The average relative deviations of the saturated vapor pressure, liquid, and vapor density are less than 1.0%, 1.5%, and 3.5%, respectively. The Vapor–Liquid Equilibrium of ten binary refrigerant mixtures containing 2,3,3,3-Tetrafluoroprop-1-ene is also calculated using the Cubic-Plus-Association Equation of State with the van der Waals mixing rule. The average relative deviations of the liquid-phase and vapor-phase mole fractions are less than 1.0% and 2.0%, respectively. Moreover, the Vapor–Liquid Equilibrium data and the model’s adaptability are analyzed and discussed.

Experimental study on the effect of liquid loading on n-heptane spray jet flame stability

Flame stability significantly influences the performance of a practical combustor. The mechanisms governing the stability limits of spray jet flames are examined here using an annular co-flow spray burner. This study focuses on investigating the impact of liquid loading on spray jet flame stability, represented by flame lift-off height (LOH) and lean blow-out (LBO) limit. This is achieved by utilizing a parametric experimental study in which co-flow temperatures (Tco-flow = 298 K, 350 K, 400 K, and 450 K), spray nozzle sizes (dorifice = 0.209 mm, 0.219 mm, 0.232 mm, and 0.237 mm), fuel/air flow rates, and velocities are independently varied. A single liquid fuel, n-heptane, is used so that the vapor/liquid fractions (droplet lifetime) can be easily predicted via simple vapor–liquid equilibrium calculations to assist in the explanation of the stability mechanisms involved. The results show that the spray flame LOH mechanisms are affected by both chemical flame speed and, to a lesser extent, vaporization. On the other hand, the LBO limit is found to be controlled by the amount of liquid fuel in the presence/entering the flame. When the co-flow temperature is increased, while keeping constant co-flow velocity, the flame stabilizes near the burner lip. However, an opposite trend is noticed for flame blow-out limits, with the flame being more difficult to blow out when lower co-flow temperatures are applied. The variation of nozzle sizes leads to similar conclusions, i.e., when larger nozzle sizes are used, leading to the formation of larger droplets, the flame stabilizes further downstream and becomes more difficult to reach blow-out. The interpretation of the results indicates that delaying the vaporization and generating local enrichment regions near the flame edge enhances the flame LBO performance. Such an approach may be used as an efficient passive control mean to enhance flame stabilization; however, secondary impacts on emissions must be considered.

On the Relationship Between the Roots of Cubic Equations of State and New Perspectives of the Vapor–Liquid Equilibrium Calculation

On the Relationship Between the Roots of Cubic Equations of State and New Perspectives of the Vapor–Liquid Equilibrium Calculation

Estimation of the Bubble Point Pressure of Multicomponent Reservoir Hydrocarbon Fluids

This study developed a novel C-sharp (C#) programming language for the estimation of bubble point pressure (BPP) of various hydrocarbon mixtures at equilibrium state. The methodology was based on vapor–liquid equilibrium calculation using Peng Robinson equation of state implementation, thermodynamic equilibrium calculation and Newton-Raphson’s method for the successive substitution of the unknown variables. The equal fugacity constraint can be satisfied by obtaining the equilibrium which serves as a criterion for two or more phases to exist at equilibrium. The problem was resolved by searching for a pressure that will satisfy the two constraints. Complex calculation was performed by successively substituting the pressure value estimated by Newton–Raphson’s method at reservoir temperature until the two constraints were satisfied. The BPP values for the eight reservoir sample fluids were within the range of 29.32–308.00 atm with an absolute error deviation ranging from 0.00–4.27 and average percentage error of 0.54%. BPP values were obtained were within the reservoir temperature range of 328.15–398.71 K. This procedure is a potential approach for the estimation of BPP for hydrocarbon mixtures with defined fluid composition irrespective of their composition.

Carbon Capture from CO2-Rich Natural Gas via Gas-Liquid Membrane Contactors with Aqueous-Amine Solvents: A Review

Gas–liquid membrane contactor is a promising process intensification technology for offshore natural gas conditioning in which weight and footprint constraints impose severe limitations. Thanks to its potential for substituting conventional packed/trayed columns for acid-gas absorption and acid-gas solvent regeneration, gas-liquid membrane contactors have been investigated experimentally and theoretically in the past two decades, wherein aqueous-amine solvents and their blends are the most employed solvents for carbon dioxide removal from natural gas in gas-liquid membrane contactors. These efforts are extensively and critically reviewed in the present work. Experimentally, there are a remarkable lack of literature data in the context of gas–liquid membrane contactors regarding the following topics: water mass transfer; outlet stream temperatures; head-loss; and light hydrocarbons (e.g., ethane, propane, and heavier) mass transfer. Theoretically, there is a lack of complete models to predict gas-liquid membrane contactor operation, considering multicomponent mass balances, energy balances, and momentum balances, with an adequate thermodynamic framework for correct reactive vapor–liquid equilibrium calculation and thermodynamic and transport property prediction. Among the few works covering modeling of gas-liquid membrane contactors and implementation in professional process simulators, none of them implemented all the above aspects in a completely successful way.

Extension of the electrolyte Trebble–Bishnoi EOS to mixed‐salt systems, and application to vapour liquid and solid (hydrate) vapour liquid equilibrium calculations

AbstractThis work examines the use of the electrolyte Trebble–Bishnoi equation of state (eTBEOS) in predicting high‐pressure phase equilibria in the presence of aqueous mixed‐salt solutions. The eTBEOS combines the Trebble–Bishnoi equation of state with a Born energy term, a mean spherical approximation term, and a cation solvation term. Shortcomings in the originally regressed set of eTBEOS parameters are identified and discussed, and a new set of equation of state parameters is subsequently regressed for 58 salts. In order to extend the eTBEOS to mixed‐salt systems, two approaches for computing the EOS parameters of the ionic species are investigated. The first approach uses the originally regressed parameter set plus parameter mixing rules, where appropriate, whereas the second approach uses the newly regressed parameters and no mixing rules. In the prediction of osmotic coefficients in mixed‐salt solutions, the maximum relative difference between the experimental and computed values was 5.70%. For the gas solubility predictions, data were available for the solubility of CO2, CH4, and N2 in a small number of mixed electrolyte solutions; the maximum relative difference was 5.79%. Finally, CH4, C2H6, C3H8, and CO2 gas hydrate formation conditions were predicted in a number of mixed‐salt solutions, with a maximum relative difference of 10.76%. Overall, it was seen that both approaches allowed for comparable accuracy in phase equilibrium calculations. However, in the case of solutions made from salt mixtures with common cations, the second approach consistently resulted in improved accuracy.

Large eddy simulations of reacting and non-reacting transcritical fuel sprays using multiphase thermodynamics

We present a novel framework for high-fidelity simulations of inert and reacting sprays at transcritical conditions with highly accurate and computationally efficient models for complex real-gas effects in high-pressure environments, especially for the hybrid subcritical/supercritical mode of evaporation during the mixing of fuel and oxidizer. The high-pressure jet disintegration is modeled using a diffuse interface method with multiphase thermodynamics, which combines multi-component real-fluid volumetric and caloric state equations with vapor–liquid equilibrium calculations for the computation of thermodynamic properties of mixtures at transcritical pressures. Combustion source terms are evaluated using a finite-rate chemistry model, including real-gas effects based on the fugacity of the species in the mixture. The adaptive local deconvolution method is used as a physically consistent turbulence model for large eddy simulation (LES). The proposed method represents multiphase turbulent fluid flows at transcritical pressures without relying on any semi-empirical breakup and evaporation models. All multiphase thermodynamic model equations are presented for general cubic state equations coupled with a rapid phase-equilibrium calculation method that is formulated in a reduced space based on the molar specific volume function. LES results show a very good agreement with available experimental data for the reacting and non-reacting engine combustion network benchmark spray A at transcritical operating conditions.

Rigorous Phase Equilibrium Calculation Methods for Strong Electrolyte Solutions: The Isothermal Flash

New algorithms for vapor – liquid (VLE) and liquid - liquid (LLE) equilibrium calculations at constant temperature, pressure and feed phase composition (PT flash), with application to mixtures containing fully dissociating electrolytes are presented. A new approach is proposed and is rigorously derived by treating phase equilibrium as a minimization problem of the Gibbs free energy, while utilizing the electro-neutrality condition as a constraint. In this way, an augmented function (Lagrange function) is formulated which serves as the basis for the equations that govern phase equilibrium. It is shown that the Lagrange multiplier which corresponds to the electro-neutrality constraint has theoretical meaning and direct relation to the electrostatic potential difference between inhomogeneous phases. Based on the new approach, named Electrochemical Ionic Approach (EIA), two new numerical methods are presented; a successive substitution method similar to the classical Rachford-Rice method and a second-order one, which is based on Newton's method. The new algorithms are general and can be readily applied to mixtures of multiple solvents and one or multiple salts without any modifications. Finally, the Mean Ionic Approach (MIA) for mixtures with multiple solvents and only one salt is discussed in detail and a successive substitution and a second-order method are formulated. Moreover, the MIA is formally extended and presented for mixtures of multiple solvents and multiple salts. All the resulting methods are applied to mixtures with multiple solvents and one or multiple strongly dissociating electrolytes. The performance and technical details of each method are discussed and compared. The calculations are performed with the electrolyte Statistical Associating Fluid Theory with the Mie potential of variable range (eSAFT-VR Mie) equation of state but the proposed methods are general and could be used with any other thermodynamic model.

Liquid–liquid equilibrium calculations of systems containing vegetable oil + fatty acids + ethanol + water using new parameters for the unifac subgroups of ethanol and water

Deacidification removes free fatty acids (FFA) from crude vegetable oils during the refining process. The removal of FFA carried out by liquid–liquid extraction has some advantages over chemical and physical refining processes: it saves energy and decreases neutral oil losses caused by undesirable chemical reactions. The knowledge of phase equilibrium behavior of systems involving vegetable oils, solvents, and FFA is necessary to design and optimize the liquid–liquid extraction processes for deacidification. In this context, the present work aims to predict the liquid–liquid equilibrium (LLE) for systems consisting of vegetable oil + fatty acids + ethanol + water, readjusting new UNIFAC interaction parameters just for the ethanol and water subgroups. Several experimental LLE data for multicomponent fatty systems available in the literature are used to adjust the new UNIFAC interaction parameters for the ethanol (EtOH) and water subgroups. The temperature range studied was 288.15 K to 323.15 K, at atmospheric pressure. The new 18 interaction parameters provide a considerably lower mean square error (0.87%) than the other works available in the literature. The results show that the developed procedures improve the capacity of the UNIFAC method to predict LLE for systems involved in the deacidification process of crude vegetable oil. The methodology employed in this work results in reduced computational calculations and a relatively small split with the complex dataset established by the UNIFAC-LL model.

CO2-binding organic liquids for high pressure CO2 absorption: Statistical mixture design approach and thermodynamic modeling of CO2 solubility using LJ-Global TPT2 EoS

CO2-binding organic liquids (CO2-BOLs) or switchable ionic liquids (SILs) are switchable polarity solvents (SPS) that can be used as non-aqueous, energy efficient solvents for CO2 absorption. In this study, the three-component CO2-BOLs comprised of a single-component CO2-BOL (tertiary alkanolamine) and a two-component CO2-BOL (superbase/alcohol) are introduced. The most efficient equimolar combination of superbase (1,8-diazabicyclo-[5.4.0]-undec-7-ene (DBU)), alcohol (methanol, n-butanol, sec-butanol, tert-butanol and hexanol) and amine (Dimethylethanolamine (DMEA), Diethylethanolamine (DEEA) and N-methyldiethanolamine (MDEA)) are obtained using screening experiments considering CO2 loading (αeq) and absorption rate (αR). The mixture design technique is employed for modeling of αeq and αR as a function of mole fraction of components at 35.0 °C and initial pressure of 25.0 bar. The DBU/DMEA/n-butanol CO2-BOL represented the best performance for CO2 uptake. The experimental CO2 solubility data in DBU/n-butanol, DBU/DMEA and DBU/DMEA/n-butanol BOLs were obtained in the temperature range of 25.0–45.0 °C and the pressure range of 1.0–45.0 bar. The DBU mole fraction was selected to be 0.1 and 0.2 while the molar ratio of DMEA to n-butanol was kept constant at 2 in the three-component BOL. The simultaneous vapor–liquid and chemical equilibrium calculation algorithm using LJ-Global TPT2 equation of state was used for the thermodynamic modeling of CO2 solubility in BOLs. The average absolute relative deviation error (AAD%) for the calculation of total pressure of DBU/n-butanol, DBU/DMEA and DBU/DMEA/n-butanol BOLs were obtained to be 8.5%, 5.8% and 8.6%, respectively.

Reply to “Comments on ‘Isobaric Vapor + Liquid Equilibrium Measurements and Calculations for Using Nontraditional Models for the Association Systems of Ethyl Acetate +2-Ethylhexanoic Acid and Propyl Acetate +2-Ethylhexanoic Acid at Atmospheric Pressure’″

Reply to “Comments on ‘Isobaric Vapor + Liquid Equilibrium Measurements and Calculations for Using Nontraditional Models for the Association Systems of Ethyl Acetate +2-Ethylhexanoic Acid and Propyl Acetate +2-Ethylhexanoic Acid at Atmospheric Pressure’″

Comment on “Isobaric Vapor + Liquid Equilibrium Measurements and Calculations for Using Nontraditional Models for the Association Systems of Ethyl Acetate + 2-Ethylhexanoic Acid and Propyl Acetate + 2-Ethylhexanoic Acid at Atmospheric Pressure”

Shen et al. have recently reported isobaric VLE data for two binary systems. The purpose of this communication is to prove that their data are actually thermodynamically inconsistent and erroneousl...

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.

Isobaric Vapor–Liquid Equilibrium Measurements and Calculations Using Nontraditional Models for the Association Systems of Ethyl Acetate + 2-Ethylhexanoic Acid and Propyl Acetate + 2-Ethylhexanoic Acid at Atmospheric Pressure

In this work, experimental isobaric vapor–liquid equilibrium data were measured for the ethyl acetate (EAC) + 2-ethylhexanoic acid (EA) and propyl acetate (PAC) + EA systems at atmospheric pressure...

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.

A Gibbs free energy minimization based model for liquid–liquid equilibrium calculation of a system containing oil, brine, and surfactant

Accurate and reliable phase equilibrium calculations of microemulsion systems are of great importance. This study deals with the thermodynamic modeling of Liquid–Liquid Equilibrium (LLE) of a system including oil (n-decane), brine (containing CaCl2 salt), and ionic surfactant (sodium dodecyl sulfonate). Two models of UNIQUAC and UNIQUAC + Debye–Hückel were used for thermodynamic calculations. The LLE experimental data were utilized to estimate the binary interaction parameters of UNIQUAC model and the adjustable parameter, b, of the Debye–Hückel model. The thermodynamic model calculates the microemulsion phase’s compositions by minimizing the Gibbs free energy of the LLE system using a combination of genetic algorithm and fmincon function in order to prevent local minima. The thermodynamic modeling results show an appropriate agreement with the experimental data. Accordingly, the presented model of this study can be used as a suitable method to investigate the liquid–liquid equilibrium of systems containing oil, water, and surfactant.

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

Confined fluid interfacial tension calculations and evaluations in nanopores

In this paper, confined fluid interfacial tensions (IFTs) in nanopores and their influential factors are studied. First, a new generalized equation of state (EOS) considering the pore radius, intermolecular interactions, and wall effect is developed analytically for calculating the thermodynamic phase behaviour of confined pure and mixing fluids in nanopores. Second, the modified model based on the new EOS and coupled with the parachor model, which also takes account for the capillary pressure and shifts of critical properties, is applied to calculate the IFTs in nanopores at different conditions. Third, the following four important factors are specifically studied to evaluate their effects on the IFTs in nanopores: feed gas to liquid ratio (FGLR), temperature, pore radius, and wall-effect distance. The newly-developed model is found to be accurate for vapour–liquid equilibrium (VLE) and IFT calculations in bulk phase and nanopores by comparing with the measured and calculated data in the literature. The IFTs in bulk phase of the pure and mixing hydrocarbon (HC) systems are always higher than those in nanopores. At low pressures, the calculated IFTs in nanopores from the new model are higher than those from the previously modified EOS, whereas they become almost equivalent at high pressures. The calculated IFTs of the simple HC systems in nanopores keep constant at different FGLRs while they are decreased by reducing the FGLRs for a multicomponent mixing HC system. Moreover, at low pressures, the gaseous CO2–mixing HC IFTs in bulk phase and nanopores are inferred to be lowered by increasing the temperature while the liquid/supercritical CO2–mixing HC IFTs may be increased. The temperature effect on the IFTs are weakened in nanopores at most pressures except for some extremely high pressure cases. The IFTs in nanopores are decreased with the reduction of pore radius but keep constant at δp/rp ≥ 1.0.