Vapor-liquid Equilibrium Calculations Research Articles

Prediction of azeotropes position of refrigerant mixtures using the PHSC EoS

The work aims is predict the azeotropes' position in refrigerant mixtures using the Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). The vapor-liquid equilibrium (VLE) of seventeen binary refrigerant mixtures has been correlated using two model-adjustable parameters. The results show that the proposed model can calculate the bubble and dew points of binary systems, accurately. The average ARD value of binary VLE calculations has been obtained 1.28 %. The azeotropes pressure and composition of binary mixtures have been predicted using the PHSC EoS with the average ARD values of 1.043 % and 2.23 %, respectively. The maximum relative deviation has been observed for R717+R125 systems with two azeotropes points; ARDx=12.2 %. The performance of the PHSC EoS has been evaluated by predicting the azeotropes position of ternary mixtures. The PHSC EoS results have been compared to three cubic-based EoSs containing the PR-vdW, PR-BM, and PR-MHV2-NRTL models. The results show that the PHSC EoS can predict the ternary VLE data and azeotropes position satisfactory. The relative absolute deviation does not exceed 1.7 % for the azeotropes pressure. The PHSC EoS can be used as a robust and efficient model for the prediction of the azeotropes' position in binary and ternary refrigerant mixtures. Prediction of azeotropic composition helps us to find promising refrigerant candidates in the pre-design stage of the desired apparatus.

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.

Evaluation of water + imidazolium ionic liquids as working pairs in absorption refrigeration cycles

Ionic Liquids (ILs) have been proposed as alternative absorption media for water in absorption refrigeration cycles to replace the currently used lithium bromide, which suffers from problems like crystallization and corrosiveness. This work investigates the use of imidazolium based ionic liquids as water absorbents in absorption refrigeration cycles. A predictive procedure is followed for calculating the parameters that mostly affect the performance of the cycle, that is the Vapor-Liquid Equilibrium (VLE) of the working pair and its heat capacity: UNIFAC is employed for the VLE calculations while a new predictive method has been developed for the heat capacity of the ILs. The effect of the alkyl chain length of the cation and the type of the anion that compose the IL is investigated, and it is shown that ILs consisting of imidazolium cation with short alkyl chain and the anions [Cl] and [DMP] exhibit the best performance in terms of Coefficient of Performance (COP) and circulation ratio (f). Comparison with the conventional LiBr absorbent indicates that the best ILs exhibit higher COP values but higher f ratios as well. Also, double cycle configurations are studied revealing the major effect of the supplied heat temperature on COP, even for the higher temperatures, compared to the single effect one. Finally, it is shown that there is a clear correlation between the COP of the refrigeration cycle and the product of the circulation ratio and the specific heat capacity of the strong solution, which is proposed in this work as a new reliable index for screening different ILs as absorbents, without the necessity of solving the mass and energy balances of the cycle.

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.

Coupling effect of critical properties shift and capillary pressure on confined fluids: A simulation study in tight reservoirs

Critical properties shift and large capillary pressure are important contributors for the phase behavior altering of nanopore fluid. However, the effects of critical properties shift and large capillary pressure on the phase behavior are ignored in traditional compositional simulators, leading to inaccurate evaluation results of tight reservoirs. In this study, phase behavior and production of confined fluid in nanopores are studied. First, we developed a method for coupling the effect of critical properties shift and capillary pressure into the vapor-liquid equilibrium calculation base on Peng-Robinson equation of state. Second, a novel fully compositional numerical simulation algorithm considering effect of critical properties shift and capillary pressure on phase behavior is accomplished. Third, we have discussed the alterations of critical properties shift effect, capillary pressure effect and coupling effect on the composition of oil and gas production in detail. The critical properties shift and capillary pressure effects on oil and gas production in tight reservoirs are analyzed quantitatively through four cases, and the influences of the two effects in oil/gas production are compared. Based on the fully compositional numerical simulation, the simulator can rigorously simulate the impacts of component changes during production. The simulation results show that both the critical properties shift effect and the capillary pressure effect reduce the bubble point pressure of Changqing shale oil, and the influence are more prevalent in pores of smaller radius. In pores is larger than 50 nm, the phase behavior altering of the fluid can be ignored. In addition, we devised four cases to comprehensively investigate the effects of critical properties shift and large capillary pressure on production performance of tight reservoirs. The comparisons between the four cases show that the capillary pressure effect impacts the reservoir production performances greater than the critical properties shift effect, such as higher oil production, higher GOR, and lower content of lighter component and higher content of heavier component in the residual oil/gas. The results of coupling effects indicate that the critical properties shift effect would suppress the effect of the capillary pressure effect. In particular, the difference between the simulation results of the coupling effects and the base case is smaller than that between the simulation results of the capillary pressure effect and the base case.

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

Assessing the quality of SAFT equations for the vapor-liquid equilibrium of pure water

The family of eight representative (and most commonly used) SAFT equations of state for water and the cubic-plus-association equation are examined with respect to their ability to predict accurately the vapor–liquid equilibrium (VLE) of water. The problem originates from the fact that all these equations use only the experimental equilibrium liquid densities and pressures for the parameter evaluation. Consequently, when reproducing the VLE calculations once the parameters are evaluated, the equilibrium properties cannot be then determined accurately by the equations, in principle, because the computation involves also the omitted vapor density. In this contribution, the errors of the predicted equilibrium densities, orthobaric pressures, and related properties are determined and discussed. It turns out that even the properties used in the equations’ parametrizations (pressure and liquid density) are not always reproduced with acceptable accuracy, with average errors being around two percent and errors of the individual data points exceeding in many cases even ten percent. Properties not included in the parametrization are then predicted with larger average errors, in general.

Estimating VLE behavior from SLE data in aqueous mixtures of choline chloride-sorbitol deep eutectic solvents: Experimental investigation and thermodynamic modeling using the e-NRTL model

Knowledge of solid–liquid equilibria (SLE) and vapor–liquid equilibria (VLE) for mixtures containing deep eutectic solvents (DESs) is of paramount importance. We have conducted experiments to obtain additional data for SLE systems and then used the e-NRTL model to predict the VLE behavior in mixtures of DESs comprised of choline chloride (ChCl), sorbitol (S), and water (W). The systems under investigation include three 2-component systems (S/W, ChCl/W, ChCl/S), and one 3-component system (DES/W) where the DES is obtained by mixing ChCl and S at a molar ratio of 1. Using the e-NRTL activity coefficient model, the adjusted binary interaction parameters of the proposed model are determined solely from the experimental SLE data obtained from this work and also those in the literature. There is an excellent agreement between the SLE solubility data and the e-NRTL results. The tuned model is then used to predict the bubble pressure in three aqueous systems (S/W, ChCl/W, and DES/W) with an overall AARD value of 2.21%. The excellent agreement between the experimental and predicted VLE data demonstrates the viability of the proposed thermodynamic modelling framework to represent the equilibrium systems containing DESs. The outcome from our study can be used to relate the SLE and VLE data without the need to perform experiments for both cases for the given system of interest. Compared to the VLE experiments, the SLE tests are much simpler and safer because there is little compressibility and the effect of pressure on solubility is minimal which makes it possible to conduct SLE tests at room conditions (at least for liquids with negligible non-ideality). Therefore, conducting the high-pressure VLE calculations without the need to perform VLE experiments and through SLE experimental data alone will be of practical significance.

A novel experimental-theoretical method to improve MMP estimation using VIT technique

In the gas injection process for enhanced oil recovery (EOR), the interfacial tension (IFT) and the minimum miscibility pressure (MMP) are two key parameters for evaluating the miscibility condition. The vanishing interfacial tension (VIT) method is an efficient method for measuring the interfacial tension of oil and gas versus pressure and can estimate the minimum miscibility pressure. A problem in the VIT test of a hydrocarbon system is that during this test, oil and gas densities vary due to the composition variation of both phases. But in the conventional interfacial measurement, this issue is ignored, and the initial and non-equilibrium densities are utilized for estimating the interfacial tension. In this study, it is tried to nominate a novel method for estimating the most accurate value of IFT. Hence, for this purpose, first a VIT test has been performed for a hydrocarbon gas and a live oil system and using the axisymmetric drop shape analysis (ADSA), the oil droplet has been analyzed, and the geometry factor, which has been defined in this paper, was calculated. After that, the volume of oil droplet and the gas have been measured and were used for vapor-liquid-equilibrium (VLE) or flash calculation using Peng-Robinson equation of state (PR-EOS). By VLE calculation fulfillment, the final composition of two phases is determined. Eventually, the densities of two phases have been calculated for VIT modification. Finally, the IFT results were plotted versus the pressure steps, and the MMP were estimated. Furthermore, to evaluate the results of VIT test and its modification, slim tube displacement (STD) test, which is known as the most reliable laboratory method for measuring the MMP in the oil industry, has been performed. The results show that the values obtained for MMP values for the VIT test with the corrected densities which are lower than the values obtained for the VIT test for not-corrected densities and the suggested experimental-theoretical method has been estimated the MMP more accurately. The MMP obtained by VIT test and modified VIT method was equal to 3858.72 and 3722.0 psi, respectively. Meanwhile, the slim tube test has measured the MMP equal to 3667.13 psi.

Extension of a square-well equation of state for chain-like molecules using perturbed hard chain theory

The Square-Well equation of state developed by Haghtalab and Mazloumi [A. Haghtalab, S.H. Mazloumi, Fluid Phase Equilib., 280 (2009) 1–8.] is extended for chain like molecules using a generalized van der Waals partition function for polyatomic fluids suggested by Donohue and Prausnitz [M.D. Donohue, J.M. Prausnitz AICHE J., 24 (1978) 849-860.]. The proposed EOS has three physical parameters per each pure fluid that are close-packed volume, characteristic temperature and one-third of external degree of freedom of the molecule. Here in, the parameters of the new EOS for a selection of pure fluids containing normal alkanes from C1 up to C20 are reported that are obtained by correlating saturated vapor pressure and liquid density of the fluids. Then, using proper mixing rules, vapor-liquid equilibrium calculation of a number of binaries are successfully carried out. The comparisons of the results with SPHCT EOS demonstrate the good accuracy of the new EOS.

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.

Vapor-liquid equilibrium predictions of refrigerant systems using COSMO based Gex-EoS methods

Combining COSMO-based excess Gibbs free energy models with the Peng-Robinson (PR) equation-of-state (EoS) via mixing rules has recently been shown as a promising method for satisfied VLE predictions on refrigerant systems by Mambo-Lomba and Paricaud. An extension is provided in this work for more systematic and dedicated evaluations focusing on a significantly larger refrigerant database and comparisons between different VLE modeling approaches. In particular, the COSMO-SAC-dsp model is combined with via the original Huron-Vidal (HVO), the modified Huron-Vidal (MHV1) and the Wong-Sandler (WS) mixing rules. Comprehensive model evaluation is performed on the basis of 447 vapor-liquid-equilibrium (VLE) experimental datasets for 233 refrigerant pairs. The results show that the combination of the COSMO-SAC-dsp with the PR yields satisfied and comparable prediction accuracy on the VLE in most cases comparing to the well-established group-contribution based Gex-EoS methods VTPR and PSRK. The performance of the three mixing rules on the studied database follows a decreasing order of MHV1 > HVO > WS but without qualitative difference. Large VLE prediction errors can appear between halogenated hydrocarbons and hydrocarbons. Moreover, errors become more significant and the VLE calculation cannot converge at all for mixtures involving R717 and R744 respectively. Improved predictive accuracy can be achieved by re-optimizing the atomic dispersion parameters of F and =O to 35.5 and 74.0 respectively.

Empirical Correlations for K-Values of Crude Oils

Based on the Soave–Redlich–Kwong equation of state, empirical correlations for the K -values of N 2 , CO 2 , H 2 S , C 1 , and C 2 are proposed. Complementarily, the binary interaction coefficients involving the plus fraction, C 7 + , were optimized by fitting into 131 experimental data from the literature. The criterion to select the form of the empirical correlations was based on the identification of the major dependencies of the equilibrium constants on the system variables (e.g., pressure, temperature, and composition). For most of the experimental data, the saturation pressure calculated via the empirical correlations is in excellent agreement with those reported from the laboratory. The empirical correlations cover a variety of temperatures (128–314°F), pressures (313–6880 psi), and compositions (N2: 0.0–1.67%; CO2: 0.0–9.11%; H2S: 0.0–3.68%; C1: 5.63–74.18%; C2: 0.84–12.45%; C7+: 10.72–83.2%). The proposed correlations are useful for rapid vapor-liquid equilibrium calculations during the compositional modeling of petroleum reservoirs.

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.

Assessment of the simultaneous regression of liquid-liquid and vapor-liquid equilibria data of binary systems using NRTL and artificial neural networks

A numerical analysis on the phase equilibrium modeling performance of the NRTL equation in binary mixtures using different data regression strategies was carried out. Several formulations for the binary interaction parameter estimation were studied including a novel approach using an artificial neural network model for the simultaneous correlation of liquid-liquid and vapor-liquid equilibria data. The artificial neural network strategy substantially improved the estimation of the liquid-liquid equilibrium data in comparison with the traditional parameter estimation strategies utilized for the thermodynamic models. A detailed analysis on the performance of the model in terms of the calculation of homogeneous and heterogeneous azeotropes was also performed. This study showed that the application of artificial intelligence tools is an interesting alternative to improve the capabilities of local composition models for the liquid-liquid and vapor-liquid equilibria calculations.

Application of modified molecular interaction volume model for phase equilibrium of PbS–Sb2S3 system in vacuum distillation

In this paper, the modified molecular interaction volume model (M-MIVM) was used to calculate the activities of components of the PbS–Sb2S3 binary matte system. On this basis, the vapor-liquid equilibrium (VLE) data of the PbS–Sb2S3 system were calculated by M-MIVM in combination with the theory of vacuum metallurgy and VLE. Additionally, the VLE experiment of the PbS–Sb2S3 binary matte system was conducted to correctly interpret the results of the model. The calculated results of the VLE of the model were consistent with the experimental values, and the VLE calculation of the PbS–Sb2S3 binary matte system by M-MIVM was reliable. This is an effective and convenient method to predict the relationship between product components with temperature and pressure in vacuum distillation of PbS and Sb2S3 mixed melts, providing theoretical guidance for vacuum separation and purification of PbS and Sb2S3.

Modeling interfacial mass transfer of highly non-ideal mixtures using an algebraic VOF method

In this work, a numerical model based on an algebraic Volume-of-Fluid (VOF) method and the Continuous Species Transfer (CST) model is presented to simulate the heating and evaporation of droplets composed of highly non-ideal mixtures. Regarding this, a non-ideal vapor-liquid equilibrium (VLE) model is coupled to the CST model to properly describe the concentration jump at the droplet’s interface. In addition, since in the CST model the transported variable is a mixture concentration, the values of concentration within the continuous and disperse phases, which are necessary for the evaluation of activity and fugacity coefficients in the VLE calculation, are unknown. Thus, a numerical procedure is proposed to estimate the concentrations in each phase from the mixture concentration. The UNIFAC method is used for activity coefficients calculation. The results for the evaporation of ethanol/iso-octane droplets with different mixture compositions in a 3D domain show good agreement when compared with analytical solutions.

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.