VLE Calculations Research Articles

Dual-functionalized amines as single-component water-lean CO2 absorbents with low-viscosity and high-capacity: The synergistic effect of alkoxy and silyl groups

Water-lean CO2 absorbents are promising alternatives to conventional aqueous alkanolamine-based solvents due to the potential benefits of reduced energy input and improved capacity. However, the exponential increase in viscosity with CO2 loading prohibits their industrial deployment by weakening internal mass and heat transfer as well as deteriorating or even blocking pipeline transportation. In this work, a series of alkoxy-silyl dual-functionalized amines have been devised as single-component CO2 absorbents in order to achieve enhanced flowability and efficiency under water-lean conditions. These nonaqueous amines were proved to be highly flowable (8–27 cP at 25 °C, 3–9 cP at 40 °C) under their maximum gravimetric capacity (11–17 wt% at 25 °C, 9–14 wt% at 40 °C), which is comparable to fully loaded 30 wt% MEA (11 cP at 25 °C, 4 cP at 40 °C). The synergistic effect of alkoxy and silyl groups on viscosity and capacity was systematically investigated by means of 13C NMR, in situ FTIR, DSC, VLE and DFT calculation, indicating that the reversible formation of carbamic acid through dual-stabilization, i.e. alkoxy-proton hydrogen bonding and silyl-oxygen complexation, should play the key role in improving both flowability and reaction stoichiometry. Meanwhile, these novel absorbents could be easily regenerated by desorption at 70 °C, and they could maintain structural integrity for at least 2 days under aerobic heating at 80 °C within closed system under CO2-loaded state. Furthermore, the intrinsic CO2-philic nature of both alkoxy and silyl functionalities would offer significant physical absorption under high pressures (20 and 30 bar). Hence, with remarkable flowability, enhanced capacity and easy reversibility, such dual-functionalized amines should certainly represent competitive candidates for further scale up and practical application.

A complementarity‐based vapor‐liquid equilibrium formulation for equation‐oriented simulation and optimization

AbstractVapor‐liquid equilibrium (VLE) is a cornerstone of computer‐aided process engineering (CAPE). Embedded within process system models, VLE calculations are inherently procedural with non‐smooth behavior that frequently requires discrete decisions. Traditionally, these features resist the incorporation of VLE within efficient, large‐scale equation‐oriented (EO) process simulation and optimization strategies. On the other hand, recent reformulation of VLE models through the incorporation of complementarity constraints has broadened its scope to deal seamlessly with phase transitions and even supercritical excursions in process simulation and optimization. In this study, we extend these VLE complementarity models to EO frameworks where procedural thermodynamic property libraries are still required. Here we develop an efficient, non‐intrusive, and intuitive “square‐flash” equation system that has been implemented within the IDAES Integrated Platform (IDAES‐IP). The effectiveness of this modular approach is demonstrated on case studies for non‐ideal flash calculations and distillation optimization, with disappearing phases and supercritical transitions.

Three-component 1,1,3,3-tetramethylguanidine based CO2-binding organic liquids: Statistical solvent design and thermodynamic modeling of CO2 solubility by LJ-Global TPT2 EoS

In this study, three-component CO2-binding organic liquids (CO2BOLs) are introduced for high pressure CO2 absorption. The non-aqueous, green solvents consist of a superbase (1,1,3,3-tetramethylguanidine (TMG)), a tertiary alkanolamine (Dimethylethanolamine (DMEA), Diethylethanolamine (DEEA) and N-methyldiethanolamine (MDEA)) and an alcohol (MeOH, n-BuOH, sec‑BuOH, tert‑BuOH and 1-HexOH). The best combination of solvent components was determined to be the TMG/DMEA/n-BuOH BOL (molar ration:1/1/1) based on both CO2 loading (αeq= 0.431 mol CO2/mol solvent) and absorption rate (αR= 0.225 mol CO2/mol solvent within 20 min) by implementing screening experiments. The mixture design approach was applied for the design of experiments, modeling and investigating the effect of components’ proportion on αeq and αR at the constant temperature of 35.0 °C and initial CO2 pressure of 25.0 bar. The highest αeq (0.573 mol CO2/mol BOL) and αR (0.362 mol CO2/mol solvent) were obtained using TMG/n-butanol (1/1) and DMEA BOLs, respectively. The CO2 solubility data in the two-component BOLs: TMG/n-BuOH, TMG/DMEA and DMEA/n-BuOH as well as the three-component TMG/DMEA/n-BuOH BOL were gathered at 25.0, 35.0 and 45.0 °C and the pressures up to 35.0 bar using equimolar solvent mixtures. The LJ-Global TPT2 EoS was used in the simultaneous VLE and chemical equilibrium calculation algorithm for the thermodynamic modeling of CO2 solubility in the BOLs. The AAD% in the modeling of TMG/n-BuOH, TMG/DMEA, DMEA/n-BuOH and TMG/DMEA/n-BuOH BOLs were calculated to be 11.5%, 12.4%, 10.5 and 12.9%, respectively. The enthalpies of CO2 absorption in BOLs and the speciation of the system components were predicted from reaction equilibrium constants and using LJ-Global TPT2 EoS.

Purification of methyl isobutyl ketone via dividing wall column with an internal boiling point of a heterogeneous azeotrope

Methyl isobutyl ketone (MIBK) is an important chemical product used in many fields and is mostly made by the acetone one-step method. It is difficult to extract high-purity MIBK from the reactants where complex azeotropes form, thus leading to traditional MIBK separation process at high energy cost and investments. In this study, a new separation process based on dividing wall column, HA-DWC-U, was developed considering the heterogeneous azeotrope with an internal boiling point. First, thermodynamic research was performed to assure the accuracy of the physical properties. The NRTL and UNIQUAC models were compared, of which some model parameters were regressed from experimental data, and two binary parameter data sets were set for the VLE and LLE calculations. Then, steady-state simulation and optimization of the traditional process and HA-DWC-U were performed, in which continuous variables were optimized in the inner loop using the sequential quadratic programing (SQP) method, while discrete variables were optimized in the outer loop using sensitivity analysis method. Remarkable, the results show that HA-DWC-U has obvious advantages over the traditional separation process, including 18.47% savings in total utility cost and 17.86% savings in total annual cost.

Modeling of H2S absorption in some ionic liquids with carboxylate anions using modified HKM plus association EoS together with RETM

In current work, mHKM-CPA EoS together with the RETM was employed to correlate H2S absorption into five carboxylate ionic liquids, including 1-ethyl-3-methylimidazolium acetate ([emim][Ace]), 1-butyl-3-methylimidazolium acetate ([bmim][Ace]), 1-hexyl-3-methylimidazolium acetate ([hmim][Ace]), 1-ethyl-3-methylimidazolium lactate ([emim][Lac]) and 1-ethyl-3-methylimidazolium propionate ([emim][Pro]). The RETM proposes a chemical reaction between IL and H2S so that the liquid phase concentrations may be obtained by solving the model. Moreover, mHKM-CPA EoS contributes to VLE calculations. In the model, H2S considered as associating component with 4 association sites while the ILs assumed as non-self-associating compounds with one electron donor/acceptor sites.Fourteen adjustable variables of mHKM-CPA EoS for pure components were calculated using experimental liquid density and vapor pressure data. Afterward, binary systems were correlated by applying RETM. Indeed, two nested loops calculate the liquid phase, total pressure, and vapor phase concentrations, respectively.The parameters of the pure ILs were calculated with maximum AAD% below 0.3. Moreover, the binary results present 4.41 as the overall AAD% for 317 data points. Furthermore, a comparison between the results of the used model with those of the SRK-CPA was performed to show the capability of the mHKM-CPA EoS. As the outputs show, the model has a good ability to correlate the H2S solubility in the ILs concerning the classic SRK-CPA EoS.

Superancillary Equations for Cubic Equations of State

Calculation of thermodynamic phase equilibrium is error-prone and can fail both near the critical point and at very low temperatures because of the limited precision available in double precision arithmetic. Most importantly, these calculations frequently represent a computational bottleneck. In this work, we extend the “superancillary” equation approach developed for reference multiparameter equations of state to classical cubic equations of state (van der Waals, Redlich–Kwong–Soave, Peng–Robinson). Iterative calculations in double precision are replaced by noniterative evaluation of prebuilt Chebyshev expansions constructed with extended precision arithmetic. Exact solutions for the equation of state constants are given. The Chebyshev expansions are shown to reproduce the equation of state values to within nearly double precision (aside from in the very near vicinity of the critical point) and are more than 40 times faster to evaluate than the VLE calculations from the fastest computational library. In this way we further expand the domains in which iterative calculations for pure fluid phase equilibria may be rendered obsolete. A C++ header implementing these expansions (and with no external dependencies) is provided as deposited data.

Simulation of H2S solubility in three acetate-based ionic liquids using PC-SAFT EoS together with RETM

In current work, Perturbed Chain- Statistical Associating Fluid Theory (PC-SAFT) EoS together with the Reaction Equilibrium Thermodynamic Model (RETM) was employed to correlate H2S solubility in three carboxylate ionic liquids including [emim][Ace], [bmim][Ace] and [hmim][Ace]. The RETM proposes a chemical reaction approach between IL (B) and H2S (A) in the liquid phase. Moreover PC-SAFT EoS contributes for VLE calculations. All the H2S and the investigated ILs, as self-associating components, assumed to follow 2B association scheme.Five adjustable variables of PC- SAFT EoS for pure components were calculated using experimental data of liquid density and vapor pressure. Afterwards, the binary systems were investigated applying RETM. Indeed, two nested loops calculate the liquid phase, total pressure and vapor phase concentrations, respectively. For these systems, AAD% equal to 2.29, 3.09 and 7.65 were obtained for all ILs respectively.

Correlation and prediction of small to large sized pharmaceuticals solubility, and crystallization in binary and ternary mixed solvents using the UNIQUAC-SAC model

The recently reported UNIversal QUAsiChemical Segment Activity coefficient (UNIQUAC-SAC) model [developed by Haghtalab and Yousefi Seyf Ind. Eng. Chem. Res. 2015, 54, 8611] provides a practical thermodynamic framework to be used in VLE, LLE, and SLE calculations. The UNIQUAC-SAC model has the advantage of being independent of area (q) and volume (r) structural parameters used in the combinatorial part. While the UNIFAC or UNIFAC-DMD could not apply to the 47% (44 of 94) of the studied molecules because of the undefined groups. Here, the numbers of solvents with identified segment numbers were extended from 82 to 130 with a slight refinement to the previous values. The model parameters obtained via a large consistent set of VLE (isobaric and isothermal), and LLE experimental data. Also, the model was tested with pharmaceutical solubility experimental data in pure (94 solutes with 6210 solubility data), binary, and ternary solvents. The model provides a robust correlation of pharmaceuticals solubility in a mono-solvent and robust prediction of pharmaceuticals solubility in mixed solvents. The UNIQUAC-SAC model was successfully evaluated in solvent screening in cooling crystallization of ibuprofen and valsartan in both pure and binary solvents mixture (combined cooling and anti-solvent crystallization). The model with 130 solvents as a robust database provides a useful and practical thermodynamic tool in the conceptual design of pharmaceutical processes. A MATLAB based graphical user interface (GUI), finally, was developed to be used in the conceptual segment numbers regression procedure.

Modeling H2S solubility in aqueous N-methyldiethanolamine solution using a new ePC_SAFT-MB equation of state

Perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS), mean spherical approximation (MSA) term and Born term are combined and proposed as a new electrolyte equation of state (ePC_SAFT-MB EoS) to model the solubility of H2S in aqueous N-methyldiethanolamine (MDEA) solutions in a wide range of temperature, pressure, MDEA concentration, and H2S loading. In order to find the best association schemes (2B, 3B and 4C) for H2O, MDEA and H2S in PC-SAFT EoS, different association schemes are considered for each one of the components in the wide range of temperature and pure parameters are determined. The binary interaction parameters (BIP) for H2O + H2S and MDEA + H2O binary systems are adjusted in the VLE calculation for different association schemes. The best result with minimum average absolute relative deviation percent (AAD%) of 2.21 and 2.72 are obtained with considering the 4C, 4C and 3B association schemes for MDEA, water and H2S, respectively. By using the obtained BIPs, 277 data points of the bubble pressure for H2O + MDEA + H2S system are predicted by PC-SAFT EoS with the AAD% of 25.5. To improve the accuracy of PC-SAFT EoS, the Born and MSA terms are added to PC-SAFT EoS. The BIPs between the ion-ion and molecules-ions are adjusted by the bubble pressure calculation algorithm using 277 experimental data points. Very good results with the AAD% of 18.6 are obtained by adjusting the binary parameters (MDEAH+−MDEA,MDEAH+−H2O,MDEAH+–H2S and MDEAH+−HS−) in H2O + MDEA + H2S ternary system. Finally, to investigate the predictive ability of the proposed ePC_SAFT-MB EoS, it is employed to model the selected 44 solubility data points of H2O + MDEA + H2S system without further adjustment for model parameters. The value of AADs% is obtained about 30.0 for the H2 S partial pressure, which shows the predictive ability of the proposed model.

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.

Molecular Simulation of Vapor-Liquid Equilibria Using the Wolf Method for Electrostatic Interactions.

The applicability of the Wolf method for calculating electrostatic interactions is verified for simulating vapor–liquid equilibria of hydrogen sulfide, methanol, and carbon dioxide. Densities, chemical potentials, and critical properties are obtained with Monte Carlo simulations using the Continuous Fractional Component version of the Gibbs Ensemble. Saturated vapor pressures are obtained from NPT simulations. Excellent agreement is found between simulation results and data from literature (simulations using the Ewald summation). It is also shown how to choose the optimal parameters for the Wolf method. Even though the Wolf method requires a large simulation box in the gas phase, due to the lack of screening of electrostatics, one can consider the Wolf method as a suitable alternative to the Ewald summation in VLE calculations.

Impact of impurities on CO2 storage in saline aquifers: Modelling of gases solubility in water

Flue gas captured contains different impurities (N2, O2, SO2, NO etc) and their concentrations depend on the capture process and the industrial sector. Moreover, the presence of impurities may change the thermophysical properties of the stream and therefore impact the conditions of CO2 storage. The aim of the paper is to investigate the solubility in water of carbon dioxide and some chosen impurities. In this work VLE calculations using a geochemical model (Corvisier, 2013) and two group contribution (GC-PR-CPA (Group Contribution-Peng Robinson-Cubic Plus Association) (Hajiw, 2014 and Hajiw et al., 2015) and E-PPR78 (Qian et al., 2013) equations of state) models are compared.

The Impact of Vapor/Liquid-Equilibria Calculations on Scale-Prediction Modeling

Summary Vapor/liquid-equilibria (VLE) calculations, particularly involving the phase behavior of carbon dioxide (CO2) and hydrogen sulfide (H2S), are used in scale-prediction modeling. In this work, the impact of VLE calculations for CO2- and H2S-rich gas phases and for acid- and sour-gas mixtures on scale-prediction calculations is evaluated. Three equations of state (EOSs)—Soave-Redlich-Kwong (SRK) (Soave 1972), Peng-Robinson (PR) (Peng and Robinson 1976), and Valderrama-Patel-Teja (VPT) (Valderrama 1990)—are implemented in the Heriot-Watt model and used in VLE calculations. The solubility of single-component CO2 and H2S in water and the solubility of a gas mixture in water were compared with experimental data in terms of the absolute relative deviation (ARD). The solubility data were then used in PHREEQC (USGS 2016) to calculate the impact of using different EOSs on carbonate and sulfide scales, particularly on calcium carbonate (CaCO3) and iron sulfide (FeS). Average ARDs of 6.04, 4.10, and 3.77% between experimental and calculated values for CO2 solubility in water were obtained for the SRK, PR, and VPT EOSs, respectively. Similarly, for H2S solubility in water, average ARDs of 6.49, 6.66, and 6.48% were obtained for each EOS, respectively. For the solubility of sour- and acid-gas mixtures in water, average ARDs of 13.92, 13.25, and 10.78% were obtained, respectively. It has thus been concluded that the VPT EOS performs better than the SRK and PR EOSs in VLE calculations for the analyzed data. The errors introduced in VLE calculations have been found to impact the calculation of the amount of CaCO3 precipitated, with consequences for scale-inhibitor selection. Higher deviations were found in the amount of CaCO3 precipitation for gas mixtures when compared with a single-component, CO2-rich phase. Furthermore, the large errors occurring in VLE calculations for H2S solubility have not been found to impact the calculation of the amount of FeS precipitated when H2S is in excess with respect to Fe2+. In addition to this, a case study that was performed by use of formation-water data from the Brazilian presalt revealed that the choice of EOS can cause errors of 6 kg of precipitate during each day of production. Scale-prediction calculations carried out with PHREEQC demonstrate that VLE calculations can have a high impact on mineral precipitation. Thus, it is recommended that the best VLE model available should always be used for scale-prediction modeling, particularly when mixtures of gases are present.

Stability analysis for multicomponent mixtures including capillary pressure

Despite the large potential of unconventional resources, many unknowns still exist regarding the physics controlling the extraction processes in these settings. These include accurate representation of phase equilibrium in tight formations and effective implementation of relevant models in simulation tools.When a fluid is confined in pore spaces of nanometer size, significant interfacial curvatures may occur that can result in large capillary pressures between the liquid and vapor phases: The pressure difference between the two phases will likely affect the vapor-liquid equilibrium state. Previous efforts have shown that this effect is negligible for conventional reservoirs (with pores in the micron range) and current commercial reservoir simulators commonly ignore the effect of capillary pressure in the VLE calculations. However, experimental and modeling efforts have shown that ignoring capillary pressure in the VLE calculations will not be a valid approximation for unconventional (tight) reservoirs.In this work, we analyze the numerical aspects of including capillarity phenomena in VLE calculations in an effort to arrive at robust and efficient algorithms for stability analysis that can be used in compositional modeling/simulation of unconventional reservoirs. While the equality of chemical potentials is a necessary condition for equilibrium, it is not a sufficient one. A sufficient condition for equilibrium is the minimization of Gibbs energy, and the latter can be tested using the tangent plane distance (TPD) criteria. We show that stability analysis based on the TPD criteria remains valid for systems with large capillary pressures and propose effective/robust algorithms for stability testing. The proposed algorithms are tested for multicomponent reservoir fluid systems over a range of relevant temperatures, pressures and pore radii.

Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub- and super-critical domains

In this paper, translated and consistent versions of the Peng-Robinson (tc-PR) and Redlich-Kwong (tc-RK) cubic equations of state (CEoS) are developed. The adjective consistent means that the α-function used in such models passes the consistency test we recently developed and which guarantees safe extrapolation in the supercritical region and safe VLE calculation in multi-component systems. The adjective translated means that a volume translation aimed at exactly reproducing the experimental saturated liquid volume at a reduced temperature of 0.8 was used. The key conclusion of this paper is that the tc-PR EoS is certainly the safest and the most accurate 3-parameter cubic EoS ever published. Indeed the average deviations over roughly 1000 compounds belonging to different chemical families are: ΔPsat<1 %, ΔvapH=ΔcP,Lsat=2% and ΔvLsat(Tr<0.9)=2.3%.In the case of a lack of experimental data to fit the 3 parameters of the α-function and to determine the value of the volume correction, the second part of this study aims at providing a generalized version of the tc-PR and tc-RK CEoS in which all parameters can be estimated from the mere knowledge of the acentric factor.

Application of the perturbed chain-SAFT equation of state for modeling CO2 solubility in aqueous monoethanolamine solutions

CO2 removal by treatment of acid gases by aqueous alkanolamines is a very significant operation from industrial and environmental point of view. To attain a comprehensive thermodynamic model of the CO2–MEA–H2O in a wide range of temperature and CO2 partial pressures, Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) EOS is applied to predict the absorption of carbon dioxide by MEA (MonoEthanolAmine). In order to find the best association scheme for MEA in PC-SAFT EOS, three pure parameter sets for MEA in the 2B, 3B and 4C association schemes are determined in temperature range 303.15–443.15K. Temperature independent binary interaction parameters have been adjusted in the VLE calculation for three schemes of MEA and two schemes of water. Binary VLE calculations show the 3B scheme for MEA and the 4C scheme for water indicate the best prediction in the MEA–H2O system. Excess enthalpy data for aqueous MEA are predicted by kij, which has been adjusted in VLE calculations. The 3B scheme for MEA and the 4C scheme for water also are used to find CO2 solubility in the ternary system of CO2–MEA–H2O system. Ideal Smith–Missen algorithm has been applied to find the concentration of all species in chemical equilibrium. Results show the 3B association scheme for MEA and the 4C association scheme for water in PC-SAFT EOS have better agreement with binary and ternary experimental data. PC-SAFT EOS is able to anticipate the CO2 solubility in the CO2–MEA–H2O system without any regression in the ternary system. The CO2 solubility in ternary system is compared to e-NRTL as a common thermodynamics model. The average absolute partial pressure deviations for PC-SAFT and e-NRTL are calculated around 36% and 42%, respectively.

A modified MMM EOS for high-pressure PVT calculations of heavy hydrocarbons

A theoretical based cubic equation of state has been proposed (MMM EOS) by Mohsen-Nia (Mohsen-Nia et al., 1995) for calculation of pure fluid and mixture properties Z=(v+1.3191b)/(v−b)−a/[RT1.5(v+b)] In previous works, the superiority of the MMM has been shown over the vdW family of EOSs for PVT and VLE calculations. In this work, a new simple functional form for its attractive and repulsive parameters [a(T) and b(T)] is introduced. The proposed EOS is applied to vapor pressure and saturated density calculations of different pure fluids. Then, the proposed equation is used to calculate high-pressure PVT of heavy hydrocarbons. The performance of the proposed EOS for VLE calculations is examined against the corresponding experimental measurements for a number of binary mixtures and the results are compared with those obtained from the cubic EOSs frequently used for thermodynamic and fluid phase equilibrium calculations. The comparisons indicate the modified MMM EOS is quite suitable for property predictions of gas and liquid systems, especially for high-pressure PVT of heavy hydrocarbon systems of interest in the oil and gas industries.

Optimized Binary Interaction Parameters for VLE Calculations of Natural Gas Mixtures via Cubic and Molecular-Based Equations of State

The objective of this study is to analyze the performance of a selected collection of equations of state (EOS) for the prediction of vapor–liquid equilibrium of the components of a typical natural gas mixture. In this work, 13 biparametric, triparametric, and tetraparametric, widely used simple-cubic-type EOS and three complex, but state-of-the-art, molecular-based EOS are used. A simple, one-fluid-based mixing rule was applied for the extension to mixtures of the models. Binary interaction parameters for the different equations were calculated by correlation of available binary vapor–liquid equilibria data in the experimental literature, in wide temperature–pressure ranges, for the key binary systems relevant to natural gases. The results allow one to infer the performance of the different EOS commonly used for phase equilibria analysis in the natural gas industry, and to study how the different complexity of the studied EOS does (or does not) lead to an improvement in the quality of the predictions.

Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures

Accurate predictive tools for VLE calculation are always needed. A new method is introduced for VLE calculation which is very simple to apply with very good results compared with previously used methods. It does not need any physical property except each binary system need tow constants only. Also, this method can be applied to calculate VLE data for any binary system at any polarity or from any group family. But the system binary should not confirm an azeotrope. This new method is expanding in application to cover a range of temperature. This expansion does not need anything except the application of the new proposed form with the system of two constants. This method with its development is applied to 56 binary mixtures with 1120 equilibrium data point with very good accuracy. The developments of this method are applied on 13 binary systems at different temperatures which gives very good accuracy.

Application of M 4 cubic equation of state for refrigerants

In this work, M 4 cubic equation of state (EOS) (proposed by Mohsen-Nia et al., 2003) is applied to calculate the saturated properties of refrigerants. A wide range of different types of refrigerants (CFCs, HCFCs, HFCS, etc.) is examined by calculating their saturated pressures, saturated liquid and vapor molar volumes. The comparison between the VLE calculation results and the experimental data, shows that the agreement of this EOS is better than two frequently-used (SRK and PR) EOSs for 42 refrigerants and some of their mixtures.