Modeling the phase equilibria of hydrogen sulfide and carbon dioxide in mixture with hydrocarbons and water using the PCP-SAFT equation of state

The perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state is applied to correlate phase equilibria for mixtures of hydrogen sulfide (H₂S) and carbon dioxide (CO₂) with alkanes, with aromatics, and with water over wide temperature and pressure ranges. The binary mixtures of H₂S–methane and CO₂–methane are studied in detail including vapor–liquid, liquid–liquid and fluid–solid phase equilibria. Very satisfying results were obtained for the binary mixtures as well as for the ternary mixture of H₂S–CO₂–methane using the (constant) interaction parameters of the binary pairs.     

Hydrate-containing phase equilibria for mixed guests of carbon dioxide and nitrogen

Hydrate-containing phase equilibria for mixtures composed of carbon dioxide, nitrogen and water are of potential importance for the flow assurance in the transportation of captured carbon dioxide. Literature data for such mixture tend to be reported on water free basis. In this study three- and four-phase equilibria were experimentally studied at the pressure ranging from 5 to 20 MPa. Isobaric dissolution temperatures of formed hydrates were measured and reported for accurately determined loading compositions. Complex phase behaviors composed of two-, three- and four- phases were observed and they were analyzed by comparing with calculations using GSMGem program developed by Sloan and Koh [1]. Phase equilibria were found to be sensitive to water contents in water dominating mixtures. CSMGem and HYSYS (version 7.1) from AspenTech calculations were found in general agreements with present and literature data.     

Phase equilibria in carbon dioxide expanded solvents: Experiments and molecular simulations

We present complementary molecular simulations and experimental results of phase equilibria for carbon dioxide expanded acetonitrile, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. The volume expansion measurements were done using a high-pressure Jerguson view cell. Molecular simulations were performed using the Gibbs ensemble Monte Carlo method. Calculations in the canonical ensemble (NVT) were performed to determine the coexistence curve of the pure solvent systems. Binary mixtures were simulated in the isobaric-isothermal distribution (NPT). Predictions of vapor-liquid equilibria of the pure components agree well with experimental data. The simulations accurately reproduced experimental data on saturated liquid and vapor densities for carbon dioxide, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. In all carbon dioxide expanded liquids (CXL's) studied, the molecular simulation results for the volume expansion of these binary mixtures were found to be as good as, and in many cases superior to, predictions based on the Peng-Robinson equation of state, demonstrating the utility of molecular simulation in the prediction of CXL phase equilibria.     

Representation for binary mixtures of n-alcohols + sub and supercritical CO2 by a group-contribution method

In order to represent vapour–liquid equilibria of binary n-alcohol–carbon dioxide mixtures the excess function-equation of state method is used in which carbon dioxide is described by the IUPAC equation of state and alcohols by a Peng–Robinson type equation where the attractive parameter is estimated by a group-contribution method. The excess function is of the Van Laar type in which the interaction parameters are calculated by a group-contribution method. This approach allows to correlate and predict with quite good accuracy VLE of binary systems of alcohols and CO₂, even for heavier alcohols.     

Vapor-liquid and vapor-liquid-liquid equilibria of carbon dioxide/n-perfluoroalkane/n-alkane ternary mixtures

Perfluoroalkanes have numerous applications (e.g., in the medical field and the chemical industry), and their high affinity for carbon dioxide makes them attractive as surfactants and cosolvents. Although research in this area has grown in the past few years, very little phase-equilibrium data is available in the open literature for these systems. In this work, we present, for the first time, predictions of vapor-liquid and vapor-liquid-liquid equilibria of binary and ternary systems of carbon dioxide/n-perfluoroalkane/n-alkane. Our results are based on the SAFT-VR EOS (statistical associating fluid theory of variable range, equation of state), and we study the influence of temperature, pressure, composition, and chain length on the phase diagram. The predicted phase diagrams are based on temperature-independent binary interaction parameters, and no ternary parameters are introduced. Comparisons to the available experimental and molecular simulation data show that the predicted diagrams should provide a good representation of the phase equilibria.     

A new approach in modelling phase equilibria and gas solubility in electrolyte solutions and its applications to gas hydrates

This paper presents a new predictive model for phase equilibria and gas solubility calculations in the presence of electrolyte solutions. It treats salts as pseudo-components in an equation of state (EoS) by defining the critical properties and acentric factor for each salt. The water–salt, gas–salt and salt–salt binary interaction parameters (BIP) have been determined by using available experimental data on freezing point depression and boiling point elevation as well as gas solubility and salt solubility data in saline solutions.The methodology has been applied in modelling sodium chloride, potassium chloride and their mixtures, as well as solubility of methane and carbon dioxide in aqueous single and mixed electrolyte solutions.The developed model is capable of accurately predicting the phase behaviour, gas hydrate stability zone and potential salt precipitation in single and mixed electrolyte solutions. The model predictions are compared with available independent experimental data, including hydrate inhibition characteristics of single and mixed electrolyte solutions, and good agreement is demonstrated.     

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.     

Vapor-liquid equilibria with supercritical gases calculated by the excess Gibbs energy method

Vetere, A., 1986. Vapor-liquid equilibria with supercritical gases calculated by the excess Gibbs energy method. Fluid Phase Equilibria, 28: 265–281.A thermodynamic method for vapor-liquid equilibria calculations of mixtures containing supercritical components is described. According to the proposed method the Raoult law is assumed as a reference point also for the supercritical gases, and the non-ideality of the liquid phase is represented by using the NRTL equation in the one parameter form.The vapor phase is described by applying the Redlich-Kwong equation. Literature data of 10 binary systems formed by N₂, CH₄, CO₂, H₂S and CH₃OH are correlated by applying the new procedure. The binary interaction parameters calculated for these systems are used for the prevision of one ternary and two quaternary systems formed by the cited gas in methanol, which is an industrial solvent used for the purification of natural streams from the sour gases.Rules are given to describe the dependence on temperature of the binary interaction parameters.     

High-pressure phase equilibria for the carbon dioxide–2-methyl-1-butanol,carbon dioxide–2-methyl-2-butanol,carbon dioxide–2-methyl-1-butanol–water,and carbon dioxide–2-methyl-2-butanol–water systems

High-pressure vapor–liquid equilibria for the binary carbon dioxide–2-methyl-1-butanol and carbon dioxide–2-methyl-2-butanol systems were measured at 313.2 K. The phase equilibrium apparatus used in this work is of the circulation type in which the coexisting phases are recirculated, on-line sampled, and analyzed. The critical pressure and corresponding mole fraction of carbon dioxide for the binary carbon dioxide–2-methyl-1-butanol system at 313.2 K were found to be 8.36 MPa and 0.980, respectively. The critical point of the binary carbon dioxide–2-methyl-2-butanol was also found 8.15 MPa and 0.970 mole fraction of carbon dioxide. In addition, the phase equilibria of the ternary carbon dioxide–2-methyl-1-butanol–water and carbon dioxide–2-methyl-2-butanol–water systems were measured at 313.2 K and several pressures. These ternary systems showed the liquid–liquid–vapor phase behavior over the range of pressure up to their critical point. The binary equilibrium data were all reasonably well correlated with the Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), and Patel–Teja (PT) equations of state with eight different mixing rules the van der Waals, Panagiotopoulos–Reid (P&R), and six Huron–Vidal type mixing rules with UNIQUAC parameters.     

Application of the perturbed Lennard–Jones chain equation of state to solute solubility in supercritical carbon dioxide

The perturbed Lennard–Jones chain (PLJC) equation of state is a thermodynamic model based on the perturbation theory of liquid state. This equation has been shown in the past to be a successful model for phase equilibria calculations of binary and ternary fluid mixtures and polymer solutions. In this work, we employed for the first time the PLJC equation to model the solubility of 39 solids in supercritical carbon dioxide. It was shown that the model achieves good correlation with three temperature independent parameters. A comparison of the PLJC with the commonly used Peng–Robinson equation reveals the PLJC equation gives better correlation to the solubility data than the Peng–Robinson model that utilizes temperature dependent parameters.     

Binary phase behavior and aggregation of dilute methanol in supercritical carbon dioxide: a Monte Carlo simulation study

Configurational-bias Monte Carlo simulations in the Gibbs and isobaric-isothermal ensembles using the transferable potentials for phase equilibria force field were carried out to investigate the thermophysical properties of mixtures containing supercritical carbon dioxide and methanol. The binary vapor-liquid coexistence curves were calculated at 333.15 and 353.15 K and are in excellent agreement with experimental measurements. The self-association of methanol in supercritical carbon dioxide was investigated over a range of temperatures and pressures near the mixture critical point. The temperature dependence of the equilibrium constants for the formation of hydrogen-bonded aggregates (from dimer to heptamer) allowed for the determination of the enthalpy of hydrogen bonding, DeltaHHB, in supercritical carbon dioxide with values for DeltaHHB of about 15 kJ mol(-1) falling within the range of previously proposed values. No strong pressure dependence was observed for the formation of aggregates. Apparently the decrease of the entropic penalty and of the enthalpic benefit upon increasing pressure or solvent density mostly cancel each other's effect on aggregate formation.     

The Effect of Functional Groups on the Phase Behavior of Carbon Dioxide Binaries and Their Role in CCS

In recent years we have focused our efforts on investigating various binary mixtures containing carbon dioxide to find the best candidate for CO₂ capture and, therefore, for applications in the field of CCS and CCUS technologies. Continuing this project, the present study investigates the phase behavior of three binary systems containing carbon dioxide and different oxygenated compounds. Two thermodynamic models are examined for their ability to predict the phase behavior of these systems. The selected models are the well-known Peng–Robinson (PR) equation of state and the General Equation of State (GEOS), which is a generalization for all cubic equations of state with two, three, and four parameters, coupled with classical van der Waals mixing rules (two-parameter conventional mixing rule, 2PCMR). The carbon dioxide + ethyl acetate, carbon dioxide + 1,4-dioxane, and carbon dioxide + 1,2-dimethoxyethane binary systems were analyzed based on GEOS and PR equation of state models. The modeling approach is entirely predictive. Previously, it was proved that this approach was successful for members of the same homologous series. Unique sets of binary interaction parameters for each equation of state, determined for the carbon dioxide + 2-butanol binary model system, based on k₁₂–l₁₂ method, were used to examine the three systems. It was shown that the models predict that CO₂ solubility in the three substances increases globally in the order 1,4-dioxane, 1,2-dimethoxyethane, and ethyl acetate. CO₂ solubility in 1,2-dimethoxyethane, 1.4-dioxane, and ethyl acetate reduces with increasing temperature for the same pressure, and increases with lowering temperature for the same pressure, indicating a physical dissolving process of CO₂ in all three substances. However, CO₂ solubility for the carbon dioxide + ether systems (1,4-dioxane, 1,2-dimethoxyethane) is better at low temperatures and pressures, and decreases with increasing pressures, leading to higher critical points for the mixtures. By contrast, the solubility of ethyl acetate in carbon dioxide is less dependent on temperatures and pressures, and the mixture has lower pressures critical points. In other words, the ethers offer better solubilization at low pressures; however, the ester has better overall miscibility in terms of lower critical pressures. Among the binary systems investigated, the 1,2-dimethoxyethane is the best solvent for CO₂ absorption.     

Calculation of vapour-liquid equilibrium of associated systems by an equation of state

A recently proposed equation of state of the van der Waals type is applied to calculate phase equilibria in hydrogen-bonding, non-electrolytic systems. Association is accounted for by treating alcohols, acids, etc., as mixtures of associated species formed by up to 14 monomers. The method involves essentially one weakly temperature-dependent adjustable parameter per binary system.The calculations cover vapour-liquid equilibrium both at low and elevated pressure in binary systems formed by an associating substance and a non-associating compound such as a hydrocarbon or halogenated hydrocarbon. An attempt has been made to include all experimental data available for these systems in the literature. A number of calculations for ternary systems as well as of liquid-liquid equilibria are included, and a limited number of solvated systems are also treated.Owing to its single adjustable parameter, the method may be used to test existing experimental data and to predict such data.     

Phase equilibria in systems containing o-cresol,p-cresol,carbon dioxide,and ethanol at 323.15–473.15 K and 10–35 MPa

Phase equilibria in binary and ternary systems containing o-cresol, p-cresol, carbon dioxide, and ethanol have been investigated experimentally at temperatures between 323.15 K and 473.15 K and pressures ranging from 10 MPa to 35 MPa. The experimental results provide a systematic basis of phase equilibrium data, yielding the effect of temperature on the influence of the position of the methyl groups of cresols that are in phase equilibria with carbon dioxide. Based on the different solubilities of the cresol isomers in carbon dioxide, the separation of o-cresol and p-cresol was investigated. The dependence of the separation factor between both cresol isomers on concentration, temperature, and pressure is obtained from experiments in the ternary system, o-cresol+p-cresol+carbon dioxide. The influence of ethanol added to each of the binary systems, cresol isomer+carbon dioxide, in order to enhance the solubility of the cresols in the carbon dioxide-rich phase is also shown. The experimental data have been correlated using seven different equations of state, whereof four explicitly account for intermolecular association: Statistical Association Fluid Theory (SAFT) by Chapman, Gubbins, Huang and Radosz, the SAFT modification by Pfohl and Brunner for near-critical fluids, a modified cubic-plus-association equation of state (CPA EOS) according to the ideas by Tassios et al., and one of the EOS by Anderko. The mixing rule proposed by Mathias, Klotz, and Prausnitz, with two binary interaction parameters per binary system influencing intermolecular attractive forces, is used for all EOS as a basis for an objective comparison of the EOS.     

The shapes of critical loci of binary fluid mixtures on the p–T plane

The relations between the shapes of the critical loci of binary fluid mixtures and the positions of the critical points of their component fluids on the p–T plane were considered theoretically. The consideration was carried out for vapor–liquid phase equilibria in the model systems without liquid–liquid equilibria. We focused only the relations between the shapes and the tangent of the straight lines connecting the critical points of the component fluids on the p–T plane, and so the effects of the distance between the critical points were out of the scope of this work. The changes in the shapes of the critical loci were classified logically into three patterns. Literature survey has shown that the two patterns exist in the experimental results for several types of mixtures. The shapes of the critical loci of the binary fluid mixtures on the p–T plane are closely related to the relative positions between the critical points of their component fluids.     

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.     

Vapor–liquid equilibria and critical points of the CO2 + 1-hexanol and CO2 + 1-heptanol systems

Vapor–liquid equilibria (VLE), vapor–liquid–liquid equilibria (VLLE) and critical point (CP) data for the carbon dioxide+1-hexanol (at 324.56, 353.93, 397.78, 403.39, 431.82 and 432.45 K up to 20 MPa) and carbon dioxide+1-heptanol (at 313.14, 333.16, 373.32, 411.99 and 431.54 K up to 21 MPa) systems are reported. Phase behavior measurements were made in a new equilibrium cell based on the static-analytic method and capable of measurements up to 60 MPa and 673 K. The Peng–Robinson equation of state (EoS) with the Wong–Sandler mixing rules and temperature independent parameters was able to correlate and extrapolate the VLE for the carbon dioxide+1-hexanol system. However, in order to obtain good agreement with experimental data for the carbon dioxide+1-heptanol system, the mixture EoS parameters were adjusted to the experimental VLE data at each temperature.     

Calculation of critical lines of hydrocarbon/water systems by extrapolating mixing rules fitted to subcritical equilibrium data

The phase behavior of water/hydrocarbon mixtures in a wide range of pressures is important for various applications ranging from reservoir engineering to environmental engineering. In this work, mutual solubility and critical loci of hydrocarbon/water systems are calculated using the Peng–Robinson–Stryjek–Vera cubic equation of state with four mixing rules: (1) van der Waals mixing rules with one binary interaction parameter (vdW-1), (2) van der Waals mixing rules with asymmetric composition dependent binary interaction parameter (vdW-A), (3) Wong–Sandler mixing rules (WS) and (4) second-order modified Huron–Vidal mixing rules (MHV2). It was found that the parameters obtained from correlating liquid–liquid equilibria using different mixing rules would lead to prediction of completely different forms of critical behavior. Unusual branches of critical loci were found with WS and MHV2 mixing rules. Therefore, equation of states models must be used with extreme caution when applied for predicting phase behavior over wide ranges of temperatures and pressures.     

Phasepy: A Python based framework for fluid phase equilibria and interfacial properties computation

Phasepy is a Python based package for fluid phase equilibria and interfacial properties calculation from equation of state (EoS). Phasepy uses several tools (i.e., NumPy, SciPy, Pandas, Matplotlib) allowing use Phasepy under Jupyter Notebooks. Phasepy models phase equilibria with the traditional ϕ –γ and ϕ –ϕ approaches, where ϕ (fugacity coefficient) can be modeled as a perfect gas, virial gas or EoS fluid, whereas γ (activity coefficient) can be described by conventional models (NRTL, Wilson, Redlich-Kister expansion, and the group contribution modified-UNIFAC). Interfacial properties are based on the square gradient theory couple to ϕ –ϕ approach. The available EoSs are the cubic EoS family extended to mixtures through the quadratic, modified-Huron-Vidal, and Wong-Sandler mixing rules. Phasepy allows to analyze phase stability, compute phase equilibria, interfacial properties, and optimize their parameters for vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria for multicomponent mixtures. Phasepy implementation, and robustness are illustrated for binary and ternary mixtures.