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.     

New (p, ρ, T) data for carbon dioxide – Nitrogen mixtures from (250 to 400) K at pressures up to 20 MPa

Comprehensive (p, ρ, T) measurements on two binary mixtures (0.10 CO₂ + 0.90 N₂ and 0.15 CO₂ + 0.85 N₂) were carried out in the gas phase at seven isotherms between (250 and 400) K and pressures up to 20 MPa using a single sinker densimeter with magnetic suspension coupling. A total of 69 (p, ρ, T) data for the first mixture and 69 (p, ρ, T) data for the second are presented in this article. The uncertainty in density was estimated to be (0.02 to 0.15)%, while the uncertainty in temperature was 3.9 mK and the uncertainty in pressure was less than 0.015% (coverage factor k = 2). Experimental results were compared with densities calculated from the GERG equation of state and with data reported by other authors for similar mixtures. Results yielded that, while deviations between experimental data and values calculated from the GERG equation were lower than 0.05% in density for low pressures, the relative error at high pressures and low temperatures increased to about (0.2 to 0.3)%. The main aim of this work was to contribute to an accurate density data base for CO₂/N₂ mixtures and to check or improve equations of state existing for these binary mixtures.     

New (p, ρ, T) data for carbon dioxide – Nitrogen mixtures from (250 to 400) K at pressures up to 20 MPa

Comprehensive (p, ρ, T) measurements on two binary mixtures (0.10 CO₂ + 0.90 N₂ and 0.15 CO₂ + 0.85 N₂) were carried out in the gas phase at seven isotherms between (250 and 400) K and pressures up to 20 MPa using a single sinker densimeter with magnetic suspension coupling. A total of 69 (p, ρ, T) data for the first mixture and 69 (p, ρ, T) data for the second are presented in this article. The uncertainty in density was estimated to be (0.02 to 0.15)%, while the uncertainty in temperature was 3.9 mK and the uncertainty in pressure was less than 0.015% (coverage factor k = 2). Experimental results were compared with densities calculated from the GERG equation of state and with data reported by other authors for similar mixtures. Results yielded that, while deviations between experimental data and values calculated from the GERG equation were lower than 0.05% in density for low pressures, the relative error at high pressures and low temperatures increased to about (0.2 to 0.3)%. The main aim of this work was to contribute to an accurate density data base for CO₂/N₂ mixtures and to check or improve equations of state existing for these binary mixtures.     

Vapor–liquid critical properties of multi-component mixtures containing carbon dioxide and n-alkanes

Vapor–liquid critical temperatures, pressures and densities of multi-component mixtures containing CO₂ and n-alkanes (C4–C7) were measured in a high-pressure view cell by direct visual observations. The molar ratio of alkanes was fixed during the experiment while the composition of CO₂ was varied over the whole range. The critical loci show type I fluid phase behavior if the n-alkanes mixture is treated as a pseudo-continuous component, while correspondingly, CO₂ is a discrete component. The critical properties were calculated by Redlich–Kwong–Soave equation of state (SRK) combined with a renormalization group correction (RG). The predictions of critical properties by SRK + RG are in good agreement with the experimental results.     

Relationship between the density of supercritical CO<Subscript>2</Subscript> + ethanol binary system and its critical properties

The dependent relation between temperature and pressure of supercritical CO₂+ ethanol binary system under the pressure range from 5 to 10 MPa with the variety of densities and mole fractions of ethanol that range from 0 to 2% was investigated by the static visual method in a constant volume. The critical temperature and pressure were experimentally determined simultaneously. The PTρ figures at different ethanol contents were described based on the determined pressure and temperature data, from which pressure of supercritical CO₂ + ethanol binary system was found to increase linearly with the increasing temperature. P-T lines show certain convergent feature in a specific concentration of ethanol and the convergent points shift to the region of higher temperature and pressure with the increasing ethanol compositions. Furthermore, the effect of density and ethanol concentration on the critical point of CO₂ + ethanol binary system was discussed in details. Critical points increase linearly with the increasing mole fraction of ethanol in specific density and critical points change at different densities. The critical compressibility factors Z_c of supercritical CO₂ + ethanol binary systems at different compositions of ethanol were calculated and Z _c -ρ figure was obtained accordingly. It was found from Z _c -ρ figure that critical compressibility factors of supercritical CO₂ unitary or binary systems decline linearly with the increasing density, by which the critical point can be predicted precisely.     

Equilibrium solubility of carbon dioxide in a 30 wt.% aqueous solution of 2-((2-aminoethyl)amino)ethanol at pressures between atmospheric and 4400 kPa: An experimental and modelling study

New experimental equilibrium data were obtained for the solubility of carbon dioxide in an aqueous solution with 30 wt.% of 2-((2-aminoethyl)amino)ethanol (AEEA) at temperatures ranging from (313.2 to 368.2) K and CO₂ partial pressures ranging from above atmospheric to 4400 kPa. A thermodynamic model based on the Deshmukh–Mather method was applied to correlate and predict the CO₂ solubility in aqueous AEEA solutions. The binary interaction parameters and equilibrium constants for the proposed reactions were determined by data regression. Using the adjusted parameters, equilibrium partial pressures of CO₂ were calculated and compared with the corresponding experimental values at the selected temperatures and pressures. Values of carbon dioxide solubility at other temperatures reported in the literature were also calculated. The average absolute deviation for all of the data points was found to be 8.2%. The enthalpy change of the absorption of CO₂ in the 30 wt.% aqueous solution of AEEA was also estimated with our model.     

Joule-Thomson coefficients and Joule-Thomson inversion curves for pure compounds and binary systems predicted with the group contribution equation of state VTPR

In this work the accuracy of the prediction of Joule-Thomson coefficients for the gases CO₂ and Ar and the binary systems CO₂-Ar and CH₄-C₂H₆ was examined using the group contribution equation of state VTPR. Furthermore the experimental and correlated data of Joule-Thomson inversion curves of a few compounds including carbon dioxide, nitrogen, benzene, toluene, methane, ethane, ethylene, propyne, and SF₆ were compared with the results of the group contribution equation of state VTPR, the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR) and the Helmholtz equation of state (HEOS). Moreover, Joule-Thomson inversion curves for pure fluids, binary (CH₄-C₂H₆, N₂-CH₄, CO₂-CH₄), and ternary systems (CO₂-CH₄-N₂, CH₄-C₂H₆-N₂, CO₂-CH₄-C₂H₆) were calculated with VTPR and compared to the results of SRK, PR, HEOS and the molecular simulation results of Vrabec et al. It was found that the calculated values for the Joule-Thomson coefficients and Joule-Thomson inversion curves are in good agreement with the experimental findings.     

Liquid-liquid equilibria in 2-methoxyethanol+alkane systems: I. Experimental results at pressures up to 400 MPa

In an optical high-pressure autoclave with sapphire windows and magnetic stirring, liquid-liquid equilibria and critical curves in binary systems of 2- methoxyethanol and different alkanes were measured in the temperature range 250–430 K and at pressures from 0.1–400 MPa. For all systems investigated upper critical solution temperatures and lower critical solution pressures were found. The upper critical solution temperature increases with increasing molecular weight of the alkane and decreases with increasing number of CH₃-groups of the alkane.     

Phase compositions and saturated densities for the binary systems of carbon dioxide with ethanol and dichloromethane

The compositions and densities of the liquid and vapor phases of two binary systems at equilibrium were measured on a new experimental apparatus over a range of temperatures and pressures. The studied systems are: CO₂–ethanol at 313.2 and 328.2 K; CO₂–dichloromethane at 308.2, 318.2 and 328.2 K and for pressures ranging from ambient up to ca. 9 MPa. Some of our measurements are critically compared with corresponding literature values. These measurements are ideally suited for testing equation-of-state models. The recently developed quasi-chemical hydrogen-bonding (QCHB) model was used for correlating the experimental data. A satisfactory agreement was obtained between experimental and calculated phase compositions and saturated densities.     

(p,V,T) Behaviour and miscibility of (polysulfone+THF+carbon dioxide) at high pressures

The (p,V,T) behaviour and the miscibility of polysulfone in binary fluid mixtures of tetrahydrofuran (THF) and carbon dioxide (CO₂) have been investigated in the temperature range from (300 to 425) K at pressures up to 70 MPa. Densities of polysulfone solutions (mass fraction=0 to 0.496) in a solvent mixture of THF and CO₂ with a mass fraction of CO₂ of 0.1 were determined as a function of pressure from the homogeneous one-phase region through the phase separation point into the two-phase region at selected temperatures. The densities at the demixing pressures at these temperatures were also determined. No significant changes in density were found across the phase boundary, indicating that coexisting phases must have similar densities, which is often the case with (liquid+liquid) phase separation in high-pressure systems. The variations of density or specific volume with polymer concentration have also been investigated at selected temperatures and pressures. The data show unique features which are helpful in understanding the phase behaviour of this system which shows multiple miscibility windows. The isothermal compressibility of the polymer solutions as determined from the density data does not show any significant dependence on polymer concentrations. The compressibilities display the expected decrease with pressure and increase with temperature.     

Phase equilibrium calculations for carbon dioxide + n-alkanes binary mixtures with the Wong–Sandler mixing rules

Phase equilibrium for carbon dioxide + n-alkanes (from methane to n-decane) asymmetric binary systems was calculated using Peng–Robinson Stryjek–Vera equation of state coupled with Wong–Sandler mixing rules. NRTL model was utilized for predicting the excess Helmholtz free energy. The second virial coefficient binary interaction parameter k₁₂ and NRTL model parameters τ₁₂ and τ₂₁ for carbon dioxide + n-alkanes binary systems were optimized trough minimization of two different objective functions: one based on the calculation of the distribution coefficients, and the other one based on the determination of bubble point pressures. Generalized correlations for mixing rule parameters as a function of the n-alkane acentric factor and the equilibrium temperature were obtained from optimal parameters determined by the first objective function. Obtained results using both objective functions were satisfactory, but the estimation of the parameters calculated by the second objective function provided a better accuracy in vapor–liquid equilibrium prediction.     

High pressure phase behavior in systems containing CO2 and heavier compounds with similar vapor pressures

The separation of the para and ortho isomers of xylene as well as the azeotropic mixture of butyl ether/o-xylene using carbon dioxide at high pressure was investigated. The phase behavior of carbon dioxide and each of these compounds along with the ternary systems; CO₂/p-xylene/o-xylene and CO₂/butyl ether/o-xylene were experimentally determined. The relative volatilities of p-xylene to o-xylene in the CO₂/p-xylene/o-xylene system compared favorably with those obtained in distillation. The results also indicated a substantial shift in the butyl ether/o-xylene azeotrope to higher butyl ether concentrations in the presence of carbon dioxide thus indicating a potential for the separation of these mixtures using carbon dioxide at low temperatures. Thermodynamic models using the Peng—Robinson equation of state were developed and better predictions of the bubble point pressures were obtained when the interaction parameter, δ_ij, was allowed to vary with phase density. This approach results in an analytically solvable quartic equation in volume and gives different δ_ij's for the vapor and liquid phases. In this model, the temperature dependence of the binary interaction parameter is contained within its density dependence and, δ_ij's obtained from fitting VLE data at a single temperature could be used for accurate prediction of equilibrium data at other temperatures. The results of such predictions were better than predictions obtained by fitting the actual data using the conventional VDW-1 mixing rules.     

Modeling the high-pressure phase equilibria of carbon dioxide–triglyceride systems: A parameterization strategy

The group contribution equation of state (GC-EOS) has been used in several published works to correlate or predict the high-pressure phase equilibria of a variety of systems of practical interest. Nevertheless, quantitative and even qualitative disagreement among predictions and experimental data has been detected in mixtures of CO₂ with heavy compounds, such as triglycerides, when operating at high pressure. For instance, phase split up to indefinitely high pressures has been computed, when the observed experimental behavior shows full miscibility at sufficiently high pressure. In the present work, we study the influence on calculated critical lines and solubilities (Pxy diagrams) of the group-based interaction parameters k_ij, for the interactions of CO₂ with both, the triglyceride (TG) group and the paraffinic groups. Based on such study, we propose a parameterization procedure that improves upon the conventional parameter regression practice. The distinguishing feature of such procedure is the repeated observation of the global phase equilibrium behavior, studying in particular the effect of the group–group interaction parameters on critical lines, on the composition of the phases at equilibrium along liquid–liquid–vapor lines, and on selected isothermal or isobaric phase equilibrium diagrams. For the case of the non-randomness parameter, we use a universal positive value, more consistent with its physical meaning.     

Phase behavior of diisobutyl adipate–carbon dioxide mixtures

Phase equilibrium data are reported for diisobutyl adipate (DiBA) in CO₂ at temperatures from 25 to 150 °C. This system exhibits a continuous mixture-critical curve with a maximum near 200 °C and 260 bar. The phase behavior of the DiBA–CO₂ system is well characterized and modeled with the Peng–Robinson equation of state using a single, fixed binary interaction parameter, k_ij. The DiBA–CO₂ data are compared to other solute–CO₂ systems with structures similar to DiBA to demonstrate the impact of the diester end groups in DiBA, which enhance DiBA solubility in CO₂ at low temperatures, relative to a single (ethyl laurate) or no ester end groups (tetradecane), and a single acid end group (tetradecanoic acid). DiBA–CO₂ data are also compared to data for two compounds each with diester groups but one containing an interior aromatic group (dibutyl phthalate) and the other containing the same number of interior carbon groups but with two less carbon groups at either end of the chain (divinyl adipate).     

Adsorption of Sulfur Dioxide from Pseudo Binary Mixtures on Hydrophobic Zeolites: Modeling of the Breakthrough Curves

The adsorption of SO₂ from pseudo binary mixtures with water and CO₂ on hydrophobic zeolites (MFI and MOR type) was investigated using the breakthrough curve method. The SO₂ and water breakthrough curves were compared with theoretical ones based on an axially dispersed plug flow through the column and the linear driving force rate equation. In addition, different semi-predictive multi-component equilibrium equations were used for the breakthrough modeling: Langmuir 1, Langmuir 2 and Langmuir-Freundlich extended models. The overall mass transfer coefficients were derived by matching theoretical with experimental breakthrough curves for single component systems, i.e., water vapor or SO₂ in a carrier gas. They were also predicted from a simplified bi-porous adsorbent model and compared with experimentally derived values. The presence of CO₂ species in ternary mixtures with water vapor and SO₂, even at relatively high concentrations of 9 vol%, had no significant effect on the breakthrough behavior of the other two species. For that reason the CO₂ species was ignored in the analysis of the resulting pseudo binary mixtures. The breakthrough model was solved by finite element orthogonal collocation method using the commercial software gPROMS. Both extended Langmuir 1 and Langmuir 2 based models gave reasonable predictions of the water and SO₂ breakthrough curves for pseudo binary mixtures involving a mordenite sample for all water concentration levels used in this study (up to 3.5 vol%). However, the same models were successfully used to predict SO₂ breakthrough curves for a MFI sample only at low water concentrations, i.e., 1.5 vol%. At the higher water levels both models failed to describe equilibrium behavior in the MFI sample due to the introduction of multi-layer adsorption in the interstices between small MFI-26 crystals.     

Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k₁₂ of the second virial coefficient and non-random two liquid model parameters τ₁₂ and τ₂₁ were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO₂ + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.     

The limited miscibility of liquids at high pressures

An accurate equation of state has been utilized to model miscibility gaps for binary liquid mixtures at high pressures. The hypothetical system studied here is an argon + argon system with imposed specific interactions. In addition to the known effects of electrostatic interactions, which may produce an upper or both an upper and a lower critical solution temperature, a strong effect on the shape of the miscibility gap is found to arise from the value of the mixture collision diameter σ_ij, determined by the constant k_ij. When k_ij is assumed to be a function of pressure (or of reduced density), it is possible to model the rare case of a miscibility gap that vanishes with increasing pressure and then reappears at very high pressures.     

Equation of state for the NH3−H2O system

An equation of state (EOS) for the NH₃–H₂O system has been developed. This EOS incorporates a highly accurate end-member EOS and on an empirical mixing rule. The mixing rule is based on an analogy with high order contributions to the virial expansion for mixtures. Comparison with experimental data indicates that the mixed system EOS can predict both phase equilibria and volumetric properties for this binary system with accuracy close to that of the experimental data from 50°C and 1 bar to critical temperatures and pressures.     

High pressure vapor–liquid equilibrium measurements of carbon dioxide with naphthalene and benzoic acid

High pressure vapor–liquid equilibrium data for binary systems of carbon dioxide with naphthalene and benzoic acid were measured at three different temperatures for each system. Experimental temperatures and pressures ranged from 373 to 458 K and 0 to 22 MPa, respectively. Dew points were also measured for naphthalene in the CO₂ rich region. The data measured provides valuable solubility information and is used to derive gas–solvent group interaction parameters for the predictive Soave–Redlich–Kwong equation of state.     

Vapor pressures of binary mixtures of carbon dioxide with benzene,n-hexane and cyclohexane up to 7 MPa

The total vapor pressures of three CO₂C₆ hydrocarbon systems; CO₂benzene, CO₂n-hexane, and CO₂cyclohexane systems, have been measured at 273.15, 283.15, 298.15 and 303.15 K over the whole composition range by a bubble point method. For the CO₂n-hexane system, the densities of the liquid mixtures have also been measured. From the data and the calculated results by the Peng—Robinson equation of state, the activity coefficients of CO₂ and the Henry's constants of CO₂ in CO₂C₆ hydrocarbon systems have been obtained. The vapor pressure data have been compared with the results calculated by the Barker's method and by the Peng—Robinson equation of state with the use of four mixing models.