Modeling the phase behavior of commercial biodegradable polymers and copolymer in supercritical fluids

Biodegradable polymers have received much attention as materials for reducing environmental problems caused by conventional plastic wastes. In this work, the thermodynamic behavior of binary and ternary systems composed by commercial biodegradable polymers and high-pressure fluids [poly(d,l-lactide) + dimethyl ether, poly(d,l-lactide) + carbon dioxide, poly(d,l-lactide) + chlorodifluoromethane, poly(d,l-lactide) + difluoromethane, poly(d,l-lactide) + trifluoromethane, poly(d,l-lactide) + 1,1,1,2-tetrafluoroethane, poly(butylene succinate) + carbon dioxide and poly(d,l-lactide) + dimethyl ether + carbon dioxide] and binary systems formed by commercial biodegradable copolymers and supercritical fluids [poly(butylene succinate-co-butylene adipate) + carbon dioxide] were studied. The Perturbed Chain-SAFT (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic EoS were used to model the liquid–fluid equilibrium (LFE) for these binary systems, by fitting one temperature-dependent binary interaction parameter. For comparison, the same data were also modeled by using the traditional Peng–Robinson (PR) cubic EoS. The three pure-component parameters of PC-SAFT and SL EoS and two pure-component of PR EoS were regressed by fitting pure-component data (liquid pressure–volume–temperature data for polymers and copolymer and vapor pressure and saturated liquid molar volume for fluids). The estimation of pure-component and binary interaction parameters was performed by using the modified maximum likelihood method with an objective function that includes the cloud point pressure. An excellent agreement was obtained with the PC-SAFT EoS, while the performance of the SL and PR EoS was less satisfactory.     

Vapor–liquid equilibria for the ternary system of carbon dioxide + ethanol + ethyl acetate at elevated pressures

Vapor–liquid equilibrium (VLE) data for the ternary system of carbon dioxide, ethanol and ethyl acetate were measured in this study at 303.2, 308.2, and 313.2 K, and at pressures from 4 to 7 MPa. A static type phase equilibrium apparatus with visual sapphire windows was used in the experimental measurements. New VLE data for CO₂ in the mixed solvent were presented. These ternary VLE data at elevated pressures were also correlated using either the modified Soave–Redlich–Kwong or Peng–Robinson equation of state, with either the van der Waals one-fluid or Huron–Vidal mixing model. Satisfactory correlation results are reported with temperature-independent binary parameters. It is observed that at 313.2 K and 7 MPa, ethanol can be separated from ethyl acetate into the vapor phase at all concentrations in the presence of high pressure CO₂.     

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.     

Modeling of (vapor + liquid) equilibrium and enthalpy of solution of carbon dioxide (CO2) in aqueous methyldiethanolamine (MDEA) solutions

A thermodynamic model was used to estimate enthalpy of solution of carbon dioxide (CO₂) in methyldiethanolamine (MDEA) aqueous solutions. The model was based on a set of equations for chemical equilibria, phase equilibria, charge, and mass balances. Non-ideality in the liquid phase was taken into account by interaction parameters fitted to (vapor + liquid) equilibrium data.The enthalpies of solution of CO₂ were derived from the model using classical thermodynamic relations and were compared to experimental values obtained in previous works.     

Vapor–liquid equilibria for the ternary mixture of carbon dioxide + 1-propanol + propyl acetate at elevated pressures

Vapor–liquid equilibrium (VLE) data for the ternary mixture of carbon dioxide, 1-propanol and propyl acetate were measured in this study at 308.2, 313.2, and 318.2 K, and at pressures ranging from 4 to 10 MPa. A static type phase equilibrium apparatus with visual sapphire windows was used in the experimental measurements. New VLE data for CO₂ in the mixed solvent were presented. These ternary VLE data at elevated pressures were also correlated using either the modified Soave–Redlich–Kwong or Peng–Robinson equation of state (EOS), and by employing either the van der Waals one-fluid or Huron–Vidal mixing model. Satisfactory correlation results from both EOS models are reported with temperature-independent binary interaction parameters. It is observed that at 318.2 K and 10 MPa, 1-propanol may probably be separated from propyl acetate into the vapor phase at the entire concentration range in the presence of high pressure CO₂.     

Modeling of CO2 solubility and carbamate concentration in DEA,MDEA and their mixtures using the Deshmukh–Mather model

The equilibrium of CO₂ and carbamate concentration data for the absorption of CO₂ in aqueous solutions of single and mixed amines was analyzed using the Deshmukh–Mather model. Data on CO₂ loading in aqueous solutions of DEA and MDEA and their mixtures at various temperature (303–323 K) and CO₂ partial pressure (0.09–100 kPa) together with carbamate concentrations in case of DEA and its mixtures with MDEA were fitted simultaneously to generate the different interaction parameters required to calculate the activity coefficients in the model. Using the generated interaction parameters, the model was applied to correlate the CO₂ loading in solutions of DEA and MDEA and their mixtures reported in the literature as well as those obtained in our laboratory and was found to be able to give a good estimation of CO₂ loading and carbamate concentration over a wide range of operating conditions in both single and mixed amine solutions.     

High-pressure phase equilibrium for the binary systems of {carbon dioxide (1) + dimethyl carbonate (2)} and {carbon dioxide (1) + diethyl carbonate (2)} at temperatures of 273 K, 283 K,and 293 K

Phase equilibrium data for the binary systems {carbon dioxide (CO₂) + dimethyl carbonate (DMC)} and {carbon dioxide (CO₂) + diethyl carbonate (DEC)} were measured at temperatures of 273 K, 283 K and 293 K in the pressure range of 0.5 MPa to 4.0 MPa. The measurements were carried out in a cylindrical autoclave with a moveable piston and an observation window. The experimental data were correlated with the Peng–Robison (PR) equation of state (EOS) and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with van der Waals-1 or Panagiotopoulos–Reid mixing rules. The correlations produced reasonable values for the interaction parameters. The comparisons between calculation results and experimental data indicate that the PRSV equation of state coupled with the Panagiotopoulos–Reid mixing rule produced the better correlated results.     

High pressure phase equilibrium for δ-tocopherol + CO2

Vapour–liquid equilibrium compositions were measured for mixtures of δ-tocopherol and carbon dioxide, at pressures from 9 up to 27 MPa, and four temperatures between 306 and 333 K. The system exhibits liquid–liquid equilibrium at high pressures, similarly to previous results for mixtures of α-tocopherol with carbon dioxide. The results were correlated with the Peng–Robinson equation of state, using the Panagiotopoulos–Reid combination rules.Comparison of the solubilities of δ-tocopherol and α-tocopherol in supercritical carbon dioxide was performed using Chrastil’s equation to correlate the data. The number of solvent CO₂ molecules per solute molecule was calculated in both cases. An enthalpy of solvation per mole of CO₂ of −10 kJ mol⁻¹ was obtained.     

Equilibrium solubility of carbon dioxide in the amine solvent system of (triethanolamine + piperazine + water)

In this study, a new set of data for the equilibrium solubility of carbon dioxide in the amine solvent system that consists of triethanolamine (TEA), piperazine (PZ), and water is presented. Equilibrium solubility values were obtained at T = (313.2, 333.2, and 353.2) K and pressures up to 153 kPa using the vapour-recirculation equilibrium cell. The TEA concentrations in the considered ternary (solvent) mixture were (2 and 3) kmol · m^?3 and those of PZ’s were (0.5, 1.0, and 1.5) kmol · m^?3. The solubility data (CO₂ loading in the amine solution) obtained were correlated as a function of CO₂ partial pressure, system temperature, and amine composition via the modified Kent–Eisenberg model. Results showed that the model applied is generally satisfactory in representing the CO₂ absorption into mixed aqueous solutions of TEA and PZ.     

Phase equilibrium data and thermodynamic modeling of the system (CO2 + biodiesel + methanol) at high pressures

The main objective of this work was to investigate the high pressure phase behavior of the binary systems {CO₂(1) + methanol(2)} and {CO₂(1) + soybean methyl esters (biodiesel)(2)} and the ternary system {CO₂(1) + biodiesel(2) + methanol(3)} were determined. Biodiesel was produced from soybean oil, purified, characterized and used in this work. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (303.15 to 343.15) K and pressures up to 21 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.2383 to 0.8666) for the binary system {CO₂(1) + methanol(2)}; (0.4201 to 0.9931) for the binary system {CO₂(1) + biodiesel(2)}; (0.4864 to 0.9767) for the ternary system {CO₂(1) + biodiesel(2) + methanol(3)} with a biodiesel to methanol molar ratio of (1:3); and (0.3732 to 0.9630) for the system {CO₂ + biodiesel + methanol} with a biodiesel to methanol molar ratio of (8:1). For these systems, (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals (PR-vdW2) and Wong-Sandler (PR–WS) mixing rules. Both thermodynamic models were able to satisfactorily correlate the phase behavior of the systems investigated and the PR–WS presented the best performance.     

Modelling of the phase behaviour for the direct synthesis of dimethyl carbonate from CO2 and methanol at supercritical or near critical conditions

This study is focused on modelling the phase equilibrium behaviour of the reaction mixture (CO₂ + methanol + DMC + H₂O) at high pressure–temperature conditions using the Patel–Teja (PT) and Peng–Robinson–Stryjek–Vera (PRSV) equations of state along with the van der Waals One-Fluid (1PVDW) mixing rule. The optimum values of the binary interaction parameters (k_ij) were calculated from VLE data found in the literature, and then adjusted to a lineal temperature equation. As a result, the temperature-dependent model was applied to predict the fluid phase equilibria of the corresponding binary a ternary sub-systems and, later, successfully contrasted with experimental data. In addition, phase equilibrium data were experimentally measured at high pressure (8 MPa to 15 MPa) for the ternary system (CO₂ + methanol + DMC), in order to confirm the ability of the model to predict the phase behaviour of the ternary system at high pressure–temperature. The agreement between the experimental data and the proposed model enables to predict the phase equilibrium behaviour of the mixture (CO₂ + methanol + DMC + H₂O), and thus, optimise the operation conditions in several reaction and separation processes.     

Measurement and thermodynamic modeling of the phase equilibrium of aqueous N-methyldiethanolamine solutions

Isobaric vapor–liquid equilibrium (VLE) measurements at 40.0, 53.3 and 66.7 kPa (300, 400 and 500 mmHg) of aqueous N-methyldiethanolamine (MDEA) solutions were performed using a modified ebulliometer. The concentration of MDEA in the liquid phase ranged from about 0.06 to 0.93 in mole fraction and the temperatures from about 76 to 186 °C. The data measured in this work, along with other experimental data taken from the literature, are used for the improvement of the thermodynamic modeling of the water/MDEA binary system.     

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).     

Phase equilibrium measurements and modelling of ternary system (carbon dioxide + ethanol + palmitic acid)

This work reports phase equilibrium measurements for the ternary system (palmitic acid + ethanol + CO₂). The motivation of this research relies on the fact that palmitic acid is the major compound of several vegetable oils. Besides, equilibrium data for palmitic acid in carbon dioxide using ethanol as co-solvent are scarce in the literature. Phase equilibrium experiments were performed using a high-pressure variable-volume view cell over the temperature range of (303 to 343) K and pressures up to 20 MPa and mole fraction of palmitic acid from 0.0199 to 0.2930. Vapour–liquid and solid–fluid transitions were visually observed for the system studied. The Peng–Robinson equation of state, with the classical van der Waals quadratic mixing rule was employed for thermodynamic modelling of the system investigated with a satisfactory agreement between experimental and calculated values.     

Phase behavior of (CO2 + methanol + lauric acid) system

In this study the phase equilibrium behaviors of the binary system (CO₂ + lauric acid) and the ternary system (CO₂ + methanol + lauric acid) were determined. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (293 to 343) K and pressures up to 24 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.7524 to 0.9955) for the binary system (CO₂ + lauric acid); (0.4616 to 0.9895) for the ternary system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (2:1); and (0.3414 to 0.9182) for the system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (6:1). For these systems (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid), and (solid + fluid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals mixing rule with a satisfactory correlation between experimental and calculated values.     

(Vapour + liquid) equilibria (VLE) of CO2 in aqueous solutions of 2-amino-2-methyl-1-propanol: New data and modelling using eNRTL-equation

This work presents new experimental results for carbon dioxide (CO₂) solubility in aqueous 2-amino-2-methyl-1-propanol (AMP) over the temperature range of (298 to 328) K and CO₂ partial pressure of about (0.4 to 1500) kPa. The concentrations of the aqueous AMP lie within the range of (2.2 to 4.9) mol · dm^?3. A thermodynamic model based on electrolyte non-random two-liquid (eNRTL) theory has been developed to correlate and predict the (vapour + liquid) equilibrium (VLE) of CO₂ in aqueous AMP. The model predictions have been in good agreement with the experimental data of CO₂ solubility in aqueous blends of this work as well as those reported in the literature. The current model can also predict speciation, heat of absorption, enthalpy of CO₂ loaded aqueous AMP, pH of the loaded solution, and AMP volatility.     

Binary and ternary solubilities of disperse dyes and their blend in supercritical carbon dioxide

Binary and ternary solubilities of C.I. Disperse Blue 134 (1,4-bis(isopropylamino)anthraquinone) C.I. Disperse Yellow 16 (3-methyl-1-phenyl-5-pyrazolone) and their dye mixture in supercritical carbon dioxide (SC-CO₂) were measured by a flow-type apparatus. The solubility measurements were carried out at the pressure ranges from 10.0 to 25.0 MPa for the binary systems at the temperatures from 323.15 to 383.15 K and for the ternary system at 383.15 K. An empirical equation was used to correlate the experimental binary solubilities of the dyes in terms of the density of carbon dioxide. To represent accurately the binary solubility of the dyes in terms of temperature and pressure, we used a modified Peng–Robinson–Stryjek–Vera equation of state (PRSV EOS). The ternary solubilities of the dye blend could be predicted successfully from binary parameters with the modified PRSV EOS.     

Phase equilibria in ternary (carbon dioxide + tetrahydrofuran + water) system in hydrate-forming region: Effects of carbon dioxide concentration and the occurrence of pseudo-retrograde hydrate phenomenon

In the present work, the three- and four-phase hydrate equilibria of (carbon dioxide (CO₂) + tetrahydrofuran (THF) + water) system are measured by using Cailletet equipment in the temperature and pressure range of (272 to 292) K and (1.0 to 7.5) MPa, respectively, at different CO₂ concentration. Throughout the study, the concentration of THF is kept constant at 5 mol% in the aqueous solution. In addition, the fluid phase transitions of L_W–L_V–V → L_W–L_V (bubble point) and L_W–L_V–V → L_W–V (dew point) are determined when they are present in the ternary system. For comparison, the three-phase hydrate equilibria of binary (CO₂ + H₂O) are also measured. Experimental measurements show that the addition of THF as a hydrate promoter extends hydrate stability region by elevating the hydrate equilibrium temperature at a specified pressure. The three-phase equilibrium line H–L_W–V is found to be independent of the overall concentration of CO₂. Contradictory, at higher pressure, the phase equilibria of the systems are significantly influenced by the overall concentration of CO₂ in the systems. A liquid–liquid phase split is observed at overall concentration of CO₂ as low as 3 mol% at elevated pressure. The region is bounded by the bubble-points line (L_W–L_V–V → L_W–L_V), dew points line (L_W–L_V–V → L_W + V) and the four-phase equilibrium line (H + L_W + L_V + V). At higher overall concentration of CO₂ in the ternary system, experimental measurements show that pseudo-retrograde behaviour exists at pressure between (2.5 and 5) MPa at temperature of 290.8 K.     

Correlation of CO2 solubility in N-methyldiethanolamine + piperazine aqueous solutions using extended Debye–Hückel model

Solubility data of CO₂ in aqueous N-methyldiethanolamine (MDEA) solutions of concentration (2.52, 3.36, and 4.28) kmol/m³ were obtained at temperatures (313, 323, and 343) K and partial pressures ranging from about (30 to 5000) kPa. A thermodynamic model based on extended Debye–Hückel theory was applied to predict and correlate of CO₂ solubility in various aqueous amine solutions. The effect of piperazine (PZ) concentration on CO₂ loading in MDEA solutions was determined at PZ concentration (0.36, 0.86, and 1.36) kmol/m³. Using experimental data in various temperatures the interaction parameters of activity coefficient model for these systems were determined. The results show the model consistency with experimental and literature data and PZ is beneficial to the CO₂ loading. The comparison of results of this study with previous data work shows the wide range of CO₂ loading considered in this work and the better agreement of model with experimental data. The average absolute relative deviation percent (δ_AAD) for all data points were 8.11%.