Mathematical modelling of phase equilibria for supercritical CO2 and polyethylene glycol of various molecular weights

The Sanchez–Lacombe equation of state and the Statistical Associating Fluid Theory were applied for modelling the phase equilibrium for the polyethylene glycol–CO₂ systems. The Aspen Plus software was used and polyethylene glycol with various molecular weights was investigated. The results were compared with previously obtained experimental values for solubility. The phase equilibrium was calculated at a temperature of 343 K, in the pressure range of 10–30 MPa and for polyethylene glycol molecular weights from 1000 to 100,000 g/mol. The binary interaction parameters for the models were optimized in order to obtain the best fit between the estimated and the experimental gas solubility data. The results suggest that both models are reliable in describing the phase equilibrium of the polyethylene glycol–CO₂ systems at the proposed conditions. Moreover, the molecular weight of the polymer affects the behaviour of the system, as observed from the variation of solubility values and of binary interaction coefficients.     

Density and viscosity of the binary polyethylene glycol/CO2 systems

Density of CO₂ saturated solutions of polyethylene glycols (PEGs) of different molecular weight was measured in pressure range from 8.0 MPa up to 47.7 MPa at a temperature of 343 K by a volumetric method. To validate the method density of pure CO₂ was measured at different pressures and a temperature of 293 K. The results were compared to the literature data and the accuracy was better than 2%. The density was between 1.17 g/mL for PEG 1000/CO₂ at 14.5 MPa and 1.78 g/mL for the system PEG 4000/CO₂ at 35 MPa. Further, the data were compared to results, obtained by a gravimetric method using magnetic suspension balance (MSB).Viscosity of CO₂ saturated solutions of polyethylene glycols (PEGs) of different molecular weight at different pressures and at a temperature of 343 K was measured using a high pressure view cell. Also a temperature impact on the viscosity of pure PEGs was observed at ambient pressure. After saturating PEG 1500 with 10 MPa of CO₂ pressure its viscosity decreases from 76.6 mPa s to 2.24 mPa s at 333 K. Further addition of CO₂ and increasing the pressure results in even lower viscosity and the highest viscosity reduction was reached at the highest pressure; at 35 MPa viscosity of the system PEG 1500/CO₂ is only 0.665 mPa s.     

Selective boron extraction by polymer supported 2-hydroxylethylamino propylene glycol functions

Boron sorption ability of polymer supported 2-hydroxyethylamino propylene glycol functions was investigated. 2-hydroxyethylamino propylene glycol was prepared by reaction of glycidol with excess ethanolamine in N-methyl, 2-pyrrolidone (NMP). This was reacted with terpolymer of glycidyl metacrylate (0.4 mol) with methyl metacrylate (0.5 mol) and divinylbenzene (0.1 mol) which was prepared in spherical beads form (210–422 μm) by suspension polymerization.The resulting terpolymer having hydroxyethylamino propylene glycol functions (1.82 mmol g⁻¹) was found to be as efficient as previously reported iminodipropylene glycol functional resins in removal of trace boron from water. The resin showed a boron loading capacity of 1.6 mmol g⁻¹. Nearly second-order kinetics, with respect to the boric acid (k = 1.65 mol l⁻¹ s⁻¹, with a correlation factor of 0.99129) was determined in non-buffered conditions.It was observed that, more than 95% of boron is extracted by this resin from very dilute H₃BO₃ solution (100 ppm initial concentration) in less than 30 min of contact time. Splitting of sorbed boron can be achieved by simple acid leaching (4 M HCl) and regenerated by NaOH (0.1 M) solution.     

The pH of CO2-saturated water at temperatures between 308 K and 423 K at pressures up to 15 MPa

We report pH measurements for CO₂-saturated water in the pressure range from (0.28 to 15.3) MPa and temperatures from (308.3 to 423.2) K. Commercially available pH and Ag/AgCl electrodes were used together with a high pressure equilibrium vessel operating under conditions of precisely controlled temperature and pressure. The results of the study indicate that pH decreases along an isotherm in proportion to −log₁₀(x), where x is the mole fraction of dissolved CO₂ in H₂O. The expanded uncertainty of the pH measurements is 0.06 pH units with a coverage factor of 2. The reported results are in good agreement with the literature in pressure ranges up to 16 MPa at temperatures below 343 K. An empirical equation has been developed to represent the present results with an expanded uncertainty of 0.05 pH units. We also compare our results with a chemical equilibrium model and find agreement to within 0.1 pH unit.     

Near-infrared spectroscopic solubility measurement for thermodynamic analysis of melting point depressions of biphenyl and naphthalene under high-pressure CO2

Melting temperatures of organic solids are often depressed by high-pressure CO₂ due to a dissolution of CO₂ in the molten organic compounds. For thermodynamic analysis of the melting point depression, solubilities of CO₂ in molten biphenyl and naphthalene were measured by near-infrared spectroscopy at various temperatures and pressures up to 20 MPa. Molarity of the organic component was determined from the 3ν_CH absorption band, and that of CO₂ from the 2ν₁ + ν₃ band. Mole fraction of CO₂ in the liquid phase was found to be an increasing function of the pressure up to 0.6 at 20 MPa and a weakly decreasing function of the temperature. The solubility data were used for modeling of the mixtures by the Peng–Robinson equation of state with a binary interaction parameter k₁₂. Calculation of the solid–liquid–gas phase equilibrium for the model fluid qualitatively described a large decrease in the melting temperature with increasing pressure up to 10 MPa followed by a small change at higher pressures. The melting point change was interpreted by the two competing effects: hydrostatic pressure effect increases the melting point by ca. 8 °C at 20 MPa, whereas CO₂ solubility effect reduces it by ca. 30 °C. Decomposition of the solubility effect into ideal and non-ideal mixing parts revealed that the non-ideality increases the melting point by more than 10 °C.     

Direct epoxidation of propylene to propylene oxide over RuO2-CuO-NaCl-TeO2-MnOx/SiO2 catalysts

Multi-metallic RuO₂-CuO-NaCl-TeO₂-MnO_x/SiO₂ catalysts were investigated for the epoxidation of propylene to propylene oxide (PO) using O₂ under atmospheric pressure. The metallic weight ratio and the total metal loading on SiO₂ support were optimized at Ru/Cu/Na/Te/Mn = 7.14/3.57/1.79/0.175/1.00 and 25.0 wt%, respectively. RuO₂ and CuO were determined to exhibit a critical bifunctional role for PO synthesis. These active sites were assisted by MnO_x and TeO₂ to increase PO formation rate and by NaCl to reduce CO₂ formation. With using the Box-Behnken design, a maximized PO formation rate of 1258 g_PO h^− 1 kg_cat^− 1 was obtained by varying O₂/propylene feed ratio and reaction temperature.     

Investigation of thermodynamic properties of the binary system polyethylene glycol/CO2 using new methods

The solubility and diffusivity of CO₂ in polyethylene glycols (PEGs) of different molecular weight measured by two different methods are discussed in the present work. Before solubility measurements, the melting temperatures of PEG with different molecular weights were determined by means of differential scanning calorimetry. For the purpose of the present study a temperature of 343 K was chosen as the working temperature for both employed methods since all studied polymers are in liquid state at this temperature. All samples were analyzed at isothermal conditions and in the pressure range from 0 MPa up to 30.0 MPa. A set of absorption experiments on the PEG/CO₂ systems was performed using an external balance method. In order to validate results obtained by the new method they were compared to the data obtained at the same process conditions by a method using magnetic suspension balance (MSB).     

Phase equilibria of (CO2 + H2O + NaCl) and (CO2 + H2O + KCl): Measurements and modeling

We report experimental measurements of the phase behavior of (CO₂ + H₂O + NaCl) and (CO₂ + H₂O + KCl) at temperatures from 323.15 K to 423.15 K, pressure up to 18.0 MPa, and molalities of 2.5 and 4.0 mol kg⁻¹. The present study was made using an analytical apparatus and is the first in which coexisting vapor- and liquid-phase composition data are provided. The new measurements are compared with the available literature data for the solubility of CO₂ in brines, many of which were measured with the synthetic method. Some literature data show large deviations from our results.The asymmetric (γ–φ) approach is used to model the phase behavior of the two systems, with the Peng–Robinson equation of state to describe the vapor phase, and the electrolyte NRTL solution model to describe the liquid phase. The model describes the mixtures in a way that preserves from our previous work on (CO₂ + H₂O) the values of the Henry's law constant and the partial molar volume of CO₂ at infinite dilution Hou et al. [22]. The activity coefficients of CO₂ in the aqueous phase are provided. Additionally, the correlation of Duan et al. [14] for the solubility of CO₂ in brines is tested against our liquid-phase data.     

Phase equilibrium of the CO2/glycerol system: Experimental data by in situ FT-IR spectroscopy and thermodynamic modeling

Phase equilibrium experimental data for the CO₂/glycerol system are reported in this paper. The measurements were performed using an in situ FT-IR method for temperatures ranging from 40 °C to 200 °C and pressures up to 35.0 MPa, allowing determination of the mutual solubility of both compounds. Concerning the CO₂ rich phase, it was observed that the glycerol solubility in CO₂ was extremely low (in the range of 10⁻⁵ in mole fraction) in the pressure and temperature domains investigated here. Conversely, the glycerol rich phase dissolved CO₂ at mole fractions up to 0.13. Negligible swelling of the glycerol rich phase has been observed. Modeling of the phase equilibrium has been performed using the Peng–Robinson equation of state (PR EoS) with classical van der Waals one fluid and EoS/G^E based mixing rules (PSRK and MHV2). Satisfactory agreement was observed between modeling results and experimental measurements when PSRK mixing rules are used in combination with UNIQUAC model, although UNIFAC predictive approach gives unsatisfactory representation of experimental behavior.     

Solubility and diffusion coefficient of supercritical-CO2 in polycarbonate and CO2 induced crystallization of polycarbonate

The solubility and diffusion coefficient of supercritical CO₂ in polycarbonate (PC) were measured using a magnetic suspension balance at sorption temperatures that ranged from 75 to 175 °C and at sorption pressures as high as 20 MPa. Above certain threshold pressures, the solubility of CO₂ decreased with time after showing a maximum value at a constant sorption temperature and pressure. This phenomenon indicated the crystallization of PC due to the plasticization effect of dissolved CO₂. A thorough investigation into the dependence of sorption temperature and pressure on the crystallinity of PC showed that the crystallization of PC occurred when the difference between the sorption temperature and the depressed glass transition temperature exceeded 40 °C (T − T_g ≥ 40 °C). Furthermore, the crystallization rate of PC was determined according to Avrami's equation. The crystallization rate increased with the sorption pressure and was at its maximum at a certain temperature under a constant pressure.     

Bubble point pressures and densities of hexamethyldisiloxane–carbon dioxide binary mixture using a constant volume view cell

The phase behavior of hexamethyldisiloxane (HMDS)–carbon dioxide (CO₂) binary mixture was investigated using a constant volume view cell. The accuracy of the measurement technique was inspected against the bubble point pressure data in the literature for ethanol (C₂H₅OH)–carbon dioxide (CO₂) binary mixture. The bubble point pressures for C₂H₅OH–CO₂ agreed well with the literature values. The bubble point pressures of HMDS–CO₂ binary mixture were determined at five different temperatures (T = 298.2 K, 308.2 K, 313.2 K, 323.2 K, 333.2 K) and at various compositions. The bubble point pressures increased with increasing temperature and CO₂ mole fraction in the binary mixture. The phase behavior of the binary mixture was modeled using the Peng–Robinson Stryjek–Vera equation of state (PRSVEoS). The binary interaction parameters were regressed from experimental bubble point pressures at each temperature and were found to exhibit a linear dependency on temperature. The HMDS–CO₂ binary mixture was also found to exhibit Type II phase behavior. Additionally, P–T–ρ measurements for the same binary system were conducted and excess molar volumes were calculated.     

Prediction of phase equilibrium of CO2/cyclic compound binary mixtures using a rigorous modeling approach

Vapor liquid equilibrium (VLE) data has significant role in designing processes which include vapor and liquid in equilibrium. Since it is impractical to measure equilibrium data at any desired temperature and pressure, particularly near critical region, thermodynamic models based on equation of state (EOS) are usually used for VLE estimating. In recent years due to the development of numerical tools like artificial intelligence methods, VLE prediction has been find new alternatives.In the present study a novel method called Least-Squares Support Vector Machine (LSSVM) used for predicting bubble/dew point pressures of binary mixtures containing carbon dioxide (CO₂) + cyclic compounds as function of reduced temperature of the system, critical pressure, acentric factor of the cyclic compound, and CO₂ composition. A 333 binary equilibrium data points of CO₂ and six cyclic compounds within temperature and pressure ranges of 308.15–473.15 K and 0.5–27.71 MPa were used to develop the model. Results show that the proposed model is able to predict VLE data for binary systems containing supercritical or near-critical CO₂/cyclic compounds with an acceptable average absolute relative deviation percent (AARD%) of 3.9381% and the coefficient of determination (R²) value of 0.9980. For detection of the probable doubtful experimental data, and applicability of the model, the Leverage statistical approach performed on the data sets. This algorithm showed that the proposed LSSVM model is statistically valid for VLE prediction and the whole phase equilibrium data points are in applicability domain of the model.     

High selectivity of TiC-CDC for CO2/N2 separation

A series of carbide-derived carbons (CDC) have been prepared starting from TiC and using different chlorine treatment temperatures (500–1200 °C). Contrary to N₂ adsorption measurements at −196 °C, CO₂ adsorption measurements at room temperature and high pressure (up to 1 MPa) together with immersion calorimetry measurements into dichloromethane suggest that the synthesized CDC exhibit a similar porous structure, in terms of narrow pore volume, independently of the temperature of the reactive extraction treatment used (samples synthesized below 1000 °C). Apparently, these carbide-derived carbons exhibit narrow constrictions were CO₂ adsorption under standard conditions (0 °C and atmospheric pressure) is kinetically restricted. The same accounts for a slightly larger molecule as N₂ at a lower adsorption temperature (−196 °C), i.e. textural parameters obtained from N₂ adsorption measurements on CDC must be underestimated. Furthermore, here we show experimentally that nitrogen exhibits an unusual behavior, poor affinity, on these carbide-derived carbons. CH₄ with a slightly larger diameter (0.39 nm) is able to partially access the inner porous structure whereas N₂, with a slightly smaller diameter (0.36 nm), does not. Consequently, these CDC can be envisaged as excellent sorbent for selective CO₂ capture in flue-gas streams.     

Supercritical CO2 extraction of lutein esters from marigold (Tagetes erecta L.) enhanced by ultrasound

As a novel technique, supercritical CO₂ (SC-CO₂) extraction enhanced by ultrasound was applied to the extraction of lutein esters from marigold and the extraction curves were described by Sovová model. The mass transfer coefficient in the solid phase (k_s) increased from 3.1 × 10⁻⁹ to 4.3 × 10⁻⁹ m/s due to ultrasound. The effect of extraction parameters including particle size of matrix, temperature, pressure, flow rate of CO₂, and ultrasonic conditions consisting of power, frequency and irradiation time/interval on the yield of lutein esters were investigated with single factor experiments. The results showed that the yield of lutein esters increased significantly with the presence of ultrasound (p < 0.05). The maximal yield of lutein esters (690 mg/100 g) was obtained for a particle size fraction of 0.245–0.350 mm, extraction pressure of 32.5 MPa, temperature of 55 °C and CO₂ flow rate of 10 kg/h with ultrasonic power of 400 W, ultrasonic frequency of 25 kHz and ultrasonic irradiation time/interval of 6/9 s.     

Laser analyses of mixture formation and the influence of solute on particle precipitation in the SAS process

Laser based Raman and elastic light scattering measurements were performed to study the process of mixture formation and the influence of the solute paracetamol onto the phase behaviour of the pseudo-binary system ethanol/CO₂ in the supercritical antisolvent process. From the Raman based technique, mole fraction and partial density distributions of CO₂ were obtained. The mole fraction distributions indicate a rapid mixture formation with fast supersaturation of the solute. At the same time, the increase of the CO₂ partial density at conditions considerably above the mixture critical point (MCP) indicate a change from a homogeneous supercritical to a multi-phase subcritical flow. This phase change goes along with particle precipitation. Thus, the results of our investigations proof, why past approaches failed to generate amorphous paracetamol nanoparticles with the system paracetamol/ethanol/CO₂ above the MCP. Process parameters like injection pressure (20.0–35.0 MPa), chamber pressure of CO₂ (7.5–17.5 MPa), temperature (313–333 K) and solute concentration (0–5 wt%) were varied.     

A novel low-temperature methanol synthesis method from CO/H2/CO2 based on the synergistic effect between solid catalyst and homogeneous catalyst

The activity of a binary catalyst in alcoholic solvents for methanol synthesis from CO/H₂/CO₂ at low temperature was investigated in a concurrent synthesis course. Experiment results showed that the combination of homogeneous potassium formate catalyst and solid copper–magnesia catalyst enhanced the conversion of CO₂-containing syngas to methanol at temperature of 423–443 K and pressure of 3–5 MPa. Under a contact time of 100 g h/mol, the maximum conversion of total carbon approached the reaction equilibrium and the selectivity of methanol was 99%. A reaction pathway involving esterification and hydrogenolysis of esters was postulated based on the integrative and separate activity tests, along with the structural characterization of the catalysts. Both potassium formate for the esterification as well as Cu/MgO for the hydrogenolysis were found to be crucial to this homogeneous and heterogeneous synergistically catalytic system. CO and H₂ were involved in the recycling of potassium formate.     

SBA-15 grafted with 3-aminopropyl triethoxysilane in supercritical propane for CO2 capture

Supercritical propane (SC-propane) was found to be a promising solvent for grafting (3-aminopropyl)triethoxysilane (APS) onto synthesized SBA-15 for CO₂ capture. The influence of operating conditions in SC-propane for CO₂ adsorption at different pressures (8.3–13.8 MPa), temperatures (85–120 °C), and periods of time (4–16 h) were evaluated. The CO₂ adsorption conditions under different partial pressures, temperatures and moisture were evaluated. The results showed a reduction in pore characteristics and an increased amount of grafted APS with increasing pressure and temperature after grafting. After grafting in SC-propane at 11.0 MPa and various temperatures for 16 h, a 3–20% increase in the amount of grafted APS and a 6–49% increase in the CO₂ adsorption capacity over the toluene refluxing was observed. The time required for grafting in SC-propane could be reduced while maintaining higher nitrogen content and CO₂ adsorption capacity compared with grafting in toluene refluxing.     

Polyoxometalate as co-catalyst of tetrabutylammonium bromide in polyethylene glycol (PEG) for coupling reaction of CO2 and propylene oxide or ethylene oxide

The coupling reaction of CO₂ and propylene oxide or ethylene oxide to produce corresponding cyclic carbonate in the presence of a catalytic system composed of n-Bu₄NBr, α₂-(n-Bu₄N)₉P₂W₁₇O₆₁(Co²⁺ · Br) (abbreviated as P₂W₁₇Co) and PEG (MW 400) has been investigated. The experimental results indicated that the synthesis of propylene carbonate (PC) or ethylene carbonate (EC) achieved with over 98% yield and 100% selectivity within 1 h at 120 °C by using the above catalyst system. When the catalyst system was recycled, the catalytic activity slowly diminished. Moreover, a plausible mechanism was proposed.     

Extraction of sunflower oil with supercritical CO2: Experiments and modeling

Extraction of sunflower oil from sunflower seeds (Heliantus annuus L.) using supercritical CO₂ was studied. The shrinking core model was applied to the modeling of the packed-bed extraction process. The experimental data were obtained for extraction conducted at the pressures of 20, 30, 40, 50 and 60 MPa; the temperatures of 313, 333 and 353 K, the CO₂ flow rates of 1–4, and 6 cm³ CO₂ min⁻¹; the mean particle diameters of 0.23, 0.55, 1.09, 2.18 mm. The supercritical CO₂ extraction process was modeled by a quasi steady state model as a function of extraction time, pressure, temperature, CO₂ flow rate, and particle diameter. The supercritical CO₂ extraction process. The intraparticle diffusion coefficient (effective diffusivity) D_e was used as adjustable parameter. The model using the best fit of D_e was correlated the data satisfactorily.     

Phase equilibria for the 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate in supercritical CO2 at various temperatures and pressures up to 20 MPa

The (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems at 313.2, 333.2, 353.2, 373.2 and 393.2 K as well as pressures up to 20.59 MPa have been investigated using variable-volume high pressure view cell by static-type. The solubility curve of 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate in the (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems increases as the temperature increases at a constant pressure. The (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems exhibit type-I phase behavior. The experimental results for the (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems correlate with the Peng–Robinson equation of state using a van der Waals one-fluid mixing rule including two adjustable parameters. The critical properties of 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate are predicted with the Joback–Lyderson group contribution and Lee–Kesler method.