Prediction of solute solubility in supercritical carbon dioxide: A novel semi-empirical model

Solubility data of solutes in supercritical fluids (SCF) are crucial for designing extraction processes, such as extraction using SCF or micronization of drug powders. A new empirical equation is proposed to correlate solute solubility in supercritical carbon dioxide (SC CO₂) with temperature, pressure and density of pure SC CO₂. The proposed equation is ln y₂ = J₀ + J₁P² + J₂T² + J₃ ln ρ where y₂ is the mole fraction solubility of the solute in the supercritical phase, J₀ − J₃ are the model constants calculated by least squares method, P (bar) is the applied pressure, T is temperature (K) and ρ is the density of pure SC CO₂. The accuracy of the proposed model and three other empirical equations employing P, T and ρ variables was evaluated using 16 published solubility data sets by calculating the average of absolute relative deviation (AARD). The mean AARD for the proposed model is 7.46 (±4.54) %, which is an acceptable error when compared with the experimental uncertainty. The AARD values for other equations were 11.70 (±23.10), 6.895 (± 3.81) and 6.39 (±6.41). The mean AARD of the new equation is significantly lower than that obtained from Chrastil et al. model and has the same accuracy as compared with Bartle et al. and Mèndez-Santiago–Teja model. The proposed model presents more accurate correlation for solubility data in SC CO₂. It can be employed to speed up the process of SCF applications in industry.     

Determination and calculation for solubility of m-nitroaniline and its mixture in supercritical carbon dioxide

Equilibrium solubility of m-nitroaniline and p-nitroaniline in supercritical carbon dioxide (SCCO₂) is essential to design the process of SCCO₂ extraction and to investigate the effect of each solute on the solubility in SCCO₂ ternary system. However, the solubility data is not reported so far. We performed the solubility measurements at the temperatures of 308–328 K and in the pressure range of 11.0–21.0 MPa. The experimental results showed the solubility of m-nitroaniline and p-nitroaniline was enhanced in m-nitroaniline + p-nitroaniline + SCCO₂ ternary system. The improvement factor (i), separation factor (μ) and separation efficiency (HE) in the ternary system were defined and calculated, and the best separation result could be obtained at 21.0 MPa and 328 K using SCCO₂ extraction, where the separation efficiency was up to 90.9%. Based on the chemical association theory, a new model was developed to calculate the solubility of mixed solutes in SCCO₂. The correlation result of the new model was tested by about 500 solubility data from 15 kinds of two solutes mixtures in SCCO₂. The correlated result showed that the new model could achieve much better AARD (%) than those of frequently used Sovova and Sovova-T models.     

Thermodynamic modeling of dealcoholization of beverages using supercritical CO2: Application to wine samples

The supercritical removal of ethanol from alcoholic beverages (brandy, wine, and cider) was studied using the GC-EoS model to represent the phase equilibria behavior of the CO₂ + beverage mixture. Each alcoholic drink was represented as the ethanol + water mixture with the corresponding ethanol concentration (35 wt% for brandy, 9-12 wt% for different wines and 6 wt% for cider). The thermodynamic modeling was based on an accurate representation of the CO₂ + ethanol and CO₂ + water binary mixtures, and the CO₂ + ethanol + water ternary mixture.The GC-EoS model was employed to simulate the countercurrent supercritical CO₂ dealcoholization of the referred beverages; the results obtained compared good with experimental data from the literature. Thus, the model was used to estimate process conditions to achieve an ethanol content reduction from ca. 10 wt% to values lower than 1 wt%. The model results were tested by carrying out several extraction assays using wine, in a 3 m height packed column at 308 K, pressures in the range of 9-18 MPa and solvent to wine ratio between 9 and 30 kg/kg.     

Aqueous piperazine derivatives for CO2 capture: Accurate screening by a wetted wall column

Concentrated aqueous piperazine (PZ) has been identified as a better solvent for CO₂ capture than monoethanolamine (MEA), because it has a greater rate of CO₂ absorption and greater CO₂ capacity. This work evaluates the effect of substitute groups on PZ performance. Many previous screening studies measured absorption/desorption with CO₂/N₂ sparging, which lacks accuracy and cannot be used to estimate actual absorber performance. In this work a wetted wall column was used to accurately measure absorption/desorption rate at typical rich and lean CO₂ loading (α) and simulate performance of real packing. The method also provides accurate measurement of CO₂ solubility at 40-100 °C. This study provided rate and solubility data at 40-100 °C and practical ranges of CO₂ loading for 8 m 1-methylpiperazine (1-MPZ), 8 m 2-methylpiperazine (2-MPZ), 4 m 2-MPZ/4 m PZ, 7.7 m N-(2-hydroxyethyl)piperazine (HEP), 6 m 1-(2-aminoethyl)piperazine (AEP), 8 m 2-piperidine ethanol (2-PE), and 2 m trans-2,5-dimethylpiperazine (2,5-DMPZ). With the measurements of CO₂ flux (NCO₂) and equilibrium driving force, liquid film mass transfer coefficients (k_g′) are calculated. The rate decreases as of 1-MPZ = PZ > 2-MPZ/PZ > 2-MPZ > HEP > MEA > AEP = 2-PE. This method also allows bracketing and determination of equilibrium CO₂ partial pressure (^*PCO₂) at each condition. Semi-empirical solubility models of CO₂ for each amine were regressed from experimental solubility data to find the lean and rich CO₂ loading corresponding to 0.500 kPa and 5 kPa CO₂ partial pressure respectively. Based on the solubility model, the actual operating capacity of the solvents without overstripping decreases in the sequence of 2-PE > 2-MPZ > 2-MPZ/PZ > 1-MPZ > PZ > HEP > AEP > MEA. The enthalpy of CO₂ absorption (ΔH_abs) of all the piperazine derivatives is around 70 kJ/mol CO₂.     

Phase behavior of the poly(neopentyl methacrylate) + supercritical fluid solvents + neopentyl methacrylate system and CO2 + neopentyl methacrylate mixtures at high pressure

High-pressure phase behaviors are measured for the CO₂ + neopentyl methacrylate (NPMA) system at 40, 60, 80, 100, and 120 °C and pressure up to 160 bar. This system exhibits type-I phase behavior with a continuous mixture-critical curve. The experimental results for the CO₂ + NPMA system are modeled using the Peng-Robinson equation of state. Experimental cloud-point data up to the temperature of 180 °C and the pressure of 2000 bar are presented for ternary mixtures of poly(neopentyl methacrylate) [poly(NPMA)] + supercritical solvents + NPMA systems. Cloud-point pressures of poly(NPMA) + CO₂ + NPMA system are measured in the temperature range of 60-180 °C and to pressures as high as 2000 bar with NPMA concentration of 0.0, 5.2, 19.0, 28.1 and 40.2 wt%. It appears that adding 51.2 wt% NPMA to the poly(NPMA) + CO₂ mixture does significantly change the phase behavior. Cloud-point curves are obtained for the binary mixtures of poly(NPMA) in supercritical propane, propylene, butane, 1-butene, and dimethyl ether (DME). The impact of dimethyl ether concentration on the phase behavior of the poly(NPMA) + CO₂ + x wt% DME system is also measured at temperature of 180 °C and pressure range of 36-2000 bar. This system changes the pressure-temperature (P-T) slope of the phase behavior curves from upper critical solution temperature (UCST) region to lower critical solution temperature (LCST) region as the NPMA concentration increases.     

Comparative study of CO and CO2 hydrogenation over supported Rh–Fe catalysts

The hydrogenation of CO, CO + CO₂, and CO₂ over titania-supported Rh, Rh–Fe, and Fe catalysts was carried out in a fixed-bed micro-reactor system nominally operating at 543 K, 20 atm, 20 cm³ min^− 1 gas flow (corresponding to a weight hourly space velocity (WHSV) of 8000 cm³ g_cat^− 1 h^− 1), with a H₂:(CO + CO₂) ratio of 1:1. A comparative study of CO and CO₂ hydrogenation shows that while Rh and Rh–Fe/TiO₂ catalysts exhibited appreciable selectivity to ethanol during CO hydrogenation, they functioned primarily as methanation catalysts during CO₂ hydrogenation. The Fe/TiO₂ sample was primarily a reverse water gas shift catalyst. Higher reaction temperatures favored methane formation over alcohol synthesis and reverse water gas shift. The effect of pressure was not significant over the range of 10 to 20 atm.     

High pressure CO2 solubility in N-methyl-2-hydroxyethylammonium protic ionic liquids

The use of ionic liquids for CO₂ capture and natural gas sweetening is being object of intense research. Within the enormous group of existing ionic liquids, those based on conjugate bases of carboxylic acids seem to be particularly promising. This work addresses the study of the high pressure CO₂ solubility (up to 80 MPa) in two protic ionic liquids, N-methyl-2-hydroxyethylammonium formate and N-methyl-2-hydroxyethylammonium acetate, in a wide range of temperatures (293-353 K). A thermodynamic model based on the Peng-Robinson equation of state with the Wong-Sandler mixing rule, using the NRTL model for the activity coefficients, was here adopted to describe and evaluate the thermodynamic consistency of the experimental data. Furthermore, the study of a ternary mixture of CO₂ + CH₄ + N-methyl-2-hydroxyethylammonium acetate was investigated showing a high selectivity from the IL towards these solutes.     

Measurement and correlation of the solid-liquid-gas equilibria for carbon dioxide + normal chain saturated aliphatic hydrocarbon systems

The pressure p-temperature T projections of solid-liquid-gas (S-L-G) three-phase coexistence lines for the carbon dioxide + tetradecanoic acid (C₁₄H₂₈O₂) system, the carbon dioxide + hexadecanoic acid (C₁₆H₃₂O₂) system, and the carbon dioxide + 1-hexadecanol (C₁₆H₃₄O) were measured by the first melting point method in which the initial appearance of the liquid phase was observed. The profiles of the p-T projections of the S-L-G lines for the carbon dioxide + acid systems are similar to each other, the S-L-G equilibria for the carbon dioxide + acid systems are, however, different from that for the carbon dioxide + 1-hexadecanol systems. The experimental p-T projections of the S-L-G lines were also correlated by the Peng-Robinson equation of state and the van der Waals type mixing rules with two binary interaction parameters introduced into attraction term and size terms, respectively. The present model gave good correlation results for all of the experimental S-L-G lines with maximum average absolute relative deviations of 0.075% for the carbon dioxide + tetradecanoic acid system, 0.14% for the carbon dioxide + hexadecanoic acid system and 0.28% for the carbon dioxide + 1-hexadecanol system, respectively.     

Extension of a compressible lattice model to CO2 + cosolvent + polymer systems

We have recently proposed a compressible lattice model for CO₂ + polymer systems in which CO₂ forms complexes with one or more functional groups in the polymer. Furthermore, we have shown that this model is able to simultaneously correlate phase equilibria, sorption behavior, and glass transition temperatures in such systems. In the present work, we extend the model to ternary CO₂ + cosolvent + polymer systems and demonstrate that cloud point behavior in CO₂ + dimethyl ether + poly (?-caprolactone), CO₂ + dimethyl ether + poly (isopropyl acrylate), and CO₂ + dimethyl ether + poly (isodecyl acrylate) systems can be predicted using parameters obtained from binary data. Our results also suggest that dimethyl ether may form weak complexes with poly (?-caprolactone), poly (isopropyl acrylate), and poly (isodecyl acrylate).     

Gas solubilities in ionic liquids using a generic van der Waals equation of state

A family of modified van der Waals equations of state (vdW EOS) is extremely useful for many industrial applications. For example, the generic Redlich-Kwong (RK) EOS or its modification by Soave (SRK EOS) and Peng-Robinson (PR EOS) are still of popular use in industry to the present day. These two most popular (“cubic”) EOSs are based on modifications [1/(V² + bV), or 1/(V² + 2bV − b²)] of the volume dependence on the attractive part of the original van der Waals EOS [1/V²] and also modifications of the temperature dependence of the attractive “a(T)” parameter of the original EOS (constant a). It is extremely rare in actual EOS applications to use the volume dependence of the original van der Waals EOS. In the present phase equilibrium calculations, we employ such a generic vdW EOS, P = RT/(V − b) − a(T)/V², with our well-tested mixing rule for multi-component mixtures. Using the same form of the “a(T)” parameter and the mixing rule, it has been found that all generic RK, PR, and vdW EOSs can present the phase behaviors (temperature-pressure-composition diagrams) equally well. It is shown that experimental gas solubility data (CO₂, CF₃-CFH₂, SO₂, and NH₃) in room-temperature ionic liquids are well correlated with the present EOS model, and also that the phase behaviors such as LLE (liquid-liquid separations) are satisfactorily predicted.     

Thermodynamic modeling of CO2 solubility in aqueous solutions of NaCl and Na2SO4

A thermodynamic model based on the electrolyte NRTL activity coefficient equation and PC-SAFT equation-of-state is developed for CO₂ solubility in aqueous solutions of NaCl and Na₂SO₄ with temperature up to 473.15 K, pressure up to 150 MPa, and salt concentrations up to saturation. The Henry's constant parameters of CO₂ in H₂O and the characteristic volume parameters for CO₂ required for pressure correction of Henry's constant are identified from fitting the experimental gas solubility of CO₂ in pure water with temperature up to 473.15 K and pressure up to 150 MPa. The NRTL binary parameters for the CO₂-(Na⁺, Cl⁻) pair and the CO₂-(Na⁺, SO₄²⁻) pair are regressed against the experimental VLE data for the CO₂-NaCl-H₂O ternary system up to 373.15 K and 20 MPa and the CO₂-Na₂SO₄-H₂O ternary system up to 433.15 K and 13 MPa, respectively. Model calculations on solubility and heat of solution of CO₂ in pure water and aqueous solutions of NaCl and Na₂SO₄ are compared to the available experimental data of the CO₂-H₂O binary, CO₂-NaCl-H₂O ternary and CO₂-Na₂SO₄-H₂O ternary systems with excellent results.     

Solubility of CO2 in aqueous solutions of NaCl, KCl, CaCl2 and their mixed salts at different temperatures and pressures

The solubility of CO₂ in water and aqueous solutions of NaCl, KCl, CaCl₂, NaCl + KCl (weight ratio = 1:1), NaCl + CaCl₂ (weight ratio = 1:1), KCl + CaCl₂ (weight ratio = 1:1), and NaCl + KCl + CaCl₂ (weight ratio = 1:1:1) was determined at 35.0, 45.0 and 55.0 °C up to 16 MPa, and the concentration of the salt was up to 14.3 wt%. It was demonstrated that solubility increased with increase in pressure, and decreased with increasing temperature. Addition of a salt or salt mixture resulted in reduction in the solubility due to the salting-out effect. At the same salt concentration (wt%), the salting-out effect of KCl was considerably smaller than those of NaCl and CaCl₂. The salting-out effect of a salt mixture is between those of its components.     

Supercritical antisolvent precipitation of andrographolide from Andrographis paniculata extracts: Effect of pressure, temperature and CO2 flow rate

Andrographis paniculata extracts were precipitated using the so-called supercritical antisolvent (SAS) technique. Ethanol was used as the solvent and compressed CO₂ as the antisolvent. The effects of process operating conditions (pressure: 5-24 MPa, temperature: 308-328 K and CO₂ flow rate: 0.5-1.5 g/min) on particle size and morphology of precipitated andrographolide were evaluated. X-ray diffraction (XRD) patterns showed significant changes in andrographolide morphology depending on process operating conditions; both column-like and slice-like crystals were observed depending on operating conditions. Crystals with mean diameters of 3.30-228.35 μm were produced, smaller crystals were obtained at high pressure, low temperature and high CO₂ flow rate and vice versa for large crystals. In addition, SAS process also produced high precipitation yields, since solubility of andrographolide is small in the supercritical CO₂ plus ethanol. When operating under subcritical conditions, amorphous particles were produced.     

Interfacial tension measurements and modelling of (carbon dioxide + n-alkane) and (carbon dioxide + water) binary mixtures at elevated pressures and temperatures

Supercritical carbon dioxide (CO₂) is often used as a process fluid for enhanced oil recovery. The storage of carbon dioxide in underground formations is a potential way of mitigating climate change during a transition period to more sustainable energy sources. Combining injection with subsequent trapping of the non-wetting supercritical carbon dioxide phase in the pores of a depleted reservoir is a promising scheme for allowing the continued use of fossil fuels with minimal environmental consequences. The design of such processes is ultimately linked to the confined behaviour of the fluids in question at reservoir conditions, which is largely controlled by interfacial forces. Measurements of the relevant interfacial tensions for systems containing alkanes, carbon dioxide and water are currently limited and inconsistent while models usually fail to capture the pressure dependence of the interfacial tension. In this work, a density functional theory based on the SAFT-VR equation of state was used to predict the interfacial tension of (H₂O + CO₂ + n-alkane) binary systems over wide ranges of temperature and pressure. The comparison with a new set of reported experimental data of three (n-alkane + CO₂) systems at pressures up to the critical points, as well as with the (H₂O + CO₂) system at pressures up to 60 MPa, for a temperature range of (298-443) K, is discussed.     

Impedance analysis of Sr-substituted CePO4 with mixed protonic and p-type electronic conduction

Members of the solid-solution series Ce_1−xSr_xPO_4−δ (x = 0, 0.01, 0.02) with mixed protonic and electronic transport have been synthesized by a nitrate-decomposition method followed by sintering at 1450 °C. Impedance spectroscopy is employed to estimate the bulk electrical conductivity in wet (∼0.03 atm) and dry atmospheres of O₂ and 10%H₂:90%N₂. Conductivity increases with dopant concentration (x), oxygen partial pressure (pO₂) and water vapour partial pressure (pH₂O) reaching ∼3.5 × 10⁻³ S cm⁻¹ at 600 °C for x = 0.02 in wet O₂. Activation energies (E_a) for the bulk conductivity of Ce_0.98Sr_0.02PO_4−δ below 650 °C are 0.44 and 0.78 eV for wet oxidising and wet reducing conditions, respectively. A moderate but positive pO₂⁺ⁿ power-law dependence (n < 1/10) of conductivity is exhibited in the pO₂ range 10^−2.5 to 10⁻¹ atm, consistent with mixed ionic and p-type electronic transport. Thermogravimetric analysis indicates that the Sr-doped materials are stable in a CO₂ atmosphere in the temperature range 25–1200 °C.     

Effect of gas pressure on the phase behaviour of organometallic compounds

The knowledge of the phase behaviour of organometallic compounds in supercritical CO₂ is the key factor for determining the feasibility of homogeneous catalysis in supercritical fluid reaction. In the present study, the solid-liquid-gas equilibrium line for the system CO₂/Cu(thd)₂, CO₂/Pt(COD)Me₂ and He/Pt(COD)Me₂ was determined from 0.1 MPa to 25 MPa. In addition, experimental solubility data of Cu(thd)₂ in CO₂ at 333 K and pressures ranging from 10 MPa to 17 MPa as well as of Pt(COD)Me₂ in CO2 at 313 K, 333 K and 353 K and pressures ranging from 12 MPa to 32 MPa are presented. The solubility data are correlated using the linear relationship between the logarithm of the solubility and the logarithm of the reduced density of pure CO₂ proposed by Kumar and Johnston as well as an extension of the theory of dilute solution proposed by Mendez-Santiago and Teja. Both approaches gave reasonable results in the correlation of the experimental solubility data.     

Thermodynamic modeling of the dissociation conditions of hydrogen sulfide clathrate hydrate in the presence of aqueous solution of inhibitor (alcohol,salt or ethylene glycol)

Hydrate dissociation conditions of hydrogen sulfide in the presence of aqueous solution of thermodynamic inhibitor (methanol, ethanol, ethylene glycol, NaCl, KCl and CaCl₂) is modeled in this communication. A thermodynamic model is developed to correlate the hydrate dissociation conditions for the systems of H₂S + water + salt (single and mixed salts of NaCl, KCl and CaCl₂), H₂S + water + alcohol (methanol or ethanol), H₂S + water + ethylene glycol and H₂S + water + mixed salt, and methanol/ethylene glycol. Extended-UNIQUAC (e-UNIQUAC) approach is used for modeling of the activity coefficient of water in aqueous phase. The structural parameters of e-UNIQUAC model are extracted from literature but interaction parameters of this model are obtained by fitting the model with experimental data. The results of the present model are in satisfactory agreement with experimental data.     

Solubility of carbon dioxide in pentaerythritol ester oils. New data and modeling using the PC-SAFT model

In this work, the solubility of carbon dioxide, CO₂, in pentaerythritol tetraheptanoate (PEC7) and in pentaerythritol tetranonanoate (PEC9) has been performed from 283 to 348 K and pressures up to 7.5 MPa in an isochoric high-pressure gas solubility apparatus. The solubility values are very similar in terms of mole fractions of CO₂ in both pentaerythritol esters. The experimental gas solubility data, together with those available in the literature for other CO₂ + pentaerythritol tetraester systems, were satisfactorily correlated with the PC-SAFT equation of state. The average absolute deviations of the gas solubility correlations were less than 3.9% for all the systems. In addition, PC-SAFT model was applied in a semi-predictive manner: the pure component's molecular parameters and the binary interaction parameter optimized from solubility data were used to calculate the types of the phase diagram as well as the densities and excess molar volumes in broad temperature and pressure ranges. The results obtained show the robustness of the model and these parameters to calculate properties not included in the fitting procedure.     

Solubility and diffusivity of CO2 in poly(l-lactide)-hydroxyapatite and poly(d,l-lactide-co-glycolide)-hydroxyapatite composite biomaterials

Solubility and diffusivity of supercritical CO₂ in poly(l-lactide)-hydroxyapatite (PLLA-HA) and poly(d,l-lactide-co-glycolide)-hydroxyapatite (PLGA-HA) composite materials were measured using a magnetic suspension balance at a temperature of 313 K and a pressures range of 10-30 MPa. The effect of the HA concentration on the solubility and diffusivity was investigated by varying filler content in the range of 0-50 wt%. For the PLLA-HA composites the solubility decreases with the increase of filler concentration. Diffusivity of the gas in the substrate is also lower as the HA content increases. In the case of PLGA-HA composites, small filler content favors the solubility and diffusivity of CO₂ due to incomplete wetting of the solid particles by the polymer. As the amount of HA increases solubility decreases. The results suggest that dense CO₂ could be used as a ‘green’ processing agent for composite biomaterials when organic solvents or high temperatures should be avoided.     

Electroless immobilization and electrochemical characteristics of nickel hexacyanoruthenate film at an aluminum substrate

The surface of an aluminum (Al) electrode was modified with a thin film of nickel hexacyanoruthenate (NiHCR) as a novel electrode material. The modification procedure of Al surface, includes two consecutive procedures: (i) the electroless deposition of metallic nickel on the Al electrode surface from NiCl₂ solution, and (ii) the chemical transformation of deposited nickel to nickel hexacyanoruthenate films in solution of 20 mM K₃[Ru(CN)₆] + 0.5 M KNO₃. Cyclic voltammogram of the modified Al electrode showed a well-defined redox reaction due to [Ni^IIRu^III/II(CN)₆]^1−/2− system. The effects of different supporting electrolytes and solution pH were studied on the electrochemical characteristics of the modified electrode. The diffusion coefficients of K⁺ and Na⁺ cations in the film (D), the transfer coefficient (α), and the charge transfer rate constant at the modifying film/electrode interface (k_s), were calculated in the presence of both K⁺ and Na⁺ cations. The stability of the modified electrode was investigated under various experimental conditions.