Correlation and estimation of solubilities of fatty acids in supercritical carbon dioxide using solution model approach

In this study, solid solubility data of five fatty acids in supercritical carbon dioxide (CO₂) at different temperatures and pressures are correlated using a two-parameter solution model developed from the regular solution model coupled with the Flory⿿Huggins equation. The developed solution model with fewer parameters yields correlated results comparable to those from commonly used semi-empirical equations. In addition, both parameters in the solution model can be further generalized with the chain length of fatty acids and a new predictive solution model is proposed for solubility prediction. The predictive solution model proposed in this study provides better predicted results and yields average deviation in predicted solubilities of 22.1%. To further apply this solution model to other compounds, solid solubility data of three triglycerides in supercritical CO₂ at 313 K are also correlated. After model simplification and generalization, a new predictive solution model for triglycerides is also proposed, which yields average deviation in predicted solubilities of 29.8%. These results demonstrate that the solution model used in this study is applicable for correlation and prediction of solid solubilities of structure-related compounds in supercritical CO₂.     

Experimental determination and activity coefficient based models for mixture solubilities of nitrophenol isomers in supercritical carbon dioxide

The experimental solubilities of the mixture of nitrophenol (m- and p-) isomers were determined at 308, 318 and 328 K over a pressure range of 10–17.55 MPa. Compared to the binary solubilities, the ternary solubilities of m-nitrophenol increased at 308, 318 and 328 K. The ternary solubilities of p-nitrophenol increased at 308 K, while the ternary solubilities decreased at lower pressures and increased at higher pressure at 318 and 328 K. The solubilities of the solid mixtures in supercritical carbon dioxide (SCCO₂) were correlated with solution models by incorporating the non-idealities using activity coefficient based models. The Wilson and NRTL activity coefficient models were applied to determine the nature of the interactions between the molecules. The equation developed by using the NRTL model has three parameters and correlates mixture solubilities of solid solutes in terms of temperature and cosolute composition. The equation derived from the Wilson model contains five parameters and correlates solubilities in terms of temperature, density and cosolute composition. These two new equations developed in this work were used to correlate the solubilities of 25 binary solid mixtures including the current data. The average AARDs of the model equations derived using the NRTL and Wilson models for the solid mixtures were found to be 7% and 4%, respectively.     

Solubility of niflumic acid and celecoxib in supercritical carbon dioxide

The solubility data of two fluorinated and non-steroidal anti-inflammatory drugs, niflumic acid (CAS No. 4394-00-7) and celecoxib (CAS No. 169590-42-5), in supercritical carbon dioxide were measured with a semi-flow type phase equilibrium apparatus at temperatures ranging from 313.2 K to 353.2 K and pressures up to 31 MPa. At the highest extraction temperature and pressure, the solubilities are 2.09 × 10⁻⁵ and 1.52 × 10⁻⁵ in mole fraction for niflumic acid and celecoxib, respectively. The saturated solubility data were correlated with the Chrastil model, the Mendez-Santiago–Teja equation, and the Peng–Robinson equation of state. The Chrastil model fitted the experimental data to about within the experimental uncertainty. The correlated results of the Mendez-Santiago–Teja model confirmed the consistency of the solubility data over the entire experimental conditions. Incorporating with two-parameter van der Waals one-fluid mixing rules, the Peng–Robinson equation of state represents satisfactorily the gas–solid equilibrium behavior of niflumic acid and celecoxib in supercritical carbon dioxide.     

Measurement and correlation of the solubility of two steroid drugs in supercritical carbon dioxide using semi empirical models

The solubilities of desoxycorticosterone acetate (DA) and clobetasole propionate (CP) in supercritical carbon dioxide (SC-CO₂) were measured at temperature ranging from (308 to 348) K and pressures from (12.2 to 35.5) MPa using a static method. The mole fraction solubilities ranged from 10⁻⁷ to 13.93 × 10⁻⁵. The crossover region was observed for DA and CP at 24.3 and 25.3 MPa, respectively. Solubility data were correlated using four semi-empirical density-based models (Chrastil, Bartle, Kumar, Johnston (K–J) and Mendez-Santiago and Teja (M–T) models). The average absolute relative deviations (AARD%) ranged from 9.3 to 13.6; 8.9 to 11.9; 6.5 to 10.3 and from 10.4 to 13.4 for Chrastil, Bartle, K–J and M–T models, respectively. A comparison among the four models revealed that the K–J model gave much better correlation of the solubilities in comparison with other models. Using the correlation results, the heat of drug–CO₂ solvation and that of drug vaporization was separately approximated in the range of −24.2 to −24.5 and 63.8 to 64.8 kJ mol⁻¹. The correlation results showed good agreement with the experimental data.     

Measurement and correlation solubility of cefixime trihydrate and oxymetholone in supercritical carbon dioxide (CO2)

The equilibrium solubilities of cefixime trihydrate and oxymetholone in supercritical carbon dioxide (CO₂) were measured using a “static method”. Cefixime trihydrate is a cephalosporin antibiotic drug and Oxymetholone is a 17alpha-alkylated anabolic-androgenic steroid drug. The experimental measurements for cefixime trihydrate were performed at temperatures of 308, 318 and 328 K as well as pressure range from 183 to 335 bar. The solubility of oxymetholone was determined at 308, 318 and 328 K and pressure range from 121 to 305 bar. The experimental solubility data (mole fraction) for cefixime trihydrate and oxymetholone was greater than 1.6 × 10⁻⁷ and 1.6 × 10⁻⁵ and less than 3.02 × 10⁻⁷ and 1.49 × 10⁻⁴, respectively. The solubilities for two drugs in CO₂ were correlated by using four semi-empirical models such as Bartle, Kumar and Johnstone (K–J), Mendez-Santiago and Teja (M–T) and Chrastil models. The results obtained from the semi-empirical models show that there is good agreement between the experimental data and the results of semi-empirical models. By using the correlation results, the heat of drug–CO₂ solvation and heat of drug vaporization for cefixime–CO₂ and oxymetholone–CO₂ systems may be approximately estimated. Also, the Peng–Robinson (PR) cubic equation of state (CEOS) along with the van der Waals combining rule was applied to correlate the drugs solubilities in supercritical CO₂. The average absolute deviation between the experimental data and the results of PR equation for cefixime trihydrate and oxymetholone was 11.92% and 11.74%, respectively.     

Solubility of chlorpheniramine maleate in supercritical carbon dioxide

Solubility of chlorpheniramine maleate in supercritical carbon dioxide at different temperatures (308–338 K) and pressures (160–400 bar) is measured using static method coupled with gravimetric method. The measured solubility data demonstrated that the solubility of chlorpheniramine maleate was changed between 1.54 × 10⁻⁵ and 4.26 × 10⁻⁴ based on the mole fraction as the temperature and pressure are changed. The general trend of measured solubility data shows a direct effect of pressure and temperature on the solubility of chlorpheniramine maleate. Finally, the obtained solubilities correlated using four semi-empirical density-based correlations including Mendez Santiago–Teja (MST), Kumar and Johnston (KJ), Bartle et al., and Chrastil models. Although the results of modeling showed that the KJ model leads to the average absolute relative deviation percent (AARD %) of 8.1% which is the lowest AARD %, deviation of other utilized correlations are rather the same.     

Solubility of thymol in supercritical carbon dioxide and its impregnation on cotton gauze

Through this study, an attempt has been made to evaluate the solubility of thymol in supercritical carbon dioxide as well to investigate a prospect of its impregnation on cotton gauze on laboratory scale. Solubility of thymol in supercritical carbon dioxide was determined at temperatures of 35 °C, 40 °C and 50 °C, and pressures ranging from 7.8 to 25 MPa (CO₂ density range 335.89–849.60 kg/m³) using a static method. The solubility data were correlated using semi-empirical equations introduced by Chrastil, Adachi and Lu and del Valle and Aguilera. Taking into account obtained results, temperature of 35 °C and pressure of 15.5 MPa were selected as operating conditions for the impregnation process. Impregnation of cotton gauze with thymol was performed in a cell using carbon dioxide as a solvent. Kinetics of the process was determined and modeled. Masses of thymol on cotton gauzes after 2 h and 24 h of impregnation were 11% and 19.6%, respectively. FT-IR analysis confirmed the presence of thymol on the surface of the cotton fibers. The impregnated gauze provided strong antimicrobial activity against tested strains of Escherichia coli, Staphylococcus aureus, Bacillus subtilis, Enterococcus faecalis and Candida albicans.     

Solubility of gabapentin in supercritical carbon dioxide

The purpose of this study was to measure the solubility of gabapentin in supercritical carbon dioxide at different pressures and temperatures of 16–40 MPa and 308–338 K, respectively. The measured solubility data revealed that solubility of gabapentin was 8.97 × 10⁻⁵–7.36 × 10⁻³ based on the mole fraction in supercritical carbon dioxide at the aforementioned operational conditions. At last, the obtained results were correlated using four density based semi-empirical correlations namely Bartle et al., Mendez-Santiago and Teja (MST), Chrastil and Kumar and Johnston (K–J). The results revealed that according to the obtained average absolute relative deviations (AARD) for the used density based correlations of MST (AARD % = 9.88%), Chrastil (AARD % = 9.47%), K–J (AARD % = 11.5%) and Bartle et al. (AARD % = 9.29%), none of the correlations can be considered as the most accurate one. In other words, all the examined semi-empirical correlations are in the same level of accuracy.     

Solubility and partial molar volume of N,N-dimethylformamide diethyl acetal in supercritical carbon dioxide: Measurement and correlations

The solubilities of N,N-dimethylformamide diethyl acetal were measured at temperatures ranging from 313 to 353 K and pressures from 7.8 to 13.3 MPa in supercritical carbon dioxide. The measured solubility data were correlated using the Chrastil, Sung and Shim (SS), and Jouyban–Chan–Foster (JCF) semiempirical models. Consequently, the calculated results showed satisfactory agreement with experimental data and differed from the measured values by between 4.56 and 6.10%. The correlated results indicated that the JCF model provided the best fitness. Solubility data were also utilized to estimate the partial molar volume for the compound in the supercritical phase using the theory developed by Kumar and Johnston.     

Experimental measurement and correlation for solubility of piroxicam (a non-steroidal anti-inflammatory drugs (NSAIDs)) in supercritical carbon dioxide

Since the knowledge of pharmaceutical solubilities in the supercritical carbon dioxide is one of the first essential necessities for designing the supercritical carbon dioxide-based processes, solubility of piroxicam a non-steroidal anti-inflammatory drug was experimentally measured. In this regard, a static method coupled with gravimetric method was used to measure the solubility of piroxicam in the supercritical carbon dioxide in temperature and pressure range of 308.15–338.15 K and 16–40 MPa, respectively. The obtained solubility data were in the range of 1.17 × 10⁻⁵ and 5.12 × 10⁻⁴ based on the mole fraction (mole piroxicam/(mole piroxicam + mole CO₂)) then modeled using four different density based correlations namely Bartle et al., Mendez-Santiago-Teja, Chrastil and Kumar and Johnston models. The results of error analysis revealed that the used correlations were potential to correlate the solubility of piroxicam with minimum and maximum average absolute relative deviation percents (AARD%) of 14.4% and 15.2%, respectively.     

Solubilities of chlormezanone,metaxalone and methocarbamol in supercritical carbon dioxide

The solubilities of three active pharmaceutical ingredients (APIs) in supercritical carbon dioxide were measured in this study using a semi-flow apparatus. These APIs are chlormezanone (C₁₁H₁₂ClNO₃S), metaxalone (C₁₂H₁₅NO₃) and methocarbamol (C₁₁H₁₅NO₅) that are all used as skeletal muscle relaxants. The solubility data are reported for three isotherms at 308.2, 318.2 and 328.2 K, with the pressure range from 12 to 24 MPa. Most solubility data are within the range of 10⁻⁶ to 10⁻⁴ mole fraction for each API. The crossover phenomena were observed from the experimental results for all three systems. These solubility data satisfied the thermodynamic consistency tests. They were then correlated using three semi-empirical models. With the optimally fitted binary interaction parameters, satisfactory correlation agreement is presented for each binary mixture.     

Solubility of Disperse Red 82 and modified Disperse Yellow 119 in supercritical carbon dioxide or nitrous oxide with ethanol as a cosolvent

Ethanol was used as a cosolvent to enhance the solubility of disperse dyestuffs in supercritical fluids. In the presence of ethanol, from (1 to 5) mol%, the gas–solid equilibrium data of the Disperse Red 82 and modified Disperse Yellow 119 in supercritical carbon dioxide or nitrous oxide have been measured at temperatures from (353.2 to 393.2) K and pressures from (15.0 to 30.0) MPa. The experimental results show that the solubility increases substantially, up to (9 to 25)-fold, by adding 5 mol% of ethanol to the supercritical fluids. In the presence of cosolvent ethanol, the solubility enhancements in nitrous oxide system are much greater than that in carbon dioxide system for modified Disperse Yellow 119 at the same temperature and pressure. The solubility data were correlated with the Chrastil and the Méndez-Santiago and Teja models. The Méndez-Santiago and Teja model yields slightly better results than Chrastil model.     

Precipitation kinetics of PMMA sub-micrometric particles with a supercritical assisted-atomization process

Sub-micrometric particles of PMMA were successfully prepared via a supercritical assisted-atomization (SAA) process using acetone as a solvent and supercritical carbon dioxide as a spraying medium. The effects of several key factors on the particle size were investigated. These factors included the concentration of polymer solution, temperature in saturator and volumetric flow rate ratio of carbon dioxide to polymer solution. The shape of the polymer's primary particles is spherical with the arithmetic mean size ranging from 82 nm to 176 nm and the mass-weighted mean size ranging from 127 nm to 300 nm. As evidenced from the experimental results, the lower concentrations of polymer solution, optimized volumetric flow rate ratios, and higher temperatures in saturator can effectively reduce the mean particle size. The precipitation kinetic parameters were determined from the particle size distributions with the aid of the population balance theory. This study found the primary nucleation to be dominant in the precipitation and diffusion may govern particle growth.     

Solubility estimations for Disperse Blue 14 in supercritical carbon dioxide

Supercritical carbon dioxide is an alternative solvent that is considered for dry dyeing processes in the textile industry. The application of this process requires a study to determine the dye solubility in supercritical carbon dioxide. The solubility in supercritical carbon dioxide of a disperse dye at temperatures of 40, 60 and 80 °C and pressures from 100 to 350 bar was evaluated in a previous study. In the work described here, these solubility values have been correlated with fairly good accuracy using a model based on thermodynamic aspects and the use of equations of state. Physical properties and critical parameters of the solid have been estimated using different group contribution methods. The thermodynamic model has been developed by means of a program based on fitting the solid sublimation pressure and binary interaction parameter. The results obtained in the solubility correlation show that the choice of group contribution method is more important than the choice of equation of state.     

Solubility of cyproheptadine in supercritical carbon dioxide; experimental and modeling approaches

Solubility of solute in supercritical fluids at different pressures and temperatures is one of the most important parameters necessary for design of any supercritical fluid-based processes. Among different supercritical fluids, carbon dioxide is one of the most widely used solvents due to its useful and green characteristics. In this work, with the assist of supercritical carbon dioxide as the solvent, solubility of cyproheptadine in different temperatures (308–338 K) and pressures (160–400 bar) are measured using static method. The obtained results demonstrated that solubility of cyproheptadine ranged between 3.35 × 10⁻⁵ and 3.09 × 10⁻³ based on mole fraction. A closer examination of measured solubility data show that not only solubility of cyproheptadine increases by increasing pressure but also experiences a cross over pressure about 200 bar. At last, the measured solubility data are correlated using four widely used density based correlations namely Mendez Santiago–Teja (MST), Kumar and Johnston (KJ), Bartle et al., and Chrastil models. The obtained results demonstrated that the best correlative capability was observed for KJ model leads to the average absolute relative deviation percent (AARD %) of 6.3%.     

Supercritical fluid extraction from Priprioca: Extraction yield and mathematical modeling based on phase equilibria between solid and supercritical phases

This study aimed to investigate the supercritical carbon dioxide extraction of Cyperus articulatus L. (Priprioca). Before the experiments were performed, the raw material was cleaned, vacuum packed and maintained at −5 °C. The moisture content of the material was determined using an oven with forced air circulation operating at 105 °C. The material was then ground, and the mean diameter of the resulting particles was determined using a set of standard sieves. Extraction was performed at pressures of 100–300 bar, temperatures of 40–50 °C, and extraction times up to 240 min using supercritical carbon dioxide as the solvent. For each load, approximately 50 g of Priprioca was packed into the extractor. According to the experimental results, the yields of extraction were significantly influenced by pressure and temperature. Additionally, this paper provides a mathematical model of the supercritical extraction of Priprioca. The employed mathematical model was based on the mass conservation law, which included two partial differential equations for the solute concentration in the solid and fluid phases. By applying a novel method, the distribution coefficient of the extract between supercritical fluid and solid phases was obtained using the criterion of equal fugacity at equilibrium. The model-predicted extraction yield was then compared with the corresponding experimental data. Additionally, the reasons for the deviations between the model and the experimental data under certain operational conditions are discussed.     

Supercritical CO2 and highly selective aromatase inhibitors: Experimental solubility and empirical data correlation

The solubility of highly selective and potent third-generation aromatase inhibitors includes the non-steroidal agents letrozole and anastrozole and the steroid exemestane in supercritical carbon dioxide (SC-CO₂) has been investigated. The experiments were carried out using the simple and static method at pressures in the range of 12.1–35.5 MPa and temperatures ranging from 308 to 348 K. The mole fraction solubilities ranged from 0.22 × 10⁻⁵ to 1.88 × 10⁻⁴. Solubility data were correlated using six empirical models (Chrastil model, dV–A model, K–J model, Bartle model, Yu model and Gordillo model). The results showed that these models can be applied to satisfactory solubility predictions at different pressures and temperatures. A comparison among the six models revealed that the K–J, and Gordillo models gave much better correlations of the solubility data with an average absolute relative deviation (AARD%) ranging from 0.2 to 2.3 and from 1.6 to 2.5%, respectively. Using the correlation results, the heat of drug–CO₂ solvation and that of drug vaporization was separately approximated in the range of −17.3 to −17.5 and 93.0–112.1 kJ mol⁻¹.     

Comparison between the artificial neural network,SAFT and PRSV approach in obtaining the solubility of solid aromatic compounds in supercritical carbon dioxide

The aim of this study is to model the solubilities of solid aromatic compounds in supercritical carbon dioxide (SCCO₂) using feed-forward artificial neural network (ANN). Temperature, pressure, critical properties and acentric factor of each solute have been used as independent variables of ANN model. The parameters of multi-layer perceptron (MLP) network have been adjusted by back propagation learning algorithm using experimental data which have been collected from various literatures. In order to find the optimal topology of the MLP, different networks were trained and examined and the network with minimum absolute average relative deviation percent (AARD%), mean square error (MSE) and suitable regression coefficient (R²) has been selected as an optimal configuration. By this procedure a single hidden layer network composed of nineteen hidden neurons has been found as an optimal topology. Sensitivity error analyses confirmed that the optimal ANN can predict experimental data with an excellent agreement (AARD% = 4.99, MSE = 7.08 × 10⁻⁷ and R² = 0.99699). Capability of the proposed ANN model has compared with those published results which have obtained by SAFT combined with eight different mixing rules (one, two and three parameters mixing rules) and PRSV equation of state (EOS). The best presented overall AARD% for SAFT approach with one, two and three parameters mixing rules are 16.15, 12.32% and 7.65%, respectively while PRSV EOS showed AARD% of 21.10%. The results emphasize that the proposed ANN model can predict the solubilities of solid aromatic compounds in SCCO₂ more accurate than SAFT and PRSV EOS.     

High-pressure phase equilibria for the binary system carbon dioxide + dibenzofuran

The experimental solubility of dibenzofuran in near-critical and supercritical carbon dioxide and the solid–liquid–vapor (SLV) equilibrium line for the CO₂ + dibenzofuran system are reported. The built in-house static view cell apparatus used in these measurements is described. The solubility of naphthalene in supercritical CO₂ and the CO₂ + naphthalene SLV line are also determined in order to assess the reliability and accuracy of the measurement technique. The solubility of dibenzofuran in carbon dioxide is determined at 301.3, 309.0, 319.2, 328.7 and 338.2 K in the 6–30 MPa pressure range. Solubility data are correlated using the Chrastil model and the Peng–Robinson equation of state. This equation is also used to predict the CO₂ + dibenzofuran SLV line. Results show the feasibility of using supercritical CO₂ to extract dibenzofuran.     

The solubility of magnesium chloride and calcium chloride in near-critical and supercritical water

Applications using supercritical water often encounter the presence of inorganic compounds in feed streams, most often with a minor concentration. These compounds can lead to damage of the equipment via erosion, scaling and corrosion or can influence and disturb the main reaction and processes inside the systems. In order to avoid these problems and to predict the influence of these compounds, it is vital to posses knowledge of the properties of the most common inorganic compounds in supercritical water.In continuation of earlier works of the authors, the solubilities of MgCl₂ and CaCl₂ are investigated via a continuous flow method in the range of 660–690 K and 18.5–23.5 MPa. Contrary to earlier experiments with single-valent salts, precipitates were found during the experiments with MgCl₂ after cleaning the setup. These precipitates were analyzed via EDX and ATF-IR. In the course of the experiments, a decrease in pH of the samples was investigated what was caused by a parallel hydrolysis reaction. The solubilities of both investigated salts were corrected for the hydrolysis reaction and correlated via a semi-empirical approach based on the phase equilibrium between the present phases.