Correlation of solute solubility in supercritical carbon dioxide using a new empirical equation

A new empirical equation is proposed to correlate solute solubility in supercritical carbon dioxide (SCCO₂). The new empirical model has four parameters per each solute that can be obtained by correlation of the experimental solubility data. The input variables of the equation are pressure, temperature and density of pure SCCO₂. The new equation is applied for correlation of solubility of 24 compounds in SCCO₂ at wide range of temperatures and pressures. The overall percent of absolute average relative deviation (%AARD) of the new equation for correlation of the experimental data is 6.54%. Comparison of the results of the present model with a three-parameter and a four-parameter empirical model demonstrates good accuracy of the new empirical model.     

Determination and calculation of solubility of bisphenol A in supercritical carbon dioxide

Supercritical fluid technology (SFT) as a new technique is very important for clean environment and removal of chemical pollutants. The lack of solubility data of solid solute in certain supercritical fluid is a great obstacle to the successful implementation of SFT. In this work, the solubility of bisphenol A in supercritical carbon dioxide was determined by the dynamic method at the temperatures ranging from 308 to 328 K and pressure range of 11.0–21.0 MPa. The effects of temperature and pressure on solubility were analyzed according to molecular motion theory. The solubility data were correlated using eight different semi-empirical models (Chrastil, Adachi–Lu, Kumar–Johnston, Tang, Sung–Shim, Bartle, Méndez Santiago–Teja and Yu). The comparison between different models was discussed. The thermodynamic properties (total enthalpy ΔH, enthalpy of sublimation Δ_subH and enthalpy of solvation Δ_solvH) of the solid solute were obtained.     

Experimental investigation and modeling of the solubility of carvedilol in supercritical carbon dioxide

This study was aimed to measure the solubility of carvedilol in the temperature and pressure ranges of 308⿿338 K and 160 bar to 400 bar, respectively. In this direction, a homemade high pressure visual equilibrium cell was used to measure the solubility of carvedilol using a static method coupled with gravimetric technique. The results revealed that the carvedilol solubility was ranged between 1.12 ÿ 10^⿿5 and 5.01 ÿ 10^⿿3 based on the mole fraction (mole of carvedilol/mole of carvedilol + mole of CO₂) in this study as the temperature and pressure was changed. Finally, the results were correlated using four density-based semi-empirical correlations including Chrastil, Mendez⿿Santiago⿿Teja (MST), Bartle et al., and Kumar and Johnston (K-J) models. Results revealed that although the K-J model leads to the lowest average absolute relative deviation percent (AARD %) of 6.27%, but it could not be considered as the most accurate correlation since all the used four correlations introduces AARD % of about 6⿿10% which may be in the same range as the experimental error.     

A comparative study between LS-SVM method and semi empirical equations for modeling the solubility of different solutes in supercritical carbon dioxide

A genetic algorithm based least square support vector machine has been used to predict the solubility of 25 different solutes in supercritical carbon dioxide. This model consists of three inputs including temperature, pressure and density of supercritical carbon dioxide and a single output which is the solubility of different solutes in supercritical carbon dioxide. The model predictions were compared with the outputs of seven well-known semi empirical correlations. Results showed that the present method has an average relative deviation of about 4.92% for 25 solutes while the best semi empirical equation resulted an average relative deviation of about 13.60% for same solutes.     

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.     

Measurement and calculation of solubility of quinine in supercritical carbon dioxide

Solubility of quinine in supercritical carbon dioxide(SCCO_2) was experimentally measured in the pressure range of 8 to 24 MPa, at three constant temperatures: 308.15 K, 318.15 K and 328.15 K. Measurement was carried out in a semi-dynamic system. Experimental data were correlated by iso-fugacity model(based on cubic equations of state, CEOS), Modified Mendez–Santiago–Teja(MST) and Modified Bartle semi-empirical models. Two cubic equations of state: Peng–Robinson(PR) and Dashtizadeh–Pazuki–Ghotbi–Taghikhani(DPTG) were adopted for calculation of equilibrium parameters in CEOS modeling. Interaction coefficients(k_(ij) l_(ij)) of van der Waals(vdW) mixing rules were considered as the correlation parameters in CEOS-based modeling and their contribution to the accuracy of model was investigated. Average Absolute Relative Deviation(AARD) between correlated and experimental data was calculated and compared as the index of validity and accuracy for different modeling systems. In this basis it was realized that the semi-empirical equations especially Modified MST can accurately support the theoretical studies on phase equilibrium behavior of quinine–SCCO_2 media. Among the cubic equations of state DPGT within two-parametric vd W mixing rules provided the best data fitting and PR within one-parametric vd W mixing rules demonstrated the highest deviation respecting to the experimental data. Overall, in each individual modeling system the best fitting was observed on the data points attained at 318 K, which could be perhaps due to the moderate thermodynamic state of supercritical phase.     

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.     

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 analysis of clozapine and lamotrigine in supercritical carbon dioxide using static system

The experimental techniques used to obtain the solubilities of clozapine and lamotrigine in supercritical carbon dioxide include a simple static technique. The solubility measurements were performed at temperatures between 318 and 348 K and pressures between 121.6 and 354.0 bar. These chemicals have solubilities with values ranging from 3.6 × 10⁻⁶ to 4.2 × 10⁻⁵ (clozapine) and 1 × 10⁻⁶ to 6 × 10⁻⁵ (lamotrigine) mole fraction. The solubility data were correlated using four semi-empirical density-based models (Chrastil, Bartle, K-J and M-T models). Correlation of the results shows good self-consistency of the data obtained with the Bartle model for clozapine with an overall average absolute relative deviation (AARD%) of 11.21. The calculated results with each four models show satisfactory agreement with the experimental data for lamotrigine with an overall AARD% 11.72, 8.99, 2.75, 3.86 for Chrastil, K-J, Bartle, M-T models, respectively. Using the correlation results, the heat of drug-CO₂ solvation and that of drug vaporization were approximated.     

Solubility of red palm oil in supercritical carbon dioxide: Measurement and modelling

The solubility of red palm oil(RPO) in supercritical carbon dioxide(scCO_2) was determined using a dynamic method at 8.5–25 MPa and, 313.15–333.15 K and at a fixed scCO_2 flow rate of 2.9 g·min~(-1) using a full factorial design. The solubility was determined under low pressures and temperatures as a preliminary study for RPO particle formation using scCO_2. The solubility of RPO was 0.5–11.3 mg·(g CO_2)~(-1) and was significantly affected by the pressure and temperature. RPO solubility increased with pressure and decreased with temperature. The Adachi–Lu model showed the best-fit for RPO solubility data with an average relative deviation of 14% with a high coefficient of determination, R~2 of 0.9667, whereas the Peng–Robinson equation of state thermodynamic model recorded deviations of 17%–30%.     

Solubility of the silver nitrate in supercritical carbon dioxide with ethanol and ethylene glycol as double cosolvents: Experimental determination and correlation

Solubility of the silver nitrate in the supercritical carbon dioxide containing ethanol and ethylene glycol as double cosolvents was measured under certain pressure and temperature range(10–25 MPa, 323.15–333.15 K). The impact of the pressure and temperature on the solubility was also investigated. Based on the experiment data,a correlation model concerning solid's solubility in supercritical fluids was established by combining the solubility parameter with the thermodynamic equation when a binary interaction parameter and a mixed solvent solubility parameter were defined. Experiments show the solubility of AgNO_3 increases with the pressure at a certain temperature. However, the influence of temperature is related to a pressure defined as the turnover pressure(12.3 MPa). When the pressure is higher(or lower) than this turnover pressure, silver nitrate's solubility shows increasing(or decreasing) trend as the temperature rises. Satisfactory accuracy of our presented model was revealed by comparing experimental data with calculated results.     

Ternary solubility of mono- and di-tert-butyl ethers of glycerol in supercritical carbon dioxide

Using a continuous flow apparatus, the ternary solubility of mono- and di-tert-butyl ethers of glycerol (MTBG and DTBG, respectively) in supercritical carbon dioxide was measured at the temperatures of 313.15, 333.15, and 348.15 K; a pressure range of 80-200 bar; and an expanded gas flow rate of 180 ± 10 mL min⁻¹ at average laboratory temperature of 300.15 K and pressure of 0.89 bar. The ternary solubility of the ethers at the constant temperatures of 333.15 and 348.15 K increased with increasing pressure up to the crossover point (i.e., 152 bar for MTBG and 170 bar for DTBG). MTBG exhibited a higher solubility than DTBG in scCO₂. The experimental data for the ternary solubility of MTBG and DTBG were correlated using the Bartle equation.     

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%.     

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.     

Evaluation of density-based models for the solubility of solids in supercritical carbon dioxide and formulation of a new model

Many models have been developed to calculate supercritical solubility behavior and most can be either a semi-empirical relationship or based on an equation of state. In this work, density-based, semi-empirical models were evaluated in terms of their ability to accurately correlate solid solubility in supercritical carbon dioxide. The models considered were the methods of Chrastil, del Valle and Aguilera, Adachi and Lu, Méndez-Santiago and Teja, and Bartle. Six binary systems (solid + supercritical carbon dioxide), each with three isotherms, were selected for this evaluation. The average error was calculated for all 18 isotherms with each of the models evaluated. The solid compounds used in this study were naphthalene, anthracene, fluorene, hydroquinone, 1,5-naphthalenediamine, and cholesterol. The solubility data were obtained from literature. Of the previously mentioned models, the Adachi-Lu and del Valle-Aguilera equations provided, in general, lower average error than the other models. Since the Adachi-Lu equation and the del Valle-Aguilera equation correct for different effects, a new model is proposed in this work as a combination of the previous two methods. The proposed equation provided the least overall average error compared to all other models considered in this study. The new model is particularly useful when the reduced density of the solvent is below 1 where previous models tend to fail. This work also emphasizes on the advantages of expressing density-based models in dimensionless form to avoid dimensional inconsistencies in Chrastil-type models. One of the benefits, for example, is that parameters obtained by different authors can be readily compared, regardless of the units used.     

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.     

Artificial Neural Network modeling of solubility of supercritical carbon dioxide in 24 commonly used ionic liquids

Application of supercritical CO₂ for separation of ionic liquids from their organic solvents or extraction of various solutes from ionic liquid solvents have found great interest during recent years. Knowledge of phase behaviors of the mixtures of supercritical CO₂+ionic liquids is therefore drastic in order to efficiently design such separation processes. In this communication, Artificial Neural Network procedure has been applied to represent the solubility of supercritical CO₂ in 24 mostly used ionic liquids. An optimized Three-Layer Feed Forward Neural Network using critical properties of ionic liquids and operational temperature and pressure has been developed. Application of this model for 1128 data points of 24 ionic liquids show squared correlation coefficients of 0.993 and average absolute deviation of 3.6% from experimental values for calculated/estimated solubilities. The aforementioned deviations show the prediction capability of the presented model.     

Measurement and modeling solubility of bioactive coumarin and its derivatives in supercritical carbon dioxide

To design a supercritical fluid extraction process for the separation of bioactive substances from natural products, a quantitative knowledge of phase equilibria between target biosolutes and solvent is necessary. How-ever, mostly no such information is available in literature to date. Thus in the present study, illustratively the solubility of bioactive coumarin and its various derivatives (i.e., hydroxy-, methyl-, and methoxy-derivatives) in supercritical CO₂ were measured at 308.15–328.15 K and 10–30 MPa. Also, the pure physical properties such as normal boiling point, critical constants, acentric factor, molar volume and standard vapor pressure for coumarin and its derivatives were estimated. By these estimated information, the measured solubilities were quantitatively correlated by an approximate lattice equation of state proposed recently by the present authors.     

Solubility prediction of disperse dyes in supercritical carbon dioxide and ethanol as co-solvent using neural network

Nowadays artificial neural networks(ANNs) with strong ability have been applied widely for prediction of nonlinear phenomenon. In this work an optimized ANN with 7 inputs that consist of temperature, pressure, critical temperature, critical pressure, density, molecular weight and acentric factor has been used for solubility prediction of three disperse dyes in supercritical carbon dioxide(SC-CO2) and ethanol as co-solvent. It was shown how a multi-layer perceptron network can be trained to represent the solubility of disperse dyes in SC-CO2. Numeric Sensitivity Analysis and Garson equation were utilized to find out the degree of effectiveness of different input variables on the efficiency of the proposed model. Results showed that our proposed ANN model has correlation coefficient, Nash–Sutcliffe model efficiency coefficient and discrepancy ratio about 0.998, 0.992, and 1.053 respectively.     

A study on the predictive capability of the SAFT-VR equation of state for solubility of solids in supercritical CO2

In this study, a version of the SAFT-VR equation of state based on the Yukawa potential is used for modeling the solubility of diverse organic compounds, mostly drugs, in supercritical carbon dioxide. Prior to any calculations, the SAFT parameters of pure CO₂ were obtained by correlating the vapor–liquid equilibrium data within the range of 220–300 K. The validity of these parameters was examined by applying them in prediction of the compressibility factor and density in wide temperature and pressure ranges. Due to dependence of the rest of the calculations on the sublimation pressure and lack of its experimental values for most of the solids, it was estimated through two main approaches: application of a group contribution method prior to correlating the solubility data, and calculating it in relation with temperature while correlating the solubility data. For each compound, the first isothermal set of the available experimental data was used for correlation and the rest were predicted. Adopting the same procedure for three empirical models and comparing the resulting deviation percents validated the superiority and high capability of this equation of state in correlating and particularly predicting the solubility in supercritical region. The predicted densities were also in very good agreement with the available experimental values.