Calculation of the solid solubilities in supercritical carbon dioxide using a new G mixing rule

The aim of this study is to develop a new EOS/G^ex-type mixing rule with special attention to calculating the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, and heavy aliphatic and aromatic alcohols in supercritical carbon dioxide. A volume correction term is applied with a combination of second and third virial coefficients which the equation for the third virial coefficient is quadratic, according to the suggestion by Hall and Iglesias-Silva. In this study, the cubic Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state have been used to calculate the solid solubilities of 23 solutes in supercritical CO₂, by using six mixing rules, namely, the Wong-Sandler (WS) rule, the Orbey-Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the new mixing rule. In all cases, the NRTL model was chosen as the excess Gibbs free energy model. The coefficients of the NRTL model and the binary interaction parameters of six mixing rules with two EOSs (PR and SRK EOSs) have been determined for 100 data sets of 23 binary systems over a wide range of temperatures and pressures covering more than 970 experimental data points which are reported in the literature. The results show that the PR EOS with the new mixing rule model is more accurate than the PR and SRK EOSs with the other mixing rules for solid solubility calculations in supercritical carbon dioxide.The regressed interaction parameters of the binary system, without any further modification, were then extended to four ternary mixtures, giving satisfactory results of the solid solubilities in supercritical CO₂.     

Development of activity coefficient model based on COSMO method for prediction of solubilities of solid solutes in supercritical carbon dioxide

A COSMO base activity coefficient model was newly developed to predict the solubilities of solid solutes in supercritical carbon dioxide. This activity coefficient model describes that the system is composed of the surface segments on the solvent molecule and vacancy unlike the conventional model based on COSMO method. The density change of supercritical fluid can be represented by the change of the surface area of the vacancy. This prediction model is referred to “COSMO-vac (vacancy)” model. The solubilities of 16 pharmaceuticals in supercritical carbon dioxide were predicted by COSMO-vac model. The averaged deviations between the logarithmic experimental and predicted results are smaller than unity. Furthermore, the predicted results for the solutes composed of only C, H and O atoms are better than those for the solutes including the other atoms. The percentage of the predicted results within the order of the experimental data at the pressure over 15 MPa is higher than that at the pressures below 15 MPa.     

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%.     

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.     

Equilibrium solubilities of a p-toluenesulfonamide and sulfanilamide mixture in supercritical carbon dioxide with and without ethanol

Supercritical separation processes for a multi-component mixture of solutes are of practical interest. In this study, the experimental equilibrium solubilities of two solute mixtures, p-toluenesulfonamide (p-TSA) and sulfanilamide (SNA), in supercritical carbon dioxide (SC CO₂) were measured at temperatures of 308, 318 and 328 K and pressures in the range of 11.0-21.0 MPa using a dynamic flow method. The effect of cosolvent on the multi-component system was investigated by the addition of a 3.5 mol% ethanol. In the ternary system (p-TSA + SNA + CO₂), the solubility of SNA increased as compared to its binary system (SNA + CO₂), while the solubility of p-TSA decreased. In the quaternary system (p-TSA + SNA + ethanol + CO₂), a significant solubility enhancement was observed for both p-TSA and SNA. The selectivity, which is thought to imply the intermolecular interactions between p-TSA and SNA, was also enhanced by the presence of ethanol so that the two solutes could be separated by a max. purity of 99.4%. The influence of the hydrogen bond interaction on solubility was discussed. The equations of Chrastil, Méndez-Santiago and Teja, and their modified forms were used to correlate the experimental data.     

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.     

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.     

A comparison between semiempirical equations to predict the solubility of pharmaceutical compounds in supercritical carbon dioxide

The aim of this work is to determine, depending on the operation conditions, which semiempirical equation provides the best fit to solubility data of pharmaceutical compounds in supercritical CO₂. Solubility data from 27 different pharmaceutical solutes were collected from literature and the different density-based models (Chrastil, Adachi-Lu, del Valle-Aguilera, Sparks, Kumar-Johnston, Bartle, Méndez Santiago-Teja) together with the Yu's model and Gordillo's model were employed. The results showed that, in general, Sparks’ equation provides the best fit to the solubility data for this kind of solids in supercritical CO₂. However, at certain specific conditions, the best correlation is obtained using Gordillo's equation. By means of a brief comparison with Peng-Robinson equation of state, semiempirical equations present a more accuracy prediction compared to cubic equations of state, and present no drawbacks such as properties estimation and computational difficulties.     

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 chemical warfare agent simulants in supercritical carbon dioxide: experiments and modeling

Solubility data are reported for ethyl phenyl sulfide (EPS) and 2-chloroethyl ethyl sulfide (CEES) in CO₂ at temperatures from 25 to 100 °C. These two sulfide-based compounds are homomorphs for chemical warfare agents (CWAs). Both sulfide–CO₂ mixtures exhibit type-I phase behavior. The maximum in the 100 °C isotherm is approximately 2600 psia for the CEES–CO₂ system and approximately 3400 psia for the EPS–CO₂ system. The Peng–Robinson equation of state (PREOS) is used to model both sulfide–CO₂ mixtures as well as the phase behavior of the 2-chloroethyl methyl sulfide (CEMS)–CO₂ system previously reported in the literature. The Joback–Lydersen group contribution method is used to estimate the critical temperature, critical pressure, and acentric factor for the sulfides. Semi-quantitative estimates of the phase behavior are obtained for the CEES–CO₂ and EPS–CO₂ systems with a constant value of k_ij, the binary interaction parameter, fit to the 75 °C isotherms. However, very poor fits are obtained for the 2-chloroethyl methyl sulfide–CO₂ system regardless of the value of k_ij. On the basis of the high solubility of EPS and CEES in CO₂, supercritical fluid (SCF)-based technology could be used to recycle or recover chemical warfare materials.     

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.     

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.     

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.     

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.     

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 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.     

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.     

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.     

Polymerization of acrylonitrile in supercritical carbon dioxide

A series of fluorinated diblock copolymers, consisting of styrene (St)-acrylonitrile (AN) copolymer [poly(St-co-AN)] and poly-2-[(perfluorononenyl)oxy]ethyl methacrylate, with various compositions as well as with different molecular weights were synthesized by atom transfer radical polymerization and characterized. Dispersion polymerization of acrylonitrile in supercritical carbon dioxide (scCO₂) at 30 MPa and at 65 °C with this kind of amphiphilic block copolymer as a stabilizer and 2,2′-azobisisobutyronitrile as an initiator was investigated. The experimental results indicated that, in the presence of a small amount of poly(St-co-AN) (5 wt% to AN), spherical particles of polyacrylonitrile (PAN) were prepared with small diameter and narrow polydispersity (d_n = 153 nm, d_w/d_n = 1.12), resulting from the high stabilizing efficiency of this fluorinated block copolymer. Furthermore, the polymerization of AN in scCO₂ under different initial pressures especially under low pressure (<14 MPa) was studied. When the polymerization was carried out around the critical pressure of CO₂ (7.7-7.8 MPa), the PANs with high molecular weight (M_ν ≈ 130,000-194,000) were synthesized at high monomer conversion (>90%) no matter whether the stabilizer was added, compared to those synthesized by dispersion polymerization at 30 MPa. It was also found that the crystallinity of PAN synthesized at 7.7-7.8 MPa was somewhat higher than that synthesized at 30 MPa, while its crystallite size did not change.     

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.