Estimation of solubility of solids in supercritical carbon dioxide

Peng-Robinson equation of state(PR EOS)was chosen for modeling the thermodynamic be-havior of supercritical(SC)-CO_2/Solid systems.The necessary critical constants and acentric factorof the solute were obtained by the Sigmund and Trebble(1992)method based on the molecular weightand boiling temperature,and the vapor pressure of the solute was calculated by its meltingtemperature and heat of fusion.This approach compared very favorably with the conventional corres-ponding state theory,but without using critical constants and vapor pressure of solutes.Four mixingrules were tested for the calculation of solid solubility in SC-CO_2.van der Waals(vdW)mixing rulewith one parameter was considered to be most suitable for the estimation of solubility.A simplecorrelation was developed for the SC-CO_2/solid binary interaction coefficient k_(ij) with the meltingtemperature of pure solutes.The solubilities of solids in SC-CO_2 were estimated for eleven binarysystems at various temperatures,the total absolute average     

A comprehensive comparison among four different approaches for predicting the solubility of pharmaceutical solid compounds in supercritical carbon dioxide

Supercritical technologies have been developed in the food, environmental, biochemical and pharmaceutical product processing during the recent decades. Obtaining accurate experimental solubilities of pharmaceutical compounds in supercritical carbon dioxide (SC-CO₂) and their correlations are highly important and essential for the design of industrial operating units. In this study, the solubilities of six pharmaceutical compounds (Anti-HIV, Antiinflammatory and Anti-cancer) in SC-CO₂ were correlated using four different models: cubic equation of state (EoS) model (SRK and modified-Pazuki EoSs), empirical and semi-empirical models (Chrastil, Mendez-Santiago-Teja, Spark et al. and Bian et al. models), regular solution model coupled with the Flory-Huggins equation, and an artificial neural network-based (ANN-based) model. In EoS calculations, twin-parametric van der Waals (vdW2) and Panagiotopoulos-Reid (mrPR) mixing rules were used for estimating the supercritical solution properties, with three different sets employed for obtaining critical and physicochemical properties of the solid compounds. To evaluate the capabilities of various approaches, a comprehensive comparison was carried out among the four models based on several statistical criteria, including AARD, R_adj and F-value. Results of the analysis of variance (ANOVA) indicated that the ANN-based model provided the best results in terms of correlating the experimental solubility of the pharmaceutical compounds in SC-CO₂.     

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.     

A predictive method for the solubility of drug in supercritical carbon dioxide

We present a predictive approach for the solubility of drug in supercritical CO₂. The fugacity of drug in the solid phase is estimated from its melting temperature and heat of fusion, and the fugacity of the drug in its hypothetical liquid state. The fugacity of the drug is calculated from the Peng–Robinson (PR) EOS. Temperature and composition dependence of the interaction parameters a(T,x) and b(x) of the PR EOS are obtained from the quantum mechanics-based, COSMO-SAC solvation model. As a consequence, the method does not require input of experimental data of the mixture. The average logarithmic deviation (ALD-x) in predicted solubility of 46 drugs in subcritical and supercritical carbon dioxide (T = 293.15–473 K, P = 8.5–50 MPa, and 1160 solubility data ranging from 10⁻⁷ to 10⁻²) was found to be 0.81 (a factor of 5.3). The same method was also examined for solid solubility in a variety of solvents (60 solids including 34 different solvents (with different polarities) and 190 drug-solvent pairs) at ambient pressure. The ALD-x was found to be slightly better (0.58 or a factor of 2.89). The proposed method, the PR + COSMOSAC EOS, is thus a useful tool for a priori prediction of solid solubility in scCO₂, as well as for other solvents.     

Analyzing the solubility of fluoxetine hydrochloride in supercritical carbon dioxide

In the pharmaceutical industry where the supercritical fluid-based technologies are utilized it is very important and vital to know the accurate value of the equilibrium solubility of solids required for the engineers to determine the size of the equipments. According to this requirement, the purpose of this study was measuring the solubility of fluoxetine hydrochloride with IUPAC name of 3-phenyl-3-[4-(trifluoromethyl)phenoxy]propan-1-amine hydrochloride using a static method coupled with gravimetric method. The measured solubility data at the temperature and pressure range of 308.15–338.15 K and 16–40 MPa was ranged between 2.65 × 10⁻⁵ and 8.12 × 10⁻⁴ based on the mole fraction. The results revealed that the solubility was increased when the pressure was increased while the effect of the temperature was more complex. Finally, the measured solubility data were correlated using three different correlations namely Bartle et al., Mendez-Santiago–Teja and Kumar and Johnston. The results of modeling revealed that the Bartle et al. model leads to the lowest average absolute relative deviation (AARD %) of 9.48.     

Modified Soave-Redlich-Kwong equations of state applied to mixtures containing supercritical carbon dioxide

The well-known equation of state Soave-Redlich-Kwong and two of its modifications are applied to describe vapor-liquid equilibrium in binary asymmetric mixtures, which contain supercritical carbon dioxide and a heavy component. Several mixing rules including the classical van der Waals mixing rules with one and two interaction parameters, non-quadratic mixing rules, and the used of a Gibbs free energy model, are used with these equations. Seven mixtures containing supercritical carbon dioxide are considered in the study. The experimental data were obtained from literature sources and the adjustable parameters were found by minimizing the errors between predicted and experimental data of the concentration of the solute in the liquid phase. The work allows concluding on the advantages, disadvantages and expected accuracy of these equations of state and mixing rules for correlating vaporliquid equilibrium data in asymmetric systems as those studied.     

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.     

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.     

胆甾醇在超临界CO2中的溶解度测定与关联

利用动态法测定了胆甾醇在超临界CO2中的溶解度。在10—30 MPa,313—343 K下,胆甾醇的溶解度摩尔分率为10-6—10-4。引入与密度有关的混合规则,将二元交互参数表示为密度的函数,采用PR状态方程,关联胆甾醇在超临界CO2中的溶解度。改进后的溶解度模型克服了采用经典混合规则的PR方程不能很好地关联胆甾醇大分子物质的缺陷,大大提高了关联精度。     

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.     

Experimental studies of solubility of elemental sulphur in supercritical carbon dioxide

In recent years, more and more problems of elemental sulphur deposits in natural gas transmission line systems have been reported. Available experimental data on the solubility of sulphur in gases are in too high ranges of temperature, pressure and hydrogen sulphide amount compared to the transport conditions of natural gas. An original experimental apparatus, designed from the study of available works on this subject, is presented and allows the measurement of sulphur solubility. An equilibrium cell establishes the solid–gas equilibrium in conditions of natural gas transportation. To measure the amount of sulphur contained in a known volume of gas, a sample of saturated gas is withdrawn from the equilibrium cell by the way of a flash and pass through a trapping solution. Gaseous elemental sulphur is reactively absorbed into a trapping mixture. Gas chromatography (GC) allows an indirect quantification of sulphur. Experimental isotherm data of sulphur solubility in supercritical carbon dioxide are presented and compared to available studies.     

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.     

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.     

超临界CO2流体中染料溶解度研究进展

综述了超临界CO2流体中染料溶解度的测试装置与方法。分析了超临界CO2流体工艺参数与染料化学结构对分散染料溶解度的影响规律；总结了国内外近二十年的分散染料在超临界CO2流体中溶解度数据，并介绍了分散染料在超临界CO2中的溶解度增溶技术。指出加强染料结构对其溶解性能作用原理及影响规律剖析，超临界CO2中染料溶解行为数据库构建，染料拼色与配色研究三方面为未来的研究重点。     

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.     

苯甲酸在含夹带剂的超临界CO2中溶解度的研究

采用流动法研究和测定了苯甲酸在35、50℃下,10.0—30.0MPa范围内,在纯超临界CO2和含醇系列夹带剂的超临界CO2中的溶解度。实验研究表明,醇系列夹带剂的加入均可明显增大苯甲酸的溶解度,但4种醇的增强作用随着碳链的增加而略有减弱。论述了温度、压力对溶解度的影响,并用Sovova方程对实验数据进行了回归。     

Extraction and solubility evaluation of functional seed oil in supercritical carbon dioxide

Hemp (Cannabis sativa L.) seed oil is valued for its nutritional properties and for the health benefits associated with it. Its greatest feature is that the ratio of linoleic acid and linolenic acid is the desirable value of 3:1. In this research, supercritical carbon dioxide was applied to extraction of functional oil from hemp seed. In order to determine the effect of temperature and pressure on the yield of extracted components, the oil was extracted from hemp seed at temperatures between 40 and 80 °C, pressures of 20–40 MPa and a CO₂ flow rate of 3 mL/min. The solubility of hemp seed oil in SCCO₂ determined experimentally was fitted to the Chrastil equation to determine the model parameters. The solubility calculated by Chrastil equation was compared with the experimental data. Finally, the fatty acid profile of the oil was evaluated by gas chromatography-flame ionization detection (GC-FID). There are no significant differences in the compositions of five abundant fatty acid components of the oil obtained at different sampling times with SCCO₂ extraction and other extraction methods.     

A new hybrid quantitative structure property relationships-support vector regression (QSPR-SVR) approach for predicting the solubility of drug compounds in supercritical carbon dioxide

The purpose of this work was to compare the performance of 7 meta-heuristics algorithms namely: Dragonfly (DA), Ant Lion (ALO), Grey Wolf (GWO), Artificial Bee Colony (ABC), Particle Swarm (PSO), Whale (WAO), and a hybrid Particle Swarm with Grey Wolf (HPSOGWO) optimizers in terms of fine-tuning hyper-parameters of a hybrid quantitative structure property relationships (QSPR)-support vector regression (SVR) for the prediction of molar fraction solubilities of drug compounds in supercritical carbon dioxide (SC-CO₂). A dataset of 168 drug compounds, 13 inputs, and 4490 experimental data points was used to achieve the goal. All 7 models were statistically and graphically approved while the HPSOGWO-SVR was found to over-perform with an average absolute relative deviation (AARD) of 0.706% and an AIC of −14,434,249. The model was subjected to an external test (validation) using 160 experimental data points that were not used in the training and the test set. The overall results proved that the obtained model has good predictivity ability and robustness.     

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.