Novel density-based model for the correlation of solid drugs solubility in supercritical carbon dioxide

A novel density-based model derived by a simple modification of the Jouyban et al. model has been proposed to correlate the solubility of solid drugs in supercritical carbon dioxide. The six-parameter model expresses the solubility only as a function of the solvent density and the equilibrium temperature. This model is in contrast to the Jouyban et al. (J. Superiority. Fluids 24 (2002) 19) model, which gives the solubility as a function of the solvent density and the equilibrium temperature and pressure. The performance of the model has been tested on a database of 100 drugs that account for 2891 experimental data points collected from the literature. The comparison in terms of the mean absolute relative deviation for each solid drug and for the entire database between the proposed model and models that have been suggested to be mostly more accurate demonstrates that the proposed model has the best global correlation performance, exhibiting an overall average absolute relative deviation of 8.13%.     

Solubility of Anthraquinone Derivatives in Supercritical Carbon Dioxide: New Correlations

Solubility of several anthraquinone derivatives in supercritical carbon dioxide was readily available in the literature, but correcting ability of the existing models was poor. Therefore, in this work, two new models have been developed for better correlation based on solid–liquid phase equilibria. The new model has five adjustable parameters correlating the solubility isotherms as a function of temperature. The accuracy of the proposed models was evaluated by correlating 25 binary systems. The proposed models observed provide the best overall correlations. The overall deviation between the experimental and the correlated results was less than 11.46% in averaged absolute relative deviation (AARD). Moreover, exiting solubility models were also evaluated for all the compounds for the comparison purpose.     

Thermodynamic model of solubility for CO2 in dimethyl sulfoxide

The solubility of CO₂ in dimethyl sulfoxide has been determined from 293.15 K to 313.15 K and partial pressure of CO₂ from 5.56 kPa to 18.2 kPa. Based on the data obtained from the CO₂ solubility experiments, a gas–liquid phase equilibrium model for CO₂–DMSO system was proposed. The average relative deviation between the experimental data of equilibrium partial pressure of CO₂ in DMSO and the corresponding data predicted by the model proposed is 4.85%, it shows that the agreement is satisfactory.     

A comparison between neural network method and semi empirical equations to predict the solubility of different compounds in supercritical carbon dioxide

Accuracy of seven semi empirical equations for the estimation of solubility of 30 different compounds in supercritical carbon dioxide has been compared with a new neural network method. To base this comparison on a fair basis, a unique set of experimental data was used for both optimization of semi empirical equations’ parameters and training, validation and testing of neural network. Results showed that neural network method with an average relative deviation of about 5.3% was more accurate than the best semi empirical equation with an average relative deviation of about 15.96% for same compounds. It was also found that the average relative deviation of semi empirical equations varies sharply among different compounds, while this quantity is less dependent on material type for neural network method.     

Modeling the entrainer effects on solubility of solutes in supercritical carbon dioxide

Applicability of a previously published equation for calculating the solubility of solutes in supercritical carbon dioxide was extended to calculate the solubility in entrained supercritical carbon dioxide employing 42 experimental data sets collected from the literature. The accuracy of the proposed model was evaluated by calculating both the average absolute relative deviation and the individual absolute relative deviation. The proposed model showed superiority to a previously published similar model, from both correlation and prediction points of view.     

Measurement and correlation of antifungal drugs solubility in pure supercritical CO2 using semiempirical models

In the present study the solubilities of two antifungal drugs of ketoconazole and clotrimazole in supercritical carbon dioxide were measured using a simple static method. The experimental data were measured at (308 to 348) K, over the pressure range of (12.2 to 35.5) MPa. The mole fraction solubilities ranged from 0.2 · 10^?6 to 17.45 · 10^?5. In this study five density based models were used to calculate the solubility of drugs in supercritical carbon dioxide. The density based models are Chrastil, modified Chrastil, Bartle, modified Bartle and Mendez-Santiago and Teja (M–T). Interaction parameters for the studied models were obtained and the percentage of average absolute relative deviation (AARD%) in each calculation was displayed. The correlation results showed good agreement with the experimental data. A comparison among the five models revealed that the Bartle and its modified models gave much better correlations of the solubility data with an average absolute relative deviation (AARD%) ranging from 4.8% to 6.2% and from 4.5% to 6.3% for ketoconazole and clotrimazole, respectively. Using the correlation results, the heat of drug–CO₂ solvation and that of drug vaporization was separately approximated in the range of (?22.1 to ?26.4 and 88.3 to 125.9) kJ · mol^?1.     

Thermodynamic modeling of hydrogen sulfide solubility in ionic liquids using modified SAFT-VR and PC-SAFT equations of state

Equations of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) and the perturbed chain statistical associating fluid theory (PC-SAFT) have been used to model the PVT behavior of ionic liquids and the solubility of H₂S in six imidazolium-based ionic liquids. The studied systems included [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], [bmim][NTF2] and [hmim][NTF2] at various temperatures and pressures.For pure components, parameters of the models have been obtained by fitting the models to experimental data on liquid densities; the average relative deviation between the calculated and experimental densities for ionic liquids is less than 2.42% in the PC-SAFT model and 5.44% in the SAFT-VR approach, the latter which incorporates the square-well potential for short-range interactions. In both models an additional term has been added to account for dipole-dipole interactions between solute molecules resulting from the permanent charges on the chain molecules of the solvents. The model parameters have also been correlated as functions of the molecular weight of the solvents. For binary mixtures of ionic liquids and H₂S, the association interactions between H₂S molecules and between the ionic liquids and H₂S molecules have also been taken into account in both approaches, using binary interaction coefficients. The results show an average deviation of less than 5% in the calculation of the mole fraction of H₂S in the ionic liquids. The effect of inclusion of the polar term has been studied for binary systems in both models.     

Solubility prediction of anthracene in mixed solvents using a minimum number of experimental data

Numerical methods to predict the solubility of anthracene in mixed solvents have been proposed. A minimum number of 3 solubility data points in sub-binary solvents has been employed to calculate the solvent-solute interaction terms of a well established colsolvency model, i.e. the combined nearly ideal binary solvent/Redlich-Kister model. The calculated interaction terms were used to predict the solubility in binary and ternary solvent systems. The predicted solubilities have been compared with experimental solubility data and the absolute percentage mean deviation (APMD) has been computed as a criterion of prediction capability. The overall APMD for 25 anthracene data sets in binary solvents is 0.40%. In order to provide a predictive method, which is based fully on theoretical calculations, the quantitative relationships between sub-binary interaction terms and physicochemical properties of the solvents have been presented. The overall APMD value for 41 binary data sets is 9.19%. The estimated binary interaction terms using a minimum number of data points and the quantitative relationships have then been used to predict anthracene solubility data in 30 ternary solvent systems. The produced APMD values are 3.72 and 15.79%, respectively. To provide an accurate correlation for solubility in ternary solvent systems, an extension to the combined nearly ideal multicomponenet solvent/Redlich-Kister (CNIMS/R-K) model was proposed and the corresponding overall AMPD is 0.38%.     

Measurements for the solid solubilities of antipyrine, 4-aminoantipyrine and 4-dimethylaminoantipyrine in supercritical carbon dioxide

The solid solubilities of three active pharmaceutical ingredients (APIs) of antipyrine, 4-aminoantipyrine and 4-dimethylaminoantipyrine in supercritical carbon dioxide were measured by a semi-flow apparatus. The experiments were taken at 308.2, 318.2 and 328.2 K. The pressure range was from 10 to 22 MPa. These experimental results were correlated by the semi-empirical models of Mendez–Santiago–Teja and Chrastil. A solution model was also employed to fit the measured data. The average absolute relative deviation in solid solubility from semi-empirical models was 4–6%, and that from the solution model was 5–8%. The measured data satisfied the self-consistency test, and the parameters in the semi-empirical models are feasible for data extrapolation.     

Theoretical and experimental study on Chloroquine drug solubility in supercritical carbon dioxide via the thermodynamic,multi-layer perceptron neural network (MLPNN), and molecular modeling

The design and development of supercritical carbon dioxide (sc-CO₂) based processes for production of pharmaceutical micro/nanoparticles is one of the interesting research topics of pharmaceutical industries owing to its attractive advantages. The solubility of drugs in sc-CO₂ at different temperatures and pressures is an essential parameter which should be determined for this purpose. Chloroquine as a traditional antirheumatic and antimalarial agent is approved as an effective drug for the treatment of Covid-19. Pishnamazi et al. (2021) measured the solubility of this drug in sc-CO₂ at the pressure range of 120–400 bar and temperature range of 308–338 K, and correlated the obtained data using some empirical models. In this work, a comprehensive computational approach was developed to more accurately study the supercritical solubility of Chloroquine. The thermodynamic models include two equations-of-state based models (Peng-Robinson and Soave-Redlich-Kowang) and two activity coefficient-based models (modified Wilson's and UNIQUAC)), as well as, a multi-layer perceptron neural network (MLPNN)) were used for this purpose. Also, molecular modeling was performed to study the electronic structure of Chloroquine and identify the potential centers of intermolecular interactions during the dissolution process. According to the obtained results, all of the theoretical models can predict Chloroquine solubility in sc-CO₂ with acceptable accuracy. Among these models, the MLPNN model possesses the highest precision with the lowest average absolute relative deviation (AARD%) of 1.76 % and the highest R_adj value of 0.999.     

Prediction of λmax of 1,4-naphthoquinone derivatives using ant colony optimization

Ant colony optimization (ACO) is a meta-heuristic algorithm, which is derived from the observation of real ants. In this paper, ACO algorithm is proposed to feature selection in quantitative structure property relationship (QSPR) modeling and to predict λ_max of 1,4-naphthoquinone derivatives. Feature selection is the most important step in classification and regression systems. The performance of the proposed algorithm (ACO) is compared with that of a stepwise regression, genetic algorithm and simulated annealing methods. The average absolute relative deviation in this QSPR study using ACO, stepwise regression, genetic algorithm and simulated annealing using multiple linear regression method for calibration and prediction sets were 5.0%, 3.4% and 6.8%, 6.1% and 5.1%, 8.6% and 6.0%, 5.7%, respectively. It has been demonstrated that the ACO is a useful tool for feature selection with nice performance.     

Aqueous solubility calculation of aromatic acids within a wide temperature range using a modified regular solution model

Abstract  

The modified RSFH model, based on the regular solution theory coupled with the Flory-Huggins entropy term, was extended to calculate the solubility of aromatic acids in water within wide temperature ranges. The aqueous solubility data on aromatic acids from the published literature were assembled and validated. A total of 1,009 aqueous solubility data points for 25 aromatic acids within the temperature range of 273–463 K were selected for modeling. The calculation results showed that the solubility of aromatic acids in water could be well represented by the proposed four-parameter solution model within a wide temperature range. The overall absolute average deviation (δ _AAD) is 6.76%. The estimated cohesive energies of the aromatic acids were found to be about 20–30 kJ mol⁻¹. For the majority of the aromatic acids investigated, the cohesive energy could be considered as a constant. Strong temperature dependency, however, was also observed for a few aromatic acids, and misleading results may be obtained if this dependency is neglected. The model also has a certain prediction ability and could be extrapolated to a high temperature range where no experimental solubility data are available.     

Prediction of CO2 Solubility in Polymers by Radial Basis Function Artificial Neural Network Based on Chaotic Self-adaptive Particle Swarm Optimization and Fuzzy Clustering Method

To replace costly and time-consuming experimentation in laboratory, a novel solubility prediction model based on chaos theory, self-adaptive particle swarm optimization （PSO）, fuzzy c-means clustering method, and radial ba- sis function artificial neural network （RBF ANN） is proposed to predict CO2 solubility in polymers, hereafter called CSPSO-FC RBF ANN. The premature convergence problem is overcome by modifying the conventional PSO using chaos theory and self-adaptive inertia weight factor. Fuzzy c-means clustering method is used to tune the hidden centers and radial basis function spreads. The modified PSO algorithm is employed to optimize the RBF ANN connection weights. Then, the proposed CSPSO-FC RBF ANN is used to investigate solubility of CO2 in polystyrene （PS）, polypropylene （PP）, poly（butylene succinate） （PBS） and poly（butylene succinate-co-adipate） （PBSA）, respec- tively. Results indicate that CSPSO-FC RBF ANN is an effective method for gas solubility in polymers. In addition, compared with conventional RBF ANN and PSO ANN, CSPSO-FC RBF ANN shows better performance. The values of average relative deviation （ARD）, squared correlation coefficient （R2） and standard deviation （SD） are 0.1071, 0.9973 and 0.0108, respectively. Statistical data demonstrate that CSPSO-FC RBF ANN has excellent prediction capability and high-accuracy, and the correlation between prediction values and experimental data is good.     

Predicting the dew point pressure for gas condensate reservoirs: empirical models and equations of state

This paper presents a new empirical model to estimate dew point pressure (DPP) for gas condensate reservoirs as a function of routinely measured gas analysis and reservoir temperature. The proposed model was developed using experimentally measured and collected data of 340 gas condensate samples covering a wide range of gas properties and reservoir temperatures. The new model has an average relative deviation (ARD) of 0.44% and average absolute deviation (AAD) of 7.68% or 346 psia (1 psia=6.894757E−3 mPa). The accuracy of the model has been compared to SRK-EOS, PR-EOS and other correlations. Gas condensate samples from this study as well as from literature have been used to check the validity of the proposed model against EOS simulation. These examples have shown that the model successfully captures the physical trend and that the model is reliable. This model is useful to provide an estimate of the DPP when experimentally measured ones are not available.The current study also shows that predicting the DPP for gas condensates depends on the EOS(s), the number of pseudo-components and the characterization of the plus fraction. For most of the gas condensates used in this study, a 10–12 pseudo-components of the heptane plus (C₇₊) fraction resulted in minimum error in calculation of DPP using PR-EOS with Pedersen et al. characterization of the plus fraction.     

Predicting solubility of anthracene in non-aqueous solvent mixtures using a combination of Jouyban-Acree and Abraham models

Quantitative structure property relationships were proposed to calculate the binary interaction terms of the Jouyban-Acree model using coefficients of Abraham solvational models. The applicability of the proposed methods for reproducing solubility data of anthracene in binary solvents has been evaluated using 56 solubility data sets collected from the literature. The mean percentage deviation (MPD) of experimental and calculated solubilities, using predicted mole fraction solubility of anthracene in solvents 1 and 2, has been computed as a measure of accuracy and the MPD of the proposed methods were 5.5 and 4.2%. The accuracy of the method was compared with that of a previously reported method where the MPD was 14.4% and the mean differences between proposed and previous methods was statistically significant. To provide a predictive model, solubility of anthracene was computed using Abraham solvational models and employed to predict the solubility in binary solvents using derived model constants of Jouyban-Acree model and the obtained MPDs were 37.9 and 22.2%, respectively.     

Solubility and micronisation of phenacetin in supercritical carbon dioxide

The rapid expansion of a supercritical solution (RESS) process represents an attractive prospect for producing sub-micron and nano-particles of medical compounds with low solubility. The solubility of phenacetin in supercritical carbon dioxide was measured by the analytical-isothermal method at pressures ranging from 9.0 MPa to 30.0 MPa and temperatures ranging from 308.0 K to 328.0 K. The results show that the mole fraction solubility of phenacetin in supercritical carbon dioxide is up to 10^?5. Four density-based semi-empirical models were introduced to correlate the experimental data. Agreement between the model predictions and experimental data is greater with the Adachi-Lu-modified Chrastil model than with the Chrastil model, Méndez-Santiago-Teja model, and the Bartle model and the average absolute relative deviation (AARD) observed is 0.0483. The preparation of fine phenacetin particles by the RESS process under different conditions of extraction temperatures (308.0–328.0 K), extraction pressures (9.0–30.0 MPa), nozzle temperatures (373.0–393.0 K), nozzle diameters (0.1–0.8 mm), and collection distance (20.0–40.0 mm) was investigated. The size and morphology of the resultant particles were analysed by SEM. A remarkable modification in size and morphology can be obtained by condition-optimisation.     

The Solubility of ammonia in ethanol between 277.35 K and 328.15 K

The solubility of ammonia in ethanol has been measured by a static vapor-liquid equilibrium method. The total pressure ranges up to about 0.72 MPa. The temperature amounts to 277.35, 288.65, 298.15, 308.75, 318.25 and 328.15 K. The experimental results are used to determine Henry's law constant. From their variation with temperature, the average absolute relative deviation of the Henry's law constant from appropriate smoothing equation is 4.42%.     

Equilibrium solubility of carbon dioxide in a 30 wt.% aqueous solution of 2-((2-aminoethyl)amino)ethanol at pressures between atmospheric and 4400 kPa: An experimental and modelling study

New experimental equilibrium data were obtained for the solubility of carbon dioxide in an aqueous solution with 30 wt.% of 2-((2-aminoethyl)amino)ethanol (AEEA) at temperatures ranging from (313.2 to 368.2) K and CO₂ partial pressures ranging from above atmospheric to 4400 kPa. A thermodynamic model based on the Deshmukh–Mather method was applied to correlate and predict the CO₂ solubility in aqueous AEEA solutions. The binary interaction parameters and equilibrium constants for the proposed reactions were determined by data regression. Using the adjusted parameters, equilibrium partial pressures of CO₂ were calculated and compared with the corresponding experimental values at the selected temperatures and pressures. Values of carbon dioxide solubility at other temperatures reported in the literature were also calculated. The average absolute deviation for all of the data points was found to be 8.2%. The enthalpy change of the absorption of CO₂ in the 30 wt.% aqueous solution of AEEA was also estimated with our model.     

Measurement and correlation of solubility of artemisinin in supercritical carbon dioxide

Artemisinin is an effective antimalarial drug isolated from the herbal medicine Artemisia annua L. Supercritical fluid extraction is an environment-friendly method for the extraction of artemisinin. In this work, the solubility of artemisinin in supercritical carbon dioxide was determined by static method at three temperatures of 313 K, 323 K, 333 K and pressures from 11 to 31 MPa. The range of experimental solubility data was from 0.498 × 10⁻³ to 2.915 × 10⁻³ mol/mol under the above-mentioned conditions. Two density-based models (Chrastil and Mendez–Santiago–Teja models) were selected to correlate the experimental data of this work, and the average absolute relative deviation (AARD) was 8.32% and 8.33%, respectively. The correlation results showed good agreement with the experimental data.