Solids In Supercritical Carbon Dioxide Research Articles

Predicting the solubility of solids in supercritical carbon dioxide using the Chrastil equation with parameters estimated from a group contribution method

Predicting the solubility of a solid in supercritical carbon dioxide (scCO2) can be useful for many applications. However, an accurate prediction is extremely difficult since current methods require knowledge about the properties of the solid in question or lengthy computational calculations and often yield significant deviations. Here, a new approach is proposed that allows the solubility of any solid in supercritical carbon dioxide to be rapidly predicted based solely on the structural formula of the solute. This approach is based on the prediction of Chrastil’s parameters using group contribution methods (GCMs) followed by their use in Chrastil’s equation. For this purpose, group contribution methods to estimate Chrastil’s parameters were developed using more than 6000 experimental data points from 210 solids. These parameters were used to predict the solubility data of 30 solids (around 1300 experimental points) in pure scCO2 with Chrastil’s equation, obtaining a relatively accurate fit for 70 % of the experimental points. The average absolute relative deviation was 51.22 % (less than 8.31 · 10−4 in absolute deviation), while the logarithmic deviation was 10.83 %. The deviations obtained were substantially lower than other estimations proposed in the literature. This methodology is easily extended, faster, and more accurate than other methods and does not require the use of computational methods or the estimation of solid properties. Moreover, new ways to predict the solubility of solids in supercritical carbon dioxide can be developed in the future based on this methodology.

A New Simple Equation of State for Calculating Solubility of Solids in Supercritical Carbon Dioxide

In this work, a modified Redlich–Kwong (βRK) equation of state has been proposed to calculate the solubilities of twenty solids including Ascorbic acid, Fluoranthene, Propyl gallate, Acenaphthene, Asprin, Climbazole, Cinnamic acid, Triclocarban, 4-methoxyphenylacetic acid, Phenoxyacetic acid, Cholesterol,Cholesteryl butyrate, Cholestrol acetat,Triphenylene, Ibuprofen, Acetanilide, Propanamide, Butanamide, Chrysene and Dodecyl gallate in supercritical carbon dioxide (440 data points). The proposed equation of state has been coupled with the van der Waals zero (vdW0) mixing rule. To distinguish the accuracy of the proposed model, the results of the model have been compared with the results of Peng–Robinson (PR) equation of state in combination with the van der Waals one (vdW1) and the Wong-Sandler (WS) mixing rules. The calculation results showed that the proposed model performed well for reproducing the solubility of these twenty solids in supercritical carbon dioxide with absolute average relative deviation (AARD) = 5.7 %.

An association and Wilson activity coefficient model for solubilities of aromatic solid pollutants in supercritical carbon dioxide

The solubilities of various solid pollutants in supercritical carbon dioxide were investigated. The intermolecular interactions play a significant role in determining the solubilities of solids in supercritical carbon dioxide. A new model equation was derived by using the concepts of association and activity coefficient model to correlate the solubilities of solids. The model equation combines the association and Wilson activity coefficient models and includes the interaction potentials between the molecules, which are useful in understanding the behavior of the solid solutes in SCCO2. The new model equation involves five adjustable parameters to correlate the solubilities of solids by incorporating the interactions between the molecules. The equation correlated 75 solid systems with an average AARD of around 9%, which was better than the correlations obtained from standard models such as Méndez Santiago–Teja (MT) model and association model.

Modeling of ternary solubilities of solids in supercritical carbon dioxide in the presence of cosolvents or cosolutes

The investigation of ternary solubilities of solids is essential for the efficient design of extraction processes. The ternary solubilities of solids for cosolvent and cosolute systems are complex functions of temperature, pressure and cosolvent/cosolute composition. The intermolecular interactions between the molecules have a significant role in the solubilities of mixed solids in SCCO2 and cosolvent ternary systems. Two model equations were developed for ternary SCCO2+cosolvent/cosolute systems by using association and activity coefficient models. Both the model equations consist of five adjustable parameters and correlate the ternary solubilities of solids in terms of temperature, pressure, density and cosolvent/cosolute composition. The model equation for cosolvent systems correlated 43 solid pollutants–cosolvent–SCCO2, while the model equation for cosolute systems correlated 19 solute–cosolute–SCCO2 systems available in literature. The average AARD of the model equations are 4.73% and 4.87% for cosolvent ternary systems and mixed solids in SCCO2, respectively.

A new semi-empirical model for correlating the solubilities of solids in supercritical carbon dioxide with cosolvents

The equilibrium solubilities of the solids in supercritical carbon dioxide (SCCO 2) are considerably enhanced in the presence of cosolvents. The solubilities of m-dinitrobenzene at 308 and 318 K over a pressure range of 9.5–14.5 MPa in the presence of 1.13–2.17 mol% methanol as cosolvent were determined. The average increase in the solubilities in the presence of methanol compared to that obtained in the absence of methanol was around 35%. A new semi-empirical equation in terms of temperature, pressure, density of SCCO 2 and cosolvent composition comprising of 7 adjustable parameters was developed. The proposed model was used to correlate the solubility of the solids in SCCO 2 for the 44 systems available in the literature along with current data. The average absolute relative deviation of the experimental data from the model equation was 3.58%, which is better than the existing models.

Comparison the capability of artificial neural network (ANN) and EOS for prediction of solid solubilities in supercritical carbon dioxide

The aim of this study is develop a feed-forward multi-layer perceptron neural network (MLPNN) model to predict the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, heavy aliphatic and aromatic alcohols in the supercritical carbon dioxide. Different networks are considered and trained using 627 data sets; the accuracy of the network is validated by 343 testing data sets. The networks were different regarding to network parameters, such as number of hidden layer, hidden neurons and training algorithm. Using validating data set, the network that is having the lowest absolute average relative deviation percent (AARD%), mean square error (MSE) and the highest regression coefficient ( R 2) is selected as an optimal configuration. To verify the network generalization, 100 different data sets of 23 binary systems have been considered. In the present work, 970 experimental data points of different works (up to now) which covers a wide range of temperatures and pressures have been used. Statistical analyses show that the artificial neural network (ANN) predictions have an excellent agreement (AARD% = 0.98, MSE = 2.8 × 10 −5 and R 2 = 0.99813) with the experimental data set. Also, accuracy of the cubic Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state 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 Esmaeilzadeh–As’adi–Lashkarbolooki (EAL) mixing rule for the prediction of solubility of solids in supercritical carbon dioxide has been compared with a developed neural network model. To base this comparison on a fair basis, same experimental data points of 23 different compounds has been used for both optimization of equations of state parameters and training, validation and testing of neural network. Results show that developed optimal ANN model is more accurate compared to the PR and SRK EOSs with mentioned mixing rules for the same compounds.

Solubilities of resorcinol and pyrocatechol and their mixture in supercritical carbon dioxide

The equilibrium solubilities of dihydroxy benzene isomers (resorcinol and pyrocatechol) and its mixture were experimentally determined at different temperatures (308, 318, 328, and 338 K) in the pressure range of 9.8–16.2 MPa. In the ternary system, the solubilities of pyrocatechol increased while the solubilities of resorcinol decreased relative to their binary solubilities. A new association model was developed based on the concept of formation of solvate complex molecules to correlate the solubility of the solid for mixed solids in supercritical carbon dioxide (SCCO 2). The model equation relates the solubility of solute in terms of the cosolute composition, temperature, pressure and density of SCCO 2. The proposed model correlated the solubilities of sixteen solid systems taken from the literature and current experimental data with an average absolute relative deviation (AARD) of around 4%.

New empirical expressions to correlate solubilities of solids in supercritical carbon dioxide

Supercritical processes are gaining importance in the last few years in the food, environmental and pharmaceutical product processing. The design of any supercritical process needs accurate experimental data on solubilities of solids in the supercritical fluids (SCFs). The empirical equations are quite successful in correlating the solubilities of solid compounds in SCF both in the presence and absence of cosolvents. In this work, existing solvate complex models are discussed and a new set of empirical equations is proposed. These equations correlate the solubilities of solids in supercritical carbon dioxide (both in the presence and absence of cosolvents) as a function of temperature, density of supercritical carbon dioxide and the mole fraction of cosolvent. The accuracy of the proposed models was evaluated by correlating 15 binary and 18 ternary systems. The proposed models provided the best overall correlations.

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.

Diffusion coefficients of solids in supercritical carbon dioxide: Modelling of near critical behaviour

Most of the models proposed in literature for binary diffusion coefficients of solids in supercritical fluids are restricted to infinite dilution; this can be explained by the fact that most of experimental data are performed in the dilute range. However some industrial processes, such as supercritical fluid separation, operate at finite concentration for complex mixtures. In this case, the concentration dependence of diffusion coefficients must be considered, especially near the upper critical endpoint (UCEP) where a strong decrease of diffusion coefficients was experimentally observed. In order to represent this slowing down, a modified version of the Darken equation was proposed in literature for naphthalene in supercritical carbon dioxide. In this paper, the conditions of application of such a modelling are investigated. In particular, we focus on the order of magnitude of the solubility of the solid and on the vicinity of the critical endpoint. Various equations proposed in literature for the modelling of the infinite dilution diffusion coefficients of the solutes are also compared. Ten binary mixtures of solids with supercritical carbon dioxide were considered for this purpose.

A comparison among three equations of state in predicting the solubility of some solids in supercritical carbon dioxide

Equations of state play an important role in chemical engineering designs, and they have assumed an expanding role in the study of the phase equilibria of fluids and fluid mixtures. In this report, a modified Peng-Robinson equation of state by Danesh et al., a modified Peng-Robinson equation of state by Gasem et al., and the Mansoori-Mohsen Nia-Modarress equation of state are used to predict the solubility of some solids in supercritical carbon dioxide. The systems studied were binary mixtures containing supercritical carbon dioxide with Ascorbic acid, Ascorbyl palmitate, Butyl hydroxyl anisole, Dodecyl gallate and Propyl gallate. Interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in each calculation is displayed.

Solubility of mixed solids in supercritical carbon dioxide

The solubilities of pure and equal-molar mixed o-phthalic acid and p-aminobenzoic acid in supercritical carbon dioxide, were determined at 308.15, 318.15, and 328.15 K, and over the pressure range from 8.0 to 21.0 MPa. The solubility of a given solid in a ternary system increased relative to the value of the corresponding binary system, and was in proportion to the solubility of the other solid in the ternary system. The selectivity of supercritical carbon dioxide to the solid mixture increased with the increasing temperature. The model proposed by Mendez-Santiago and Teja was applied using statistical software to correlate the solubility data of both binary and ternary systems with good results.

Temperature independent mixing rules to correlate the solubility of solids in supercritical carbon dioxide

Temperature independent mixing rules in cubic equations of state (EoS) have been used to correlate the solubility of solids in supercritical carbon dioxide. The mixing rules of [Chem. Eng. Sci. 41 (5) (1986) 1303] who proposed a transformation of standard cubic equations of state so that the equations of state constants are really constants, have been evaluated and modified. The modification consists of introducing a volume interaction parameter that affects the solute contribution only as proposed by one of the authors [Ing. Quim. Spain 34 (394) (2002) 380], into the Peng–Robinson equation of state. Literature data for eight binary mixtures containing supercritical carbon dioxide and a solid solute were used for testing the proposed models. The systems studied were binary mixtures containing supercritical carbon dioxide with 2,3-dimethylnaphthalene, 2,6-dimethylnaphthalene, naphthalene, phenanthrene, anthracene, pyrene, benzoic acid and caffeine. The proposed model, in which the equation of state constants and the mixing rules are all temperature independent, correlates the solute concentration in the gas phase similar and better than models that use temperature dependent constants and temperature dependent mixing rules.

Application of the perturbed Lennard–Jones chain equation of state to solute solubility in supercritical carbon dioxide

The perturbed Lennard–Jones chain (PLJC) equation of state is a thermodynamic model based on the perturbation theory of liquid state. This equation has been shown in the past to be a successful model for phase equilibria calculations of binary and ternary fluid mixtures and polymer solutions. In this work, we employed for the first time the PLJC equation to model the solubility of 39 solids in supercritical carbon dioxide. It was shown that the model achieves good correlation with three temperature independent parameters. A comparison of the PLJC with the commonly used Peng–Robinson equation reveals the PLJC equation gives better correlation to the solubility data than the Peng–Robinson model that utilizes temperature dependent parameters.

Spectroscopic measurement of solid solubility in supercritical fluids

AbstractDifferent in situ spectroscopic techniques, including infrared, ultraviolet, and fluorescence, were developed to measure the solubility of organic solids in supercritical carbon dioxide (scCO2). These techniques are applicable over a wide range of concentrations, as low as 10−6 or 10−7 mol fraction, where the conventional flow method is ineffective and less accurate. No separate calibration is required; in fact, the molar absorptivity is determined at the saturation point as an additional benefit. While this technique requires more time per data point, it is more accurate and unbiased than traditional methods at lower concentrations. The Patel‐Teja equation of state was used to correlate the data and expand the data for the ternary system. Data are reported for anthracene, 1,4‐naphthoquinone, and 2‐naphthol in scCO2 and CO2 with methanol cosolvent at 313 K and a pressure range from 7 to 21 MPa.

A Static Method Coupled with Gravimetric Analysis for the Determination of Solubilities of Solids in Supercritical Carbon Dioxide

A static method coupled with gravimetric analysis was developed to measure the solubility of solids in supercritical carbon dioxide. To test the validity and accuracy of this method, the solubilities of naphthalene and phenanthrene were determined. Excellent agreement was obtained between the data in the literature and the data obtained using this method.

A short-cut method to predict the solubilities of solids in supercritical carbon dioxide

A simple empirical method is proposed to evaluate the solubilities of polar and non-polar solids in supercritical carbon dioxide. The method requires as input parameters only two easily obtained properties of pure solids: the molecular weight, M, and the melting temperature, t m. From these data a pseudo-sublimation enthalpy is derived for several classes of compounds grouped according to their polarity degree and M and t m values. The enthalpic datum is inserted in a slightly modified form of a well known relation which links the enhancement factor, E, to the density of supercritical gas. Two empirical parameters embodied in the resulting equation, in turn, are correlated with M and t m for each class of compounds. The density of carbon dioxide is calculated according to the Vetere EOS from the experimental data of pressure and temperature. The method was applied to several compounds which range from high molecular weight hydrocarbons to molecules of biological interest, like vitamins and anti-inflammatory drugs.

An “Excess function-Equation of state” model for solubility of hydrocarbon solids in supercritical carbon dioxide

Abstract The calculation of solubility in supercritical fluids requires models of high precision in the near-critical region, and this is not always the case with classical models. The model proposed here is based on the relations which exist between the Heimholte energy of pure components and the excess Helmholtz energy in a mixing process at constant packing fraction. The pure component properties are represented using any equation of state which is actually included in the equation of state of the mixture. The expression of van Laar was used for the residual term of the excess function. This model was applied to the solid-fluid equilibria occurring in the binary systems composed of a hydrocarbon solid and supercritical carbon dioxide. The best results in the calculations of solubility and molar volumes of the mixture were obtained by using precise equations of state for each compound.

Solubility modeling of solids in supercritical fluids using the Kirkwood-Buff fluctuation integral with the hard-sphere expansion (RISE) theory

The hard-sphere expansion (HSE) theory is incorporated in the Kirkwood-Buff fluctuation integral to predict solubilities of solids in supercritical carbon dioxide and ethylene. While an equation-of-state only for pure supercritical solvent is needed in the HSE model and, thus, there is no need to know the critical properties of solids, three adjustable parameters (two molecular size parameters α 11, α 12, and one dimensionless parameter α 12) in the HSE model are determined to fit experimental solubility data. The results on the solubility prediction by the HSE model with the Peng-Robinson equation-of-state for pure component were better than the Peng-Robinson equation-of-state with the classical mixing rule in both cases: (1) when the molecular parameters in the HSE model and the binary interaction parameter k 12 in the mixing rule were assumed to be temperature-dependent; and (2) when α 12 and k 12 were considered as temperature-dependent.

Solid solubilities in supercritical fluids from group contributions

Inclusion of a covolume dependent mixing rule for the energy parameter enables the prediction of solubility of solids in supercritical fluids. This approach avoids the use of difficult-to-obtain critical properties and acentric factors and involves simple characteristic properties, namely the van der Waals volume and the heat of sublimation of the solid. These properties are predicted using the molecular structure and the Bondi's group contribution method. The predictions of solubilities by the proposed model, including those not employed in the development of the model, are found to be in good agreement with the experimental data on solubilities of a range of solids in supercritical carbon dioxide, ethane, and ethylene.