Correlating and estimating the solubilities of solid organic compounds in supercritical CO2 based on the modified expanded liquid model and the group contribution method

doi:10.1016/j.fluid.2014.10.036

Fluid Phase Equilibria

Volume 385, 15 January 2015, Pages 10-24

https://doi.org/10.1016/j.fluid.2014.10.036 Get rights and content

Highlights

•
Accurate solubility parameters of sc-CO₂ are necessary in solution models.
•
The variables in the solution models are nearly temperature-independent.
•
A modified solution model was proposed based on the linear fit of δ₂ and δ₁/v₁.
•
Group contribution method was developed to estimate the fitting parameters.
•
The solubilities can be estimated in the order of magnitude for most compounds.

Abstract

The expanded liquid model was investigated and a modified solution model was proposed in this paper. The results showed that in the expanded liquid model the accuracy of the solubility parameters of supercritical CO₂ (sc-CO₂) can affect the change of the variables. If the solubility parameters of sc-CO₂ are accurate, the variables in the expanded liquid model are nearly temperature-independent. If the inaccurate solubility parameters of sc-CO₂ were used, the variables in the model would be slightly temperature-dependent. When using the solubility parameter of the solute as variable and calculating the solubility parameters of sc-CO₂ with accurate method in the expanded liquid model, it is found that the solubility parameter of the solute is the linear function of the ratio of the solubility parameter and molar volume of sc-CO₂ (δ₁/v₁). Based on this linear function, the expanded liquid model was modified. In the modified model, the slope and the intercept of the linear function were used as the fitting parameters. The modified model was compared with the other two-parameter expanded liquid models and the results showed the modified model can provide better correlation results with the average absolute relative deviation (AARD) being 13.31%. A group contribution method was developed to estimate the parameters in the modified model. Based on the modified model and the group contribution method, the solubilitis of most of the solutes in sc-CO₂ can be estimated in the order of magnitude.

Graphical abstract

Introduction

Carbon dioxide is often recognized as the green solvent and it is often used as efficient solvent in reaction, separation, crystallization and dyeing processes these days. In the use of sc-CO₂, the solubilities of related compounds are the fundamental data. Determining the solubilities by experiments is laborious. So the simple and quick solubility estimation methods are necessary especially in the early process development when a lot of solubility data are needed.

The compressed gas model is often used in solubility prediction [1], [2] and it is regarded as the most promising model for solubility prediction. However, when using the compressed gas model, empirical parameters are often included in the mixing rules to improve the correlation results. The empirical parameters often change with temperature and are difficult to correlate with the properties and structures of the related compounds. The mixing rules based on G^ex have better theoretical basis, but they are only accurate when the pressure is zero or approaches infinity [3], [4], [5]. In addition to the mixing rules, the compressed gas model has some other limitations. For example, the critical properties, ancentric factors and sublimation pressures of related compounds are necessary. For many compounds, these properties have to be estimated and the estimation errors are unavoidable.

The expanded liquid model is often used in solubility correlation. The advantage of using the expanded liquid model is that only the melting point and melting enthalpy of related compound are needed. These properties can be easily determined by experiments. As the supercritical solution is not the ideal solution, empirical parameters are often included in activity coefficient. By estimating the empirical parameters with appropriate method, the expanded liquid model can also be used in solubility prediction [6], [7].

In this paper, the expanded liquid model is investigated. The calculation methods of the solubility parameters of sc-CO₂ and their effect on the variables in the expanded models were studied. A modified expanded liquid model was proposed and its correlation capability was compared with the other two-parameter expanded liquid models. A group contribution method was developed to estimate the parameters in this new model. Based on the group contribution method, the modified model can be used to predict the solubilities of most of the compounds in the order of magnitude.

Section snippets

Mathematical model

If the supercritical fluid is regarded as the expanded liquid, the solubility of solid solute in the supercritical fluid can be expressed as: $y_{2} = \frac{1}{γ_{2}} \frac{f_{2}^{s}}{f_{2}^{l}}$ where y₂ is the solubility of the solute, γ₂ is the activity coefficient of the solute. The fugacity ratio of pure solid solute and liquid solute can be calculated according to Ref. [8]. $ln (\frac{f_{2}^{s}}{f_{2}^{l}}) = \frac{{- Δ H}_{m}}{R T_{m}} (\frac{T_{m}}{T} - 1) + \frac{{Δ c}_{p}}{R} (\frac{T_{m}}{T} - 1) - \frac{{Δ c}_{p}}{R} ln (\frac{T_{m}}{T})$ where R is the gas constant, T is the temperature, △H_m is the melting enthalpy of the solute, T_m is the

Effect of the solubility parameters of sc-CO₂ from different methods on the variables

The solubility parameters of sc-CO₂ were calculated according to Gidding’s method (Eq. (14)), Williams’ method and the definition of the solubility parameter. In Gidding’s method and Williams’ method, the density or molar volume of sc-CO₂ was calculated using Huang’s 27-parameter EoS. The calculation results are showed in Fig. 1. It can be seen that the solubility parameters calculated using Eq. (15) combined with Huang’s 27-parameter equation or Wagner’s equation is nearly the same. They are

Conclusions

The expanded liquid model and compressed gas model are widely used in solubility prediction for compounds in supercritical fluids. For the compounds with accurate critical properties, ancentric factor and sublimation pressures, the compressed gas model can be used. However, for the compounds without these accurate data, the expanded liquid model is the better choice. In the expanded liquid model, only the melting point and the melting enthalpy of the solute are needed and they can be obtained

Acknowledgement

This work was supported by the National Natural Science Foundations of China (Grant No. 21206077, 21106107).

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Correlating and estimating the solubilities of solid organic compounds in supercritical CO2 based on the modified expanded liquid model and the group contribution method

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Mathematical model

Effect of the solubility parameters of sc-CO2 from different methods on the variables

Conclusions

Acknowledgement

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Fluid Phase Equilib.

Fluid Phase Equilib.

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Cubic equation of state and local composition mixing rules correlation and predictions. Application to the solubility of solids in supercritical solvents

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J. Chem. Eng. Data

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Ind. Eng. Chem. Res.

A method for estimating both the solubility parameters and molar volumes of liquids

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Correlating and estimating the solubilities of solid organic compounds in supercritical CO₂ based on the modified expanded liquid model and the group contribution method

Effect of the solubility parameters of sc-CO₂ from different methods on the variables

Prediction of solubility of the aromatic compounds in supercritical CO₂ using molecular topology