Thermodynamic modelling of supercritical fluid–solid phase equilibrium data

doi:10.1016/j.compchemeng.2005.04.001

Computers & Chemical Engineering

Volume 29, Issue 9, 15 August 2005, Pages 1885-1890

https://doi.org/10.1016/j.compchemeng.2005.04.001 Get rights and content

Abstract

The design and development of processes involving supercritical fluids depend on how easy the phase equilibrium can be accurately modelled and predicted. In the work described herein, the supercritical fluid–solid equilibrium has been considered. Modelling the fluid–solid equilibrium is associated with a number of drawbacks, even when it is possible to obtain the experimental solubility data for the solute in the supercritical fluid. In most cases it is necessary to introduce additional adjustment parameters into the model. The developed program, realized in Visual Basic^® language, is based on the fitting of two parameters – the binary interaction parameter (k₁₂) and the solid sublimation pressure ( $P_{2}^{sat}$ ). This program can be used for any fluid–solid equilibrium even when both parameters are known or supposed. The model has been applied to several systems and, as example, in this work, the Penicillin G-CO₂ phase equilibrium data are shown. The results obtained allow affirm that the thermodynamic model applied to fluid–solid equilibrium calculations is useful to predict the behaviour of this system.

Introduction

The interest in the supercritical fluid extraction lies in the possibility developing a process for the antibiotics separation and purification that is able to simplify the number of stages of the actual production process, thus minimizing the economical cost of industrial production and reducing the risk of environmental impact by eliminating the use of organic solvents, besides which increasing the quality of the extracted product. This aspect is of vital important if we think about the nature of the product and its use by humans. Obviously, the first step in order to evaluate the possibilities of the supercritical extraction as an alternative process for the extraction of liquid solvents is to determine the solubility of the penicillins in supercritical solvent and its variation under pressure and temperature (Gordillo, Blanco, Molero, & Martínez de la Ossa, 1999).

Many of the current models are unable to predict the supercritical fluid–solid equilibrium near to the key region for the conditions in which the solvent functions. Another significant problem is that, in most cases, the solute molecules are voluminous and polar, while the solvent molecules are often small and of low polarity.

For these reasons, modelling the fluid–solid equilibrium is associated with a number of drawbacks, even when it is possible to obtain the experimental solubility data for the solute in the supercritical fluid. In most cases it is necessary to introduce additional adjustment parameters into the model.

The thermodynamic development of the system is accompanied by complex mathematical relationships as well as iterative calculations. Cubic equations of state are the basic tools for supercritical fluid–solid equilibria calculations (Coutsikos, Magoulas, & Kontogeorgis, 2003).

There are many properties that affect the results of calculations of solid solubilities in supercritical carbon dioxide using equations of state and mixing rules. Besides the critical constants, the sublimation pressures of solids also have a significant influence on the results of the calculations. The sublimation pressures of high molecular weight compounds are too small for accurate experimental measurement. Reverchon et al. suggested that the sublimation pressure should be considered as an adjustable parameter (Reverchon, Della Porta, Taddeo, Pallado, & Stassi, 1995). Cortesi et al. and Huang et al. have reported data for the sublimation pressures of solids obtained in this way (Cortesi, Kikic, Alessi, Turtoi, & Garnier, 1999; Huang, Tang, Tao, & Chen, 2001).

The aforementioned problem is more marked in the case of organic compounds for which data do not exist above the melting temperature. In such cases the boiling and critical temperature values do not have physical meaning and, moreover, they are parameters that can only be adjusted on the basis of experimental data or can be considered for the correlation of the empirical data obtained.

In this way, it is essential to use a calculation program considering all those considerations. The program developed in this work can be used with three equations of state, two mixing rules and several group contribution methods.

Section snippets

Thermodynamic model

In this work, Peng–Robinson (PR) equation of state (EOS) with Van der Waals (VDW) and Lorentz–Berthelot (LB) mixing rules (MR) have been used.

Several group contribution methods (GCM) for normal boiling temperature (necessary to estimate the critical temperature by some methods), critical temperature and critical pressure of Penicillin G have been used to analyze the reliability of this correlation method and to study the influence of each parameter. Critical parameters have been estimated using

Results and discussion

In an effort to study the influence of the GCM on the thermodynamic model, all of the possible combinations of GCM with the PR EOS and VDW and LB MR were analyzed. The results obtained are shown in Table 2, Table 3 respectively. The values of R² in the lineal adjustment of k₁₂ with temperature and the adjustment of the sublimation pressure to the Clapeyron equation are also shown in these Tables. For a given EOS and a MR, similar trends and AARD values are obtained with all GCM and the

Conclusions

The thermodynamic model developed, that involves the use of the binary interaction parameter and the solid sublimation pressure as adjustment parameters, provides good results in all cases studied for the Penicillin G-CO₂ equilibrium.

The Peng–Robinson equations of state provide good predictions for the solid-fluid equilibrium of the Penicillin G-CO₂ system. Significant differences were not observed in the values of AARD and the trends obtained with each EOS and MR used in this work. Differences

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Thermodynamic modelling of supercritical fluid–solid phase equilibrium data

Abstract

Introduction

Section snippets

Thermodynamic model

Results and discussion

Conclusions

Fluid Phase Equilibria

Journal of Supercritical Fluids

Journal of Supercritical Fluids

Journal of Supercritical Fluids

Journal of Supercritical Fluids

Dyes and Pigments

Fluid Phase Equilibria

New group contribution method for estimating properties of pure compounds

AIChE Journal