Question 12.1.6: Solubility of a Solid in Supercritical Fluid (SCF) Using an ...

Using the data in Illustration 12.1-1 and Table 6.6-1, and one of the Peng-Robinson mixture programs discussed in Appendix B and on the website to calculate the vapor-phase fugacities, the following results are obtained.

\ln \left[\frac{x_{1}\left(T_{1}\right) \gamma_{1}\left(\underline{x}, T_{1}\right)}{x_{1}\left(T_{2}\right) \gamma_{1}\left(\underline{x}, T_{2}\right)}\right]=-\frac{\Delta_{ fus } \underline{H}_{1}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right]=-\frac{\triangle_{ fus } \underline{H}_{1}}{R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right] (12.1-19a)

\ln \left[\frac{x_{1}\left(T_{1}\right)}{x_{1}\left(T_{2}\right)}\right]=-\frac{\Delta_{\text {fus }} \underline{H}_{1}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right]=-\frac{\triangle_{\text {fus }} \underline{H}_{1}}{R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right] (12.1-19b)

The predicted and measured naphthalene mole fractions in supercritical carbon dioxide are plotted in Fig. 12.1-1.

Comments

1. Note that the predictions for these extreme conditions are good. Indeed, with only one adjustable parameter \left(k_{ CO _{2}- N }=0.103\right), reasonable predictions are obtained for the solubility of naphthalene in supercritical carbon dioxide for a range of temperatures in the near critical region, and to moderately high pressures.

2. The enhancement factors here are very large, in fact, among the larger nonideal corrections encountered in chemical engineering thermodynamics. (Enhancement factors for other mixtures at cryogenic conditions of 10^{9} and larger have been reported.) Note that at T = 35°C and P = 255.3 bar, the solubility of naphthalene is enhanced by a factor of more than 17 700 above its ideal value; however, its total solubility is still small at less than 2 mol%.

3. The solubility of naphthalene in supercritical carbon dioxide at 60.4◦C increases from a mole fraction of 0.00240 at 1 bar (Illustration 12.1-4) to 0.098 at 291.3 bar. This illustrates the large increase in the solubility of a solute that may occur with increasing pressure, which is the basis of supercritical extraction to, for example, remove caffeine from coffee beans or fragrances and oils from plant material.

4. The Poynting corrections in this illustration are large, reaching values greater than 3. Consequently, the Poynting factor could not be ignored in this example. However, the main contribution to the enhancement factor arises from gas-phase nonidealities (the species fugacity coefficient, \bar{\phi}_{ i }).