Poynting enhancement factor

The numerator quantifies the effect of hydrostatic pressure on the fugacity of the solid phase. The exponential term is known as the Poynting correction (17). The denominator quantifies the fluid phase intermolecular interactions and density effects. Note that the enhancement factor is dependent on the solid volume as well as the interactions in the supercritical fluid. A solute with a large solid molar volume will have a larger enhancement factor than a solute with a smaller solid molar volume at the same temperature and pressure when the interactions in the supercritical phase are identical. To further understand the molecular interactions in supercritical fluids, it is interesting to decompose the enhancement factor into these two effects. We may define a fluid enhancement factor, Ep, and a Poynting enhancement factor, Ep,... 

The enhancement factor contains three terms supercritical phase, ideal behaviour of the pure component 2 in the vapour phase at the sublimation pressure, and the Poynting factor that describes the influence of the pressure on the fugacity of pure solid 2. 

Note that the enhancement factor E has contributions from both the Poynting factor and the vapor-phase fugacity coefficient, both of which are important at high pressure, and that —> 1 as 7 —> 7 . 

Assuming that the COj-naphthalene mixture obeys the Peng-Robinson equation of state with C02-n = 0.103, estimate the.solubility of naphthalene in the CO2 supercritical fluid (SCF). Also compute the predicted enhancement factors and the contribution of the Poynting factor to the enhancement factor. 

The first term A is for ideal gas solubility, the second term B accounts for the non-ideality, while the third term C (Poynting correction) accounts for the pressure effects. The product of the second and third terms is often referred as the Enhancement Factor (over the ideal). In the absence of data, the sublimation pressure may be approximated through extrapolation of the vapor pressure information. 

Figure 12.12 Supercritical enhancement of the solubility of solid methane(l) in fluid hydro-gen(2) at 76 K. Points are experimental data of Hiza and Herring [8]. Solid line is from the ideal-gas law dashed line is the ideal-gas result corrected by a Poynting factor dash-dot line is the approximation (12.2.14) with the fugacity coefficient computed from the simple virial equation via (12.2.16). Figure after Chueh and Prausnitz [7].

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