Distillation of Substances with Widely Differing Heats of Vaporization: The Peters Transform
This Demonstration computes the number of theoretical stages needed to achieve a separation both with and without the CMO (constant molar overflow) assumption. It is observed, for this particular case, that the CMO analysis overestimates the number of theoretical plates. The binary mixture considered here is composed of ethanol and acetic acid. Vapor-liquid equilibrium data were obtained using a commercial process simulator (ASPEN Properties by ASPEN Technology Inc.) and the Wilson and the Hayden O'Connell models. The column is fed with saturated liquid. You can set the composition of the feed as well as distillate and bottom specifications. Since the two latent heats of vaporization of ethanol and acetic acid are quite different ( and cal/g mol, respectively), one has to use a rigorous analysis where the operating curves are not linear. If the Peters transform is applied,
then the operating and feed lines are again linear and the usual McCabe and Thiele graphical construction can be applied. The Peters method is valid only if the enthalpy-composition lines are straight. (The author checked this condition for this particular mixture with DISTIL, a commercial software product by Hyprotech Ltd.) The chosen reflux ratio is set equal to 1.3 times the minimum reflux ratio, . It should be noted that the CMO assumption overestimates the minimum reflux ratio when . Finally, one can easily see that the following relation is true, when the feed is saturated liquid and the distillate is almost pure ethanol:
, where is the feed composition and .
The red curve in the graphical construction is the equilibrium curve, while the blue, cyan, and magenta lines are the feed line and the rectifying and stripping operating lines, respectively. Finally, the staircase construction, shown in black, allows one to determine of the number of theoretical stages.