(23b) On Separation Efficiency

Rising energy costs have renewed interest in energy efficient separations. Such efficiencies can be defined as the free energy of unmixing divided by the free energy that must be added to the process. The greatest efficiencies occur when the energy cost far exceeds any capital cost. In this limit, rate processes are not important, and efficiency is governed by thermodynamics. However, even for isothermal processes, these efficiencies are constrained by the second law of thermodynamics.

The results are interest, especially for dilute solutions. For example, we show that the maximum possible efficiency η for gas absorption and stripping is

(2/(-ln(HSy0/HA)))

where HS and HA are the Henry's law constants of the dilute gas being separated in the absorber and stripper, respectively; and y0 is the mole fraction of this dilute gas exiting the absorber. Similar results for extraction, adsorption, crystallization, and membrane separations seem consistent with earlier estimates for distillation by Agrawal and Herron (AIChE J. 43, 2884-2996 (1997)).