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Keywords:

  • residue curve maps;
  • distillation lines;
  • distillation boundaries;
  • mass transfer;
  • Maxwell–Stefan formulation;
  • efficiency;
  • tray columns;
  • packed columns

Abstract

The relationship is explored between residue curves and composition trajectories in tray and packed distillation columns. The standard model for residue curves as described by, for example, Doherty and Malone is completely consistent, and that published attempts to modify this model to take into account mass transfer effects are flawed. The packed and tray column composition trajectories at total reflux collapse onto the residue curves when each species in the vapor phase has an identical facility for mass transfer (and there is no resistance to mass transfer in the liquid phase). The stationary points of a residue curve map (RCM) and a composition trajectory map (CTM) are the same (pure components and azeotropes). Thus, mass transfer effects do not change the basic structure of the RCM. However, distillation boundaries computed from a mass transfer model are not, in general, identical to those in the RCM. Differences between residue curves and composition trajectories are characterized by the relative length of and angle between the two composition vectors. The relative length of the composition vectors characterizes the separation process and can be best understood as an average efficiency for a multicomponent mixture. For a binary system in a tray column the new efficiency is equal to the Murphree efficiency. For a binary system in a packed column the vector average efficiency is equal to the overall number of transfer units. The average efficiency may also be viewed as the local ratio of the arc length of the actual composition profile to the arc length of the composition trajectory for a reference (virtual) column in which all species have the same facility for mass transfer. The reference composition profile is coincident with a residue curve. © 2004 American Institute of Chemical Engineers AIChE J, 50:3134–3148, 2004