McCabe

Fig. 25. McCabe-Thiele diagram, (a) Number of theoretical plates, 5 (b) number of actual plates, 8.

The McCabe-Thiele approach has been developed to describe the Sorbex process (76). Two feed components, A and B, with a suitable adsorbent and a desorbent, C, are separated ia an isothermal continuous countercurrent operation. If A is the more strongly adsorbed component and the system is linear and noninteracting, the flows ia each section of the process must satisfy the foUowiag constraints for complete separation of A from B ... 

McCabe-Thiele diagrams for nonlinear and more practical systems with pertinent inequaUty constraints are illustrated in Figures 11 and 12. The convex isotherms are generally observed for 2eohtic adsorbents, particularly in hydrocarbon separation systems, whereas the concave isotherms are observed for ion-exchange resins used in sugar separations. 

Alternative approaches are to be found in the hterature. Derivations of the above equations are given in numerous texts (2,10—12), which also describe graphical or analytical solutions to the problem. Many of these have direct analogues in other separation processes such as distillation (qv) and hquid—hquid extraction, and use plots such as the McCabe-Thiele diagram or Ponchon-Savarit diagram. 

MicroMENTOR is an educational package for solving distillation problems and includes MCCABE, PONCH, and BATCH for the MaCabe-Thiele, Ponchon-Savarit, and Batch binary distillations (11). The commercially available distillation software packages have been surveyed (15). Por reactive distillation, ASPEN software (16) is weU-known and widely adopted. 

The graphics capabiUties of the CAD/CAM environment offer a number of opportunities for data manipulation, pattern recognition, and image creation. The direct appHcation of computer graphics to the automation of graphic solution techniques, such as a McCabe-Thiele binary distillation method, or to the preparation of data plots are obvious examples. Graphic simulation has been appHed to the optimisation of chemical process systems as a technique for energy analysis (84). 

R. W. Rousseau and W. L. McCabe, Paperpresented at the World Congress on Chemical Engineering, Amsterdam, June 1976. 

Fig. 3. A McCabe-Thiele diagram for a hypothetical square cascade section illustrating pinching. Terms are defined ia text.

Fig. 8. McCabe-Thiele diagram. Terms are defined in text.

The McCabe-Thiele method employs the simplifying assumption that the molal overflows in the stripping and the rectification sections are constant. This assumption reduces the rectifying and stripping operating line equations to ... 

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

W. L. McCabe andj. C. Smith, Unit Operations of Chemical Engineering, 3rd ed., McGraw-HiU Book Co., Inc., New York, 1976, Chapt. 19. 

McCabe, Smith, and Harriott, Unit Operations of Chemical Engineeiing, 5th ed., McGraw-Hill, 1993. 

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