With McCabe-Thiele method

Figure 12-11. Total reflux and minimum stages with McCabe-Thiele method. (Reproduced with permission from reference 18. Copyright 1997, American Chemical Society.)...

The McCabe-Thiele method can be used for the design of columns with side streams and multiple feeds. The liquid and vapour flows in the sections between the feed and take-off points are calculated and operating lines drawn for each section. 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

The plot at right shows points taken from the operating lines in the rigorous ChemSep separation and compares them with the ROL and SOL calculated using the McCabe-Thiele method. These calculated operating lines are the straight, solid lines on the plot. 

The feed, at a flow rate of 100 kmol/h, is sent as saturated vapor to the distillation column. The column is equipped with a partial condenser with a vapor product, and a reboiler. For a solvent rate of 500 kmol/h, it is required to determine the required number of equilibrium stages and the optimum feed location for a reflux ratio of 1.5 times the minimum. The McCabe-Thiele method may be used on a solvent-free basis. 

To apply the McCabe-Thiele method to extraction, the equilibrium data are shown on a rectangular graph, where the mass fraction of solute in the extract or V phase is plotted as the ordinate and the mass fraction of solute in the raffinate phase as the abscissa. For a type I system, the equilibrium line ends with equal compositions at the plait point. The use of only one concentration to characterize a ternary mixture may seem strange, but if the phases leaving a given stage are in equilibrium, only one concentration is needed to fix the compositions of both phases. 

Calculate, by modified McCabe-Thiele methods, residue composition and distillation time for binary batch rectification with constant reflux for a given number of ideal stages, boil-up rate, and specified average distillate composition. 

McCabe-Thiele method helps the identification of design troubles that could arrive with non-ideal mixtures when the equilibrium curve shows inflection points, as displayed in Fig. 16.2. 

Figure 16.2 McCabe-Thiele method for mixtures showing equilibrium curves with tangent pinch. Left Position of tangent pinch and critical distillate composition. Right Minimum reflux and feed composition A - feed pinch control, B - tangent pinch control...

Total reflux corresponds to a situation where there is no feed, distillate, or bottoms and where the minimum number of stages is required to achieve a desired separation. It will be recalled that in the McCabe-Thiele method this situation corresponded to having the operating line coincide with the y = x line. 

According to the McCabe-Thiele method, the system for separation is considered on a quasi-binary basis. In this approach, it must be possible to neglect the influence of the solvent, which is acceptable if the phase boundary lines (solubilities) do not change much with concentration during separation. In this case, the number of theoretical stages, the minimal reflux (ratio), the minimum number of theoretical stages, and their mutual dependence can be determined. 

Determination of separating stages by the McCabe-Thiele method for equilibrium curves with an inflection point or an azeotropic point... 

Finally, the calculating procedures described in section 4.7.5 have been summarized below and compared with the graphical McCabe-Thiele method for a particular example of a separation (see the summary). 

A modified McCabe-Thiele method employed in extractive distillation has been described by Nagel and Sinn [78]. Kortiim and Faltusz [79] have dealt with a variety of problems involved in selective separating processes ranging from the design of an automatic apparatus of special steel for continuous operation to the calculation of the minimum reflux ratio and the required amount of additive. 

For the separation of the liquid feed M (composition x ) into two streams of composition Xg (product, distillate) and Xf, (bottom product), the required number of theoretical plates can be determined graphically with the aid of the McCabe-Thiele method, which was used in the past because no computers were available to solve the extensive systems of equations for mass balances and equilibrium relationships. This method is no longer of practical importance, but it is an excellent didactic aid for understanding the basic principles of rectification. 

Short-cut methods and graphical procedures such as the McCabe-Thiele method have declined in importance, since the combination of computer programs with material databanks allows rapid treatment of distillation processes. 

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