Defined McCabe-Thiele method

Whereas Example 17.2 was solved based on the McCabe-Thiele method, the way this example is defined favors the shortcut, Fenske-Underwood-Gilliland approach. This method may be used for multicomponent mixtures, but it is not a method selection criterion in this example, which is a binary system. 

Equilibrium data must be converted to ratio units, Y vs. X. These values can be greater than 1.0, since Y = y/(l - y) and X = x/(l - x). The Y = X line has no significance in absorption. As usual the stages are counted at the equilibrium curve. A minimum S/G ratio can be defined as shown in Figure 12-9. If the system is not isothermal, the operating line will not be affected, but the equilibrium line will be. Then the McCabe-Thiele method must be modified to include changing equilibrium curves. 

And we define a function to optimize including the McCabe-Thiele method for the number of trays assuming constant relative volatility. We compute the operating lines as a function of the compositions of the feed, the distillate, and the residue. Next, we use a while statement to compute the number of theoretical trays. Finally, we compute the cost of the vessel and that of the energy required at the boiler. 

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