Multistage Evaporation Rectification

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. 

The McCabe-Thiele method makes the following assmnptions  

The column consists of theoretical plates, that is, equilibrium exists at each plate. The vapor (D in moles per unit time) and liquid (F in moles per unit time) streams in the rectification and stripping sections are constant (prerequisite the molar enthalpies of evaporation of A and B are almost equal and adiabatic conditions are present). 

Total mass balance around the rectification section  

With the reflux ratio v = F/ this gives the balance line around the rectification section  

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