McCabe-Thiele method constant molal overflow

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 ... 

Example 8.1. Using graphical (McCabe-Thiele) methods, calculate the number of stages required to make the separation described in Section 8.2 and Fig. 8.3. Assume constant molal overflow V = 40kgmole/hr). 

The McCabe-Thiele constructions described in Chapter 8 embody rather restrictive tenets. The assumptions of constant molal overflow in distillation and of interphase transfer of solute only in extraction seriously curtail the general utility of the method. Continued use of McCabe-Thiele procedures can be ascribed to the fact that (a) they often represent a fairly good engineering approximation and (b) sufficient thermodynamic data to justify a more accurate approach is often lacking. In the case of distillation, enthalpy-concentration data needed for making stage-to-stage enthalpy balances are often unavailable, while, in the Case of absorption or extraction, complete phase equilibrium data may not be at hand. 

Introduction. In Section 11.4B the McCabe-Thiele method was used to calculate the number of theoretical steps or trays needed for a given separation of a binary mixture of A and B by rectification or fractional distillation. The main assumptions in the method are that the latent heats are equal, sensible heat differences are negligible, and constant molal overflow occurs in each section of the distillation tower. In this section we shall consider fractional distillation using enthalpy-concentration data where the molal overflow rates are not necessarily constant. The analysis will be made using enthalpy as well as material balances. 

Consider, therefore, Figure 4.6, which denotes a graphical membrane calculation based on the McCabe-Thiele method for distillation. The ordinate, y here, denotes the composition of the permeate phase(s) V. The abscissa, x here, denotes the composition of the reject phase(s) L. Constant values of V and L are assumed throughout, equivalent to a condition of constant molal overflow. To represent the equations, a continuum is... 

This overall approach involving the enthalpy balance with resultant constant molal overflow is known as the McCabe-Thiele method. 

Two common graphical procedures used to calculate the number of theoretical plates for a separation system involving binary mixtures are the McCabe-Thiele and the Ponchon-Savarit methods. The former method is based on the assumptions of constant vapor and liquid flow rates, or constant molal overflow, throughout the column and negligible heat losses, whereas the latter method does not assume constant molal overflow. Before developing the appropriate material balances for either procedure, some standard notation and definitions are necessary. 

The subscripts on V and L have been omitted since constant molal overflow is assumed in the McCabe-Thiele method. Thus, V and L remain constant throughout the rectifying section of the column. Rearranging and solving for yn + i gives... 

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