Computational procedures that enable the rigorous solution of equilibrium-stage multicomponent distillation problems to be effected rapidly to an accuracy depending only on equilibrium and enthalpy data. There are four types of restricting equations in the equilibrium stage model. (p. 330)

1. 1 The equilibrium relation:

   $$y_{i,n}=K_{i,n}{x}_{i,n}$$

2. 2 Componential mass balance for stage n:

   $$L_{i,n}+V_{i,n}-L_{i,n+1}-V_{i,n+1}-f_{i,n}=0$$

   where f_i,n represents the feed or side stream.

3. 3 Energy balance for stage n:

   $$L_n{h}_n+V_n{h}_n-L_{n+1}{h}_{n+1}-V_{n-1}{h}_{n-1}-f_n{h}_{f,n}-q_n=0$$

   where q_n represents the heat input on stage n.

4. 4 Inherent restrictions on mole fractions:

   $$\begin{array}{l}{\displaystyle \sum x_{i,n}=1.0}\\ {\displaystyle \sum y_{i,n}=1.0}\end{array}$$

These equations are insufficient in number to define a unique operation of a column and fix the concentrations, temperature, pressure, and flow-rate variable in the column. For a column with a single feed, a total condenser, and a partial reboiler, the number of design variables is C+2N+9 for C components with N-1 trays.