Fenske (1932) derived a rigorous solution for binary and multicomponent distillation at total reflux. The derivation assumes that the stages are equilibrium stages.
Consider the multicomponent distillation column operating at total reflux shown in Figure 7-1, which has a total condenser and a partial reboiler. For an equilibrium partial reboiler for any two components A and B,
Equation (7-1) is just the definition of the relative volatility applied to the reboiler. Material ...