Extended Smoker’s Equation for Calculating Number of Stages in Distillation

In 1938, Smoker proposed an analytical closed form formula to calculate the number of stages in a binary distillation column. The equation assumes constant relative volatility and constant molar overflow. For many mixtures, it is practical to assume constant relative volatility. However, the latent heat of vaporization of the different components are generally not equal and hence, the analytical formula fails to predict the number of equilibrium stages with reasonable accuracy. Due to this non-uniform latent heat requirement, the operating lines in McCabe-Thiele diagram are no longer straight but curved. In this paper, a closed form formula is derived without assuming the constant molar overflow. Proposed extended formula predicts the number of equilibrium stages in a binary distillation with constant relative volatility and unequal latent heat requirement.