Details

Multistage batch distillation can obtain much higher product purity than simple batch distillation. The overall mass balance is:

,

where is the initial molar quantity of the feed mixture, is the molar quantity in the bottoms vessel (the "waste" product), and is the total molar quantity of collected distillate. The component mass balance is:

,

where is the initial mole fraction of component in the feed, is the average mole fraction of component within the collected distillate, and is the final mole fraction within the bottoms vessel.

Each tray in the column is assumed to be in vapor-liquid equilibrium:

.

The function represents an equilibrium curve, plotted on an - diagram. The composition of each stage lies somewhere upon this curve.

An operating line relates the composition of a stage to the adjacent stage composition. The operating line equation is:

,

where is the vapor mole fraction of at stage , is the reflux ratio, and is the liquid mole fraction of at stage . The reflux ratio is:

,

where is the flow rate of liquid returning from the condenser to the column, and is the flow rate of distillate being collected. The Rayleigh equation can be used to solve for the final composition of distillate and bottoms:

,

but the relationship between distillate composition and bottoms composition is complicated with multistage columns, and the mole fractions are obtained numerically.

Reference

[1] P. C. Wankat, "Batch Distillation," Separation Process Engineering: Includes Mass Transfer Analysis, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 2012 pp. 329–347.