9.5. Multistage Batch Distillation

The separation achieved in a single equilibrium stage is often not large enough to both obtain the desired distillate concentration and a low enough bottoms concentration. In this case a distillation column is placed above the reboiler as shown in Figure 9-2. The calculation procedure will be detailed here for a staged column, but packed columns can easily be designed using the procedures explained in Chapter 10.

For multistage systems x_D and x_W are no longer in equilibrium. Thus, the Rayleigh equation, Eq. (9-7), cannot be integrated until a relationship between x_D and x_W is found. This relationship can be obtained from stage-by-stage calculations. We will assume that there is negligible holdup on each plate, in the condenser, and in the accumulator. Then at any specific time we can write mass and energy balances around stage j and the top of the column as shown in Figure 9-2A. These balances simplify to