Page 142 - Separation process engineering

Chapter 4. Binary Column Distillation: Internal Stage-by-Stage

Balances

4.1 Internal Balances

In Chapter 3 we introduced column distillation and developed the external balance equations. In this
chapter we start looking inside the column. For binary systems the number of stages required for the
separation can conveniently be obtained by use of stage-by-stage balances. We start at the top of the
column and write the balances and equilibrium relationship for the first stage, and then once we have
determined the unknown variables for the first stage we write balances for the second stage. Utilizing the
variables just calculated we can again calculate the unknowns. We can now proceed down the column in

this stage-by-stage fashion until we reach the bottom. We could also start at the bottom and proceed
upwards. This procedure assumes that each stage is an equilibrium stage, but this assumption may not be
true. Ways to handle nonequilibrium stages are discussed in Section 4.11.
In the enriching section of the column it is convenient to use a balance envelope that goes around the
desired stage and around the condenser. This is shown in Figure 4-1. For the first stage the balance

envelope is shown in Figure 4-1A. The overall mass balance is then

(4-1, stage 1)

Figure 4-1. Enriching section balance envelopes; (A) stage 1, (B) stage 2, (C) stage j

The more volatile component mass balance is

(4-2, stage 1)
For a well-insulated, adiabatic column (Q column = 0), the energy balance is