Page 144 - Separation process engineering

and energy balances are

(4-1, stage j)

(4-2, stage j)

and

(4-3, stage j)

while the equilibrium relationships are

(4-4, stage j)

When we reach stage j, the values of y, Q , D, and h will be known, and the unknown variables will be
c
j
D
L, V , x, y , H , and h. At the feed stage, the mass and energy balances will change because of the
j+1
j
j+1
j
j+1
j
addition of the feed stream.
Before continuing, we will stop to note the symmetry of the mass and energy balances and the equilibrium
relationships as we go from stage to stage. A look at Eqs. (4-1) for stages 1, 2, and j will show that these
equations all have the same structure and differ only in subscripts. Equations (4-1, stage 1) or (4-1, stage
2) can be obtained from the general Eq. (4-1, stage j) by replacing j with 1 or 2, respectively. The same
observations can be made for the other Eqs. (4-2, 4-3, 4-4a, 4-4b, and 4-4c). The unknown variables as
we go from stage to stage are also similar and differ in subscript only.
In addition to this symmetry from stage to stage, there is symmetry between equations for the same stage.
Thus Eqs. (4-1, stage j), (4-2, stage j), and (4-3, stage j) are all steady-state balances that state

Input = output

In all three equations the output (of overall mass, solute, or energy) is associated with streams L and D.
j
The input is associated with stream V and (for energy) with the cooling load, Q .
c
j+1
Below the feed stage the balance equations must change, but the equilibrium relationships in Eqs. (4-4a,
b, c) will be unchanged. The balance envelopes in the stripping section are shown in Figure 4-2 for a
column with a partial reboiler. The bars over flow rates signify that they are in the stripping section. It is
traditional and simplest to write the stripping section balances around the bottom of the column using the
balance envelope shown in Figure 4-2. Then these balances around stage f + 1 (immediately below the
feed plate) are

(4-5, stage f + 1)

(4-6, stage f + 1)

(4-7, stage f + 1)