Page 275 - Separation process engineering

(7-2a)

and

(7-2b)

However, at total reflux, B = 0 and L = V . Thus the mass balances become
R
N

(7-3)

For a binary system this naturally means that the operating line is the y = x line. Combining Eqs. (7-1) and
(7-3),

(7-4)

If we now move up the column to stage N, the equilibrium equation is

The mass balances around stage N simplify to

Combining these equations, we have

(7-5)

Then Eqs. (7-4) and (7-5) can be combined to give

(7-6)

which relates the ratio of liquid mole fractions leaving stage N−1 to the ratio in the reboiler.

Repeating this procedure for stage N−1, we obtain

(7-7)

We can alternate between the operating and equilibrium equations until we reach the top stage. The result
is