Page 251 - Separation process engineering

(6-6)

Equations (6-4) and (6-5) are valid for all stages in the column, 2 ≤ j ≤ N − 1, and are repeated for each
of the C components. If a stage has no feed, then F = D = 0.
j j
For a total condenser, the mass balance is

(6-7)

Since x = x y = K x and x = /L , this equation becomes
D, 2
2 2
1
1
1
1
(6-8)
where

(6-9)

Note that only B does not follow the general formulas of Eq. (6-6). This occurs because the total
1
condenser is not an equilibrium contact.
For the reboiler, the mass balance is

(6-10)

Substituting y = K x and = L x = Bx , we get
bot
N N
N
N N
N
(6-11)
where

(6-12)

In matrix notation, the component mass balance and equilibrium relationship for each component is

(6-13)

This set of simultaneous linear algebraic equations can be solved by inverting the ABC matrix. This can