Page 279 - Separation process engineering

a. Find N at total reflux.
b. Find FR at total reflux.
C,dist
B. Explore. Since operation is at total reflux and relative volatilities are constant, we can use the
Fenske equation.

C. Plan. Calculate N min from Eq. (7-15), and then calculate FR C,dist from Eq. (7-17).

D. Do It. Equation (7-15) gives

Note that α = α = 1/α = 1/α . Equation (7-17) gives
AB tol−cumene BA cumene−tol

which is the desired benzene recovery in the distillate. Note that

E. Check. The results can be checked by calculating FR C,dist using component A instead of B. The

same answer is obtained.
F. Generalize. We could continue this problem by calculating Dx and Bx for each component
i,dist i,bot
from Eqs. (7-13) and (7-14). Then distillate and bottoms flow rates can be found from Eqs. (7-
19), and the distillate and bottoms compositions can be calculated.

7.2 Minimum Reflux: Underwood Equations

For binary systems, the pinch point usually occurs at the feed plate. When this occurs, an analytical
solution for the limiting flows can be derived (King, 1980) that is also valid for multicomponent systems
as long as the pinch point occurs at the feed stage. Unfortunately, for multicomponent systems there will
be separate pinch points in both the stripping and enriching sections if there are nondistributing
components. In this case an alternative analysis procedure developed by Underwood (1948) is used to
find the minimum reflux ratio.

The development of the Underwood equations is quite complex and is presented in detail by Underwood
(1948), Smith (1963), and King (1980). Since for most practicing engineers the details of the
development are not as important as the use of the Underwood equations, we will follow the approximate
derivation of Thompson (1980). Thus we will outline the important points but wave our hands about the
mathematical details of the derivation.

If there are nondistributing HNKs present, a “pinch point” of constant composition will occur at minimum
reflux in the enriching section above where the HNKs are fractionated out. With nondistributing LNKs
present, a pinch point will occur in the stripping section. For the enriching section in Figure 7-2, the mass
balance for component i is

(7-20)