Page 276 - Separation process engineering

(7-8)

If we define α AB as the geometric average relative volatility,

(7-9)

Eq. (7-8) becomes

(7-10)

Solving Eq. (7-10) for N min , we obtain

(7-11)

which is one form of the Fenske equation. N min is the number of equilibrium contacts including the partial

reboiler required at total reflux. If the relative volatility is constant, Eq. (7-11) is exact.
An alternative form of the Fenske equation that is very convenient for multicomponent calculations is

easily derived. Equation (7-11) can also be written as

(7-12)

(Dx ) is equal to the fractional recovery of A in the distillate multiplied by the amount of A in the feed.
A dist

(7-13)

where (FR ) is the fractional recovery of A in the distillate. From the definition of fractional recovery,
A dist

(7-14)
Substituting Eqs. (7-13) and (7-14) and the corresponding equations for component B into Eq. (7-12)

gives