Page 277 - Separation process engineering

(7-15)

Note that in this form of the Fenske equation, (FR ) is the fractional recovery of A in the distillate,
A dist
while (FR ) is the fractional recovery of B in the bottoms. Equation (7-15) is in a convenient form for
B bot
multicomponent systems.
The derivation up to this point has been for any number of components. If we now restrict ourselves to a
binary system where x = 1 − x , Eq. (7-11) becomes
B
A

(7-16)

where x = x is the mole fraction of the more volatile component. The use of the Fenske equation for
A
binary systems is quite straightforward. With distillate and bottoms mole fractions of the more volatile
component specified, N min is easily calculated if α AB is known. If the relative volatility is not constant,
α AB can be estimated from a geometric average as shown in Eq. (7-9). This can be estimated for a first

trial as
α avg = (α α ) 1/2
1 R
where α is determined from the bottoms composition and α from the distillate composition.
R
1
For multicomponent systems calculation with the Fenske equation is straightforward if fractional
recoveries of the two keys, A and B, are specified. Equation (7-15) can now be used directly to find N .
min
The relative volatility can be approximated by a geometric average. Once N min is known, the fractional
recoveries of the non-keys (NK) can be found by writing Eq. (7-15) for an NK component, C, and either
key component. Then solve for (FR ) or (FR ) . When this is done, Eq. (7-15) becomes
C bot
C dist

(7-17)

If two mole fractions are specified, say x LK,bot and x HK,dist , the multicomponent calculation is more
difficult. We can’t use the Fenske equation directly, but several alternatives are possible. If we can
assume that all NKs are nondistributing, we have

(7-18a)

(7-18b)

As shown in Chapter 5, Eqs. (7-18) can be solved along with the light key (LK) and heavy key (HK) mass
balances and the equations