Page 106 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521832772c04 CB644-Petlyuk-v1 June 11, 2004 17:49

80 Trajectories of Thermodynamically Reversible Distillation

In addition, the product points should lie on the straight line passing through
the liquid–vapor tie-line of feeding. Hence, it follows that the maximum length
of reversible distillation trajectory is achieved at the intersection of this straight
line with the hyperfaces of concentration simplex that (hyperfaces) correspond to
(n − 1)-component constituents C n−1 of the initial mixture (sharp separation).

4.2.3. Sharp and Nonsharp Reversible Distillation of Ideal Mixtures
For the ideal mixture, one and the same order of increase and decrease of phase
equilibrium coefficients is consistent throughout the whole concentration simplex:
F
F
K > K > ··· > K F > K F (4.9)
1 2 n−1 n
At the sharp separation, the top product contains all the components except the
heaviest component n and the bottom product contains all the components except
the lightest component 1.
Feasible sharp reversible distillation split of ideal mixtures can be presented as
follows: 1, 2,... (n − 1) : 2, 3 ... n. Therefore, at the reversible distillation, com-
ponents 2, 3,... (n − 1) are distributed among the top and the bottom products.
At nonsharp and semisharp reversible distillation, both products contain all the
components or one of the products does not contain the lightest or the heaviest
component. At nonsharp reversible distillation, product points lie in the same
straight line as at sharp distillation but at some distance from the hyperfaces of
the concentration simplex.
The mode of sharp reversible distillation is the most interesting. As far as
x Dn = 0, Eq. (4.6) for this mode for component n looks as follows:
(4.10)
VK n x n = Lx n
i.e., L/V = K n (4.11)

Similarly, for the lower section and for component 1,

Lx 1 = VK 1 x 1 (4.12)
i.e., L/V = K 1 (4.13)

Therefore, in an arbitrary cross-section of upper (lower) section at sharp re-
versible distillation the ratio of liquid and vapor flows is equal to the phase equilib-
rium coefficient of the heaviest (lightest) component (i.e., the component absent
in the product of the section).
If we take an ideal mixture with constant relative volatilities (α i = const),

(4.14)
K i = α i K r
then we’ll get from Eqs. (4.6) and (4.8) for an arbitrary cross-section of the sharp
reversible distillation column:

(i = 1, 2,... n − 1) (for the top section) (4.15)
x i /x j = x Fi /x Fj
x i /x j = x Fi /x Fj (i = 2, 3,... n) (for the bottom section) (4.16)