Page 143 - Distillation theory

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5.2 Calculation of Distillation at Minimum Reflux for Ideal Mixtures 117

5.2.3. Evolution of Separation Product Compositions of Two-Section Columns
at Set Feed Composition
The evolution of separation product compositions of two-section columns in con-
trast to one-section columns depends on two parameters: on the reflux number
and on the withdrawal of top product D/F.
The Underwood equation system investigates the whole set of product compo-
sitions at the given feed composition and at the variable parameters R and D/F
(Petlyuk et al., 1968).
Figures 5.3 and 5.4 show these sets of product compositions correspondingly
for three- and four-component mixtures (calculations are made at α 1 = 1.5, α 2 =
1.1, α 3 = 1.0, and x F = [0.2; 0.3; 0.5] for three-component mixture and at α 1 =
1.8, α 2 = 1.5, α 3 = 1.1, α 4 = 1.0, and x F = [0.1; 0.2; 0.3; 0.4] for four-component
mixture).
Let’s examine the evolution of product points of two-section column at the
increase of R and at D/F = const. At small R (the first class of fractioning, nonsharp
separation), both product points x D and x B lie at the straight line, passing though
liquid–vapor tie-line of feeding x F , and zones of constant concentrations of both

x
D

x
F
2
x B

1
R = 4.4
lim
(D/F) =0.263
pr
1 4
x
F

3
Figure 5.4. Top product compositions x D for an ideal mix-
ture with α 1 = 1.8, α 2 = 1.5, α 3 = 1.1, α 4 = 1.0, x F1 = 0.1,
x F2 = 0.2, x F3 = 0.3, and x F4 = 0.4 at minimum reflux for
different R min and D/F. Lines with arrows − D/F = const.