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7.3 Design Calculation of Two-Section Columns 231

become more and more precise, while obtained points x calc and x calc come nearer
f −1 f
to the sought-for points x f − 1 and x f . The column trajectory at quasisharp separa-
tion, with the calculation finished, may be presented as follows:
1 2 2
x D → qS → qS → x f −1 ⇒⇓ x f ← qS s
r
r
Reg D Reg t Reg t qsh,R qsh,R Reg t
r r [x f −1 ] ∈ Reg sep,r [x f ] ∈ Reg sep,s s
1
← qS ← x B .
s
Reg t Reg B
s
To entirely solve the design task, the described algorithm is applied for the
fixed set of points (x f −1 ) sh at segment [x f −1 ] sh and for the fixed set of excess
lin lin
reflux factors σ = R/R min .
Therefore, the above-described algorithm includes the following steps:
2
3
1
1. The stationary points of section trajectory bundles S , S , S ... N and
+
r r r r
3
2
1
S , S , S ... N are determined for the set value σ = R/R min . We note that
+
s s s s
for azeotropic mixtures stationary points can be located not only at the
corresponding boundary elements of the concentrations simplex, but also
2(α)
at the α-manifolds (the example of location of point S s at an α-surface
is given in Fig. 5.28b).
2. The ends of segments [x f −1 ] sh and [x f ] sh are determined for the set value
lin lin
of σ = R/R min .
3. Preliminary values of little concentrations of impurity non-key components
in separation products x ◦ D,k+2 , x ◦ D,k+3 ,..., x ◦ D,n , x B,1 , x ◦ B,2 ,..., x ◦ B,k−1 are de-
◦
termined for the set value of σ = R/R min and for the set point (x f −1 ) sh at
lin
sh
segment [x f −1 ] .
lin
4. Coefficients a i,j and b i,j of Eqs. (7.5) and (7.6) are determined for the set
sh
value of σ = R/R min and for set point (x f −1 ) .
lin
5. The system of equations for componentwise discrepancies of material bal-
ance in the feed cross-section (Eq. [7.7]) is solved, determining specified
values of little concentrations of the impurity non-key components in the
separation products, for the set value of σ = R/R min and the set point
sh
(x f −1 ) .
lin
6. Steps 4 and 5 are repeated to ensure the set precision of componentwise
material balances in the feed cross-section.
7. Steps 3, 4, and 5 are repeated for different points (x f −1 ) sh at segment
lin
sh
sh
[x f −1 ] , determining point opt (x f −1 ) .
lin lin
8. Points 1 ÷ 7 are repeated for different values of σ = R/R min .
The above-described algorithm can be somewhat modified for more precise
determination of the value R min and the coordinates of the segments [x f − 1 ] lin and
[x f ] lin at nonsharp separation. The modified algorithm should take into consid-
eration that at nonsharp separation in the mode of minimum reflux each prod-
uct contains only key non-product components as impurity ones (i.e., for split
1, 2 ... k : k + 1, k + 2 ... n, the top product contains impurity component k + 1,