Page 265 - Distillation theory

P1: JPJ/FFX P2: JMT/FFX QC: FCH/FFX T1: FCH
0521820928c07 CB644-Petlyuk-v1 June 11, 2004 20:18

7.3 Design Calculation of Two-Section Columns 239

sh
sh
)
on parameter [(x f −1 ) sh − (x ∞ ) ]/[(x min sh − (x ∞ ) ], the maximum value of
lin f −1 lin f −1 lin f −1 lin
this parameter is not 1.0, but 0.8.
7.3.3. Splits with a Distributed Component

The number of splits with distributed components 1, 2,..., k − 1, k : k, k + 1 ... n
x D,k D
equals (n − 2). The coefficient of distribution of this component β = can be
x B,k B
set (specified) arbitrarily. At the set value of β, the joining of section trajectories
is possible at a unique pair of composition x f−1 and x f . Optimal value of β opt at
which energy expenses for separation are minimum.
The existence of a unique pair of composition x f−1 and x f leads to a necessity
for a change in the algorithm that would make it different from the algorithm for
intermediate splits without distributed components. The new algorithm includes
the following steps:

1. The stationary points of trajectory bundles of the sections are determined
for the set value of σ = R/R min in the same way as in the algorithm for
splits without distributed components.
sh
sh
2. Points (x f −1 ) and (x f ) , are determined for the set value σ = R/R min .
lin lin
Coefficients of equations describing two straight lines of intersection of
2
1
1
2
linear manifolds x F − S − S − N and S − S − N and of linear man-
+
+
r
r
r
s
s
s
2
1
2
1
ifolds x F − S − S − N and S − S − N are determined for this pur-
+
+
s s s r r r
sh
pose. Points (x f −1 ) and (x f ) sh meeting condition of material balance in
lin lin
the feed cross-section are found at these straight lines.
3. Preliminary values of little concentrations of impurity non-key components
in separation products x ◦ , x ◦ ,... x ◦ , x ◦ , x ◦ ,... x ◦ and pre-
D,k+2 D,k+3 D,n B,1 B,2 B,k−2
◦
◦
liminary values of number of trays N and N are determined for the set
r s
value of σ = R/R min . For this purpose, the concentrations and tray numbers
in each section are varied and trial calculations of sections from the ends
of the column to tray composition points, the distance from which to point
(x f −1 ) sh or (x f ) sh is minimal, are realized. At x ◦ , x ◦ ,... x ◦ and
lin lin D,k+2 D,k+3 D,n
◦
N , the trajectory of the top section is finished in point x ◦ , the distance
r f −1
from which to point (x f −1 ) sh is minimum of trial section calculations. This
lin
step of algorithm differs from the corresponding step of the algorithm for
intermediate splits by the fact that tray numbers in the sections are inde-
pendent variables during the process of search, but they are not determined
during the process of calculation of section trajectories. A similar search is
carriedoutforthebottomsection.Sectiontrajectoriesatquasisharpsplitaf-
1
x ◦ D → qS → x ◦ f −1
r
ter preliminary calculation may be put as follows: t qsh,R
1
x ◦ → qS → x ◦ Reg D Reg r Reg sep,r
f
and B s t qsh,R .
Reg Reg Reg
B s sep,s
Because for points x ◦ and x ◦ the material balance in the feed
f −1 f
cross-section is not valid, and further more precise definition of little