Page 90 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: VINOD/IYP T1: FCH
0521820928c03 CB644-Petlyuk-v1 June 11, 2004 20:12

64 Trajectories of Distillation in Infinite Columns Under Infinite Reflux

1 2 3 4 5 12 23 24 25
a)
11 1 1 1
2 1 1 1 1
3 1 1 1 1
4 1 1 1
51 1 1
12 1 1 1 1 1 1
23 1 1 1
24 1 1
25 1 Figure 3.17. An example of identification of
12 → 1 →→ 4 → 5 → 25 connection chains by means of structural ma-
3
trix. Thick line with arrow, bond; dotted line,
transfer to next bond: (a) first chain 12 →
1 2 3 4 5 12 23 24 25 1 → 3 → 4 → 5 → 25, and (b) second chain
b)
1 1 1 1 1 12 → 2 → 23 → 24 → 25.
2 1 1 1 1
3 1 1 1 1
4 1 1 1
51 1 1
12 1 1 1 1 1 1
23 1 1 1
24 1 1
25 1
12 → 2 → 23 → 24 → 25

components of the mixture being separated (i.e., determination of the dis-
tillation subregions Reg sub )
2. Determination of the product simplexes Reg simp from each bonds chain,
for which m > n
3. Checkup of which product simplexes feed point belongs to (x F ∈ Reg simp )
To illustrate the first step, determination of the first and second bonds chain
from structural matrix is shown in Figs. 3.17a, b, respectively. Let’s note that the
attempt to use bond 1 → 4 at creation of the second bonds chain does not lead to
positive result (bonds chain 12 → 1 → 4 → 5 → 25 does not include component
3). To isolate the product simplexes Reg simp from bonds chain with m > n (second
step), the combinations of n stationary points from m are being examined. For
example, for the chain 12 → 1 → 3 → 4 → 5 → 25(12 ⇒ 25), it is possible to get
the following product simplexes Reg simp :
1. 12 → 1 → 3 → 4 → 5
2. 12 → 3 → 4 → 5 → 25
3. 1 → 3 → 4 → 5 → 25
Theothercombinationsofsixstationarypoints12,1,3,4,5,and25,fiveatatime,
do not form product simplexes because they do not contain all the components.
The checkup of belonging of the feed point to one or another product simplex
(third step) should be performed for all the product simplexes. This checkup is