Page 151 - Distillation theory

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5.3 Trajectory Tear-Off Theory and Necessary Conditions 125

2 2

a) b)

12 321 23 12 321 23

231 α 13 231 α 13
213 213
312 123 312 123
123 123
1 3 1 3
13 α 23 α 12 13 α 23 α 12
132 132
i, j,k t(2)
Figure 5.10. Component-order regions Reg , trajectory tear-off regions Reg and
ord r
Reg t(2) , and sharp split regions Reg i: j and Reg i: j (hatched for bottom section and shaded
s
sh,r
sh,s
for top section, hatched and shaded for two section) for the acetone(1)-chloroform(2)-
methanol(3) mixture for splits: (a)1,3 : 1,2 (Reg 1,3:1,2 and Reg 1,3:1,2 ) and (b) 2,3 : 1,2 (Reg 2,3:1,2
sh,r sh,s sh,r
and Reg 2,3:1,2 ).
sh,s
point belongs (top product boundary element) there is a region where all the
components absent in the product are the heaviest ones (trajectory tear-off region
j
of the top section Reg t(k) ), and at the boundary element to which the bottom
r
i
product point belongs (bottom product boundary element) there is a region where
all the components absent in the product are the lightest ones (trajectory tear-off
j
region of the bottom section Reg t(k) ).
s
i
If the split without distributed components is set, then the mentioned trajectory
tear-off regions of sections should be boundary elements of one sharp split region
i: j i: j
Reg = Reg (Fig. 5.9).
sh,r sh,s
If the split with distributed components is set, then the mentioned trajectory
tear-off regions of sections should be boundary elements of two different for the
top and bottom sections, but partially overlapping regions of section sharp split
i: j i: j
(Reg
= Reg , Fig. 5.10).
sh,r sh,s
Product points can belong only to those boundary elements of concentration
simplex that contain trajectory tear-off regions. Along with that, product points
should be located at these boundary elements within the limits of some region,
j j
(k) (k)
that we call possible product region Reg or Reg .
D B
i i
The process of sharp distillation is feasible only if each product point belongs to
j
(k)
possible product region in boundary element of concentration simplex (x D ∈ Reg
D
j i
(m)
and x B ∈ Reg ).Thequestionofdeterminationofboundariesofpossibleproduct
B
i
regions at sharp distillation are discussed in the following sections of this Chapter
and in Chapter 8.