Page 150 - Distillation theory

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124 Distillation Trajectories and Conditions of Mixture Separability

2 2

a) b)
α α
23 23

132 α 132 α
13 13

123 312 123 312
1 3 1 3
α 13 α 13
23 23
i, j,k
Figure 5.9. Component-order regions Reg ord , trajectory tear-off regions Reg r t(2) and Reg t(2) ,
s
and sharp split regions Reg i: j (hatched) for the acetone(1)-benzene(2)-chloroform(3) mixture
sh
for two splits: (a) 1 : 2,3 (Reg 1:2,3 ) and (b) 1,3 : 2 (Reg 1,3:2 ); 123, 132, 312, component orders in
sh sh
which the phase equilibrium coefficients decrease in component-order region Reg i, j,k .
ord
Now we can introduce the new important notion – sharp split region for column
section at set sharp split (i.e., at fixed set of the components present i and absent j in
the product of column section).
We call for the top section the region, in points of which phase equilibrium
coefficients of the components present in the product (x D,i > 0) are greater than
i: j
those of the components absent (x D,j = 0) “sharp split region” Reg (K Di > K Dj ),
sh,r
i: j
and vice versa for the bottom section Reg (K Bi < K Bj ).
sh,s
As far as Eqs. (5.15) and (5.16) should be valid for the points of trajectory
located inside concentration simplex, the whole trajectory of the section from
tear-off point to point of junction with the trajectory of the second section should
i: j i: j
be located in one region of section sharp split Reg or Reg . For each sharp
sh,r sh,s
i: j i: j
split region, Reg sh,r or Reg sh,s consist of quite definite component-order regions
ijk
Reg . Therefore, for different splits section sharp regions, Reg i: j and Reg i: j are
ord sh,r sh,s
different. For splits without distributed components, sharp split regions of both
i: j i: j
sections coincide with each other Reg = Reg (Fig. 5.9).
sh,r sh,s
For splits with distributed components, sharp split regions of two sections are
different (Fig. 5.10). Reversible distillation regions Reg h rev,r and Reg l rev,s , which
are discussed in Chapter 4, are a particular case of sharp split regions (in this case,
component h is absent in overhead and component l is absent in bottom).
j j
Figures 5.9 and 5.10 show trajectory tear-off regions Reg t(2) and Reg t(2) and
r
s
i: j i: j i i
sharp split regions Reg and Reg of sections at the examples of
sh,r sh,s
three-component azeotropic mixtures acetone(1)-benzene(2)-chloroform(3) and
acetone(1)-methanol(2)-chloroform(3).
5.3.3. Necessary Condition of Mixture Separability for the Set Split

Let’s formulate now the main necessary condition of mixtures separability for the
set split: it is necessary that at the boundary element to which the top product