Page 152 - Distillation theory

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0521820928c05 CB644-Petlyuk-v1 June 11, 2004 20:15

126 Distillation Trajectories and Conditions of Mixture Separability

j j
The notions of trajectory tear-off regions Reg t(k) or Reg t(k) , possible product
r r
j j i i
(k) (k) i: j i: j
regions Reg and Reg and sharp split regions Reg and Reg at finite
D B sh,r sh,s
i i
reflux are analogous to the notions of trajectory tear-off regions Reg t(n−1) and
rev,r
Reg t(n−1) , possible product regions Reg D and Reg , and reversible distillation
rev,s
B
regions Reg h rev,r and Reg l rev,s for the process of reversible distillation. The sharp
i: j i: j
distillation region of a section Reg or Reg includes the section’s trajectories at
sh,r sh,s
the chosen split, at any reflux, at any product composition (i.e., Reg R,i: j ∈ Reg i: j
w,r sh,r
and Reg R,i: j ∈ Reg i: j for any reflux R and any product point x D or x B ).
w,s sh,s
5.4. Structure and Evolution of Section Trajectory Bundles
for Three-Component Mixtures
To understand the structure of section trajectory bundles for multicomponent
mixtures and their evolution with the increase of reflux number, let’s examine
first three-component mixtures, basing on the regularities of distillation trajectory
tear-off at finite reflux and the regularities of location of reversible distillation
trajectories.
We limit ourselves by examination, mostly, only of the top section in vies of
symmetry of the distillation process and we use the parameter L/V instead of R
(Petlyuk & Danilov, 1998).

5.4.1. The Product Is a Pure Component (k = 1)

The pure component is a separation product of three-component mixture at direct
and indirect splits (1 : 2,3 or 1,2 : 3) if this component is the lightest or the heaviest
one (i.e., if component point is node point of concentration triangle).
Let’s examine, first, the ideal mixture (K 1 > K 2 > K 3 , x D1 = 1; Fig. 5.11). We
1
1
gradually increase the parameter L/V.At L/V < K (K is phase equilibrium
3 3
coefficient of component 3 in vertex 1) Eq. (5.9) is not valid for sides 1-2 and 1-3
adjacent with vertex 1. Therefore, vertex 1 is the stable node N (Fig. 5.11a) (i.e.,
+
it can not be distillation product point). At such values of the parameter L/V the
process, opposite to distillation process, the process of distillation flows mixing is
feasible (see Chapter 2).
1
At L/V = K , there is first bifurcation, Eq. (5.9) becomes valid for side 1-3 and
3
not valid for side 1-2, vertex 1 turns into saddle S (Fig. 5.11b).
1
At L/V = K , there is second bifurcation, trajectory tear-off from vertex 1
2
along sides 1-2 and 1-3 becomes feasible (i.e., inside concentration triangle vertex
turns into unstable node N ) (Fig. 5.11c), distillation process for the product point
−
under consideration becomes feasible, trajectory bundle with the saddle point S at
+
side 1-2 and, with the stable node N at side 1-3 in the vicinity of vertex 1, appears
2,3 S r (2) +(2)
R
−
Reg w,r ≡ N ⇒ N r (N → S → N ). L/V is equal to K 2 in point S and K 3 in
+
−
r
1
point N (see Eq. 5.6).
+