Page 155 - Distillation theory

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5.4 Evolution of Section Trajectory Bundles for Three-Component Mixture 129

two-section columns to the phenomenon of “tangential pinch,” which we examine
in Section 5.6. In our case, when vertex 1 is separation product of three-component
1
+
mixture, at L/V = K the points S and N appear at sides 1-2 and 1-3 not in the
2
vicinity of vertex 1, as in the previous case, but at some distance from it (the tear-
t
off point s 1 ≡ min x ). Therefore, the part of concentration triangle, adjacent to
2
vertex 1 (pinch region Reg tang ), is not filled up with distillation trajectories at any
values of the parameter L/V (Fig. 5.12c).
Another deviation appears in the case of availability of α 23 -line inside concen-
tration triangle. This line is one of the branches of reversible distillation trajectory
for the product point x D1 = 1. At the increase of the parameter L/V first trajectory
+
bundle appears N → S → N . Point S moves along side 1-2 to α 23 – point, and
−
(1)
point N + moves along side 1-3. Second trajectory bundle appears when point S
(1)
+
coincides with α 23 – point on side 1-2 N → S → N . Then point S moves along
−
(2)
α 23 – line, point N + moves along side 1-3 to α 23 – point, and point N + moves
(1) (2)
along side 1-2 from α 23 – point. First trajectory bundle disappears when point S
coincides with α 23 – point on side 1-3. Then point S moves along side 1-3 to vertex
3, and point N + moves along side 1-2 to vertex 2 (Fig. 5.13).
(2)
Along separatrix S − N + (Fig. 5.13b) the temperature decreases abnor-
(1)
mally from point S on α 23 -line to point N + (down along column). In con-
(1)
trast to that along separatrix S − N + the temperature increases normally from
(2)
point S to point N . It is the result of inflection of residue curves on α 23 –
+
(2)
line. The first trajectory bundle is the working one, if composition point in feed
crossection lies on separatrix S − N , and the second trajectory bundle is the
+
(1)
working one, if composition point in feed crossection lies on separatrix S − N .
+
(2)
Let’s note that temperature cannot decrease down along column at the big enough
value of parameter L/V, because temperature increases along residue curves. For
the more the temperature can decrease only if the value of parameter L/V near
enough to (L/V) min .
5.4.2. The Product Is a Binary Mixture (k = 2)
The binary mixture is the separation product of three-component mixture in the
case of split with a distributed component (1,2 : 2,3), including the case of prefer-
able split and in the case of the top section at indirect separation (1,2 : 3).
Let’s start again with the ideal mixture (K 1 > K 2 > K 3 , x D3 , = 0; Fig. 5.14).
Reversible distillation trajectory tear-off from side 1-2 goes on in some point
t
t
x ,defined by Eq. (4.17), at (L/V) t = K 3 (x ) (see Chapter 4). Therefore, at
rev rev rev
L/V < (L/V) t point x D at side 1-2 cannot be the distillation top product point.
rev
t
Alongwiththat,atside1-2thereisastablenode(Fig.5.14a).At(L/V) = (L/V) ,
rev
the bifurcation goes on. Distillation trajectory tear-off from side 1-2 inside con-
centration triangle and the distillation process becomes feasible. The stable node
t
at side 1-2 turns into a saddle in point x . The trajectory bundle appears with
rev
saddle point S at side 1-2 and with the stable node N inside concentration triangle
+
t
at reversible distillation trajectory in the vicinity of point x . At further increase
rev