Page 160 - Distillation theory

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

134 Distillation Trajectories and Conditions of Mixture Separability

vertex 1(x B → x t1 →1) and with the node N rev in the point of azeotrope 13(x B →
rev
x t2 →13).
rev
t1
In the tear-off point of the first of this trajectories x , the value of the parame-
rev
ter V/L (for the bottom section, it plays the same role as the parameter L/V for the
t1
top section) equals (V/L) t1 = 1/K 1 (x ), and in tear-off point x t2 of the second
rev rev rev
t1
t2
trajectory (V/L) t2 = 1/K 1 (x ). At V/L < 1/K 1 (x ), there is no trajectory tear-
rev rev rev
off from side 2-3, and there is stable node N at this side that at increase of V/L
+
t1
moves to the point x t1 (Fig. 5.16a). At V/L = (V/L) , there is bifurcation. Dis-
rev rev
tillation trajectory tear-off from side 2-3 becomes feasible. The stable node turns
+
into saddle S. Distillation trajectory with the stable node N at the first of re-
1
versible distillation trajectories (separatrix sharp split region S → N ≡ Reg sh,R )
+
sep,s
2,3
appears (Fig. 5.16b). At further increase of the parameter V/L, the point S moves
from the point x t1 to the point x t2 that reaches at V/L = (V/L) r2 . In this mo-
rev rev rev
ment, there is the second bifurcation – saddle S again turns into the stable node
+
N , distillation trajectory tear-off from side 2-3 becomes unfeasible (Fig. 5.16c).
Therefore, the distillation process is feasible in limited interval of the value of the
parameter V/L (Petlyuk et al., 1984):
(5.17)
(V/L) max > V/L > (V/L) min
As far as the value V/L for the bottom section or the value L/V for the top sec-
tion in the case under consideration is limited from above; the length of trajectory
inside concentration triangle is also limited.
The analogous situation arises in the case if reversible distillation trajectory
bundle does not have node points. For the mixture under consideration, such
reversible distillation trajectories are available for the top product points, located
3
at a small segment of side 1-2, adjacent to vertex 1 (Fig. 5.17b − Reg sh,R ).
sep,r
1,2
Nonmonotony of change of the parameter L/V along the reversible distillation
trajectory inside concentration triangle for the mixture under consideration be-
come apparent if the top product point is located at side 1-3 (Fig. 5.18a). At some
t
value of the parameter L/V = (L/V) , there is a section distillation trajectory
rev
and reversible distillation trajectory tear-off from side 1-3 in point x t = S 1 . Along
rev
with that, stable node N + comes into being at reversible distillation trajectory at
+
some distance from side 1-3 (in point N ). Therefore, at reversible distillation
1
trajectory there is a segment at which there are no points N at any values of the
+
t
parameter L/V. In the example under consideration, (L/V) t = K 2 (x ) = 0, 77.
rev rev
Reversible distillation trajectory intersects two isolines K 2 = 0,77. The first point of
intersection coincides with reversible distillation trajectory tear-off point x t and
rev
t
with adiabatic distillation trajectory tear-off x at L/V = 0,77 (i.e., with the saddle
+
point S 1 ) and the second point of intersection coincides with the stable node N .
1
This fact is connected with that the dependence (L/V) rev = K 2 along reversible
distillation trajectory has minimum (Fig. 5.19). In the two-section column, such