Page 169 - Distillation theory

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5.5 Trajectory Bundles for Four- and Multicomponent Mixtures 143

Figure 5.24 shows the evolution of separatrix sharp split region of top section
3,4
2
1
1
S → S → N ≡ S ⇒ N ≡ Reg sh,R at separation of four-component ideal mix-
+
+
sep,r
1,2
ture, when the product is binary mixture 1,2 (i.e., at the intermediate split) (K 1 >
K 2 > K 3 > K 4 , x D1 + x D2 = 1).
+
At small values of the parameter L/V, the stable node N that at the increase
of the parameter L/V moves away from the product point x D in the direction
to vertex 2 appears at edge 1-2 (Fig. 5.24a). After this node reaches reversible
distillation trajectory tear-off point x t1 into face 1-2-4, it turns into the saddle
rev
with one trajectory going out (Fig. 5.24b). After reaching reversible distillation
trajectory tear-off point x t2 into face 1-2-3, it turns into the saddle with two
rev
trajectories going out (Fig. 5.24c). After that two-dimensional separatrix sharp split
3,4
region Reg sh,R that increases at the increase of the parameter L/V appears. The
sep,r
1,2
2
1
stationary points S , S , and N move correspondingly along reversible distillation
+
trajectories at edge 1-2, at face 1-2-3, and at face 1-2-4. Operating [Eq. (5.9)] and
structural[Eq.(5.15)]conditionsoftrajectorytear-offfromtheboundaryelements
2
1
of concentration simplex should be valid for the points S and S . The section’s
2(3)
(2) 1(2) S r +(3)
trajectory can be put in brief as follows: x → S r ⇒ N r .
D
Reg Reg t
D r
Figure 5.25 shows the evolution of top section trajectory bundle at separation
of four-component ideal mixture, when the product is ternary mixture 1,2,3 (i.e., at
indirect split) (K 1 > K 2 > K 3 > K 4 , x D1 + x D2 + x D3 = 1). At small values of the pa-
rameter L/V, the stable node N that at the increase of the parameter L/V moves
+
away from the product point along reversible distillation trajectory appears at face
1-2-3 (Fig. 5.25a). After this node reaches reversible distillation trajectory tear-off
point x t from face 1-2-3 inside concentration tetrahedron, it turns into the saddle
rev
4
1
+
S and one-dimensional separatrix sharp split region Reg sh,R ≡ S → N (one tra-
sep,r
1,2,3
jectory) appears inside concentration tetrahedron (Fig. 5.25b). At further increase
of the parameter L/V, stationary points S and N move correspondingly along re-
+
versible distillation trajectories at face 1-2-3 and inside concentration tetrahedron.
(3) 1(3) +(4)
The section’s trajectory can be put in brief as follows: x .
D → S r t → N r
Reg Reg
D r
Deviations from the described evolution for nonideal zeotropic and azeotropic
mixtures are analogous to those that were discussed before for three-component
mixtures. As an example of such deviation, let’s examine separation of four-
component mixture, the top product of which is component 1 and inside con-
centration tetrahedron there is α 23 -surface, that divides it into component-order
1,2,3,4 1,3,2,4
regions Reg ord and Reg ord . Figure 5.26 shows the evolution of top section region
2,3,4
Reg R ≡ Reg 1 for this case.
w,r att
1
We examine other deviations from ideal behavior at the example of the mix-
ture acetone(1)-benzene(2)-chloroform(3)-toluol(4). Figures 4.15 and 4.16 show