Page 178 - Distillation theory

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

152 Distillation Trajectories and Conditions of Mixture Separability

2
2
+
+
Therefore, points x f −1 and x f cannot lie in bundles S − N and S − N at ar-
r r s s
bitrary values of the parameter (L/V) r , but only at one definite value of this
parameter.
The question about location of points x f −1 and x f for splits with distributed
component is discussed below.
The task of calculation of minimum reflux mode consists in the determination
of parameter (L/V) min and of compositions x f−1 and x f at the joining of sections
r
trajectories. Conditions of joining of sections trajectories are different for different
splits: for direct and indirect ones, for intermediate ones, and for splits with dis-
tributed component. Therefore, algorithms of calculation of minimum reflux mode
aredifferentforthesesplitsbutincludecommonpreliminarystages:(1)calculation
2
1
2
1
of coordinates of sections bundles stationary points S , S , S , S ,... N , N at
+
+
s
r
s
s
r
r
gradually increasing value of the parameter (L/V) r (i.e., calculation of reversible
distillation trajectories of sections for set product points), and (2) linearization
1
1
of separatrix trajectory bundles Reg sh,R ≡ (S ⇒ N ) and Reg sh,R ≡ (S ⇒ N )
+
+
sep,r r r sep,s s s
2
+
(rectifying and stripping sharp split regions) and Reg min,R ≡ (S ⇒ N ) and
r
sep,r
r
2
Reg min,R ≡ (S ⇒ N )(rectifying and stripping min-reflux regions) (i.e., calcu-
+
sep,s s s
lation of linear equation coefficients, describing the straight lines, planes, or hy-
perplanes, going through the stationary points of these bundles at different values
of the parameter [L/V] r ).
The method of reversible distillation trajectories calculation is described above
in Section 4.4. To determine coefficients of linear equations, describing straight
lines, planes, and hyperplanes, going trough stationary points, by coordinates of
these points well-known formulas of analytic geometry are used.
Let’s now examine posterior stages for various splits.
5.6.3. Direct and Indirect Splits (One of the Products Is Pure
Component or Azeotrope)
Taking into consideration the symmetry of these splits, we confine the discussion
to the direct split. In the mode of minimum reflux, point x f should coincide with
the stable node N , and point x f −1 should belong to rectifying minimum re-
+
s
2
flux bundle S − N (Fig. 5.30). Along with that, Eq. (5.18) should be valid. The
+
r
r
search for the value (L/V) min is carried out in the following way: at different values
r
(L/V) r , the coordinates of point x f ≡ N are determined by means of the method
+
s
“tray by tray” for bottom section and then the coordinates of point x f −1 are de-
termined by Eq. (5.18). At (L/V) r < (L/V) min , points x f −1 and x D are located on
r
2
different sides from the plane or hyperplane S − N and, at (L/V) r > (L/V) min ,
+
r r r
these points are located on one side. That finds approximate values (L/V) min (not
r
2
taking into consideration curvature of bundle S − N ) and approximate coordi-
+
r r
nates of points x f −1 and x f . To determine exact values (L/V) min and coordinates
r
x f −1 and x f , one varies the values of (L/V) r in the vicinity of found approximate
value (L/V) min . Then one realizes trial calculations of top section trajectories by
r
means of the method “tray by tray” from feed cross-section to the product. If at