Page 181 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c05 CB644-Petlyuk-v1 June 11, 2004 20:15

5.6 Conditions of Section Trajectories Joining and Methods 155

value of with the step (L/V) r . If at some value of (L/V) r the bundles do not
intersect each other and at the next value they do intersect each other, then the
value of (L/V) min lies between these trial values.
r
At the second stage, one turns to more exact model of feed plate (Fig. 5.29a),
using the result of the first stage as good initial approximation.
As far as it follows from Eq. (5.18) that points x f −1 , x f and x F should be located
2 +
at one straight line, point x f−1 should lie in rectifying bundle S − N and point x f
r r
2
should lie in stripping bundle S − N . Point x f −1 is found as intersection point of
+
s s
2
2
+
+
linear manifolds S − N and x F − S − N and point x f is found as intersection
s
r
r
s
2
2
point of linear manifolds S − N and x F − S − N . After that, one calculates
+
+
s
s
r
r
discrepancy of material balance in feed cross-section:
(5.19)
ϕ(L r /V r ) = L r x f −1 + L F x F − L s x f
This discrepancy is monotonous function of the value of the parameter (L/V) r
in small vicinity of the value (L/V) r , found at the first stage of the algorithm.
Therefore, determination of more precise value of (L/V) min at the second stage
r
of the algorithm does not cause any calculation difficulties (Fig. 5.33).
At necessity, at the third stage of the algorithm, one takes into consideration
2
2
nonlinearity of rectifying and stripping trajectory bundles S − N and S − N +
+
s
r
r
s
(Petlyuk & Danilov, 2002), which is not considerable even for azeotropic mixtures.
2,4
2
1
As an example, Fig. 5.32 shows nonlinearity of the bundle S − S − N ≡ Reg sh,R
+
r r r sep,r
1,3
for split 1,3 : 2,4 of the azeotropic mixture acetone(1)-benzene(2)-chloroform(3)-
toluene(4).
At nonsharp separation at minimum reflux, the only one impurity component
in each product is the key nonproduct component: in the case of split 1, 2 ... k :
k + 1, ... n, it will be component k + 1 in the top product and component k in the
bottom product. At set product purities η D and η B ,
x D,k+1 = 1 − η D
x B,k = 1 − η B (5.20)
D
2
F
2 Figure 5.32. The curvature of the separatrix sharp
B r S
1 2 +
split region for rectifying section S − S − N ≡
r r r
2,4
Reg sh,R (shaded) for the split 1,3 : 2,4 of the ace-
sep,r
1,3
1 4 + tone(1)-benzene(2)-chloroform(3)-toluene(4) mix-
r N ture.
x
D
1
r S
13
3