Page 179 - 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 153

1
+ 2
N r −
N r
a) 2
α 23 x t1 rev S r
1
S s
t2
+ x rev 1,2,3 N s +
x ≡ N s α
f
x 13
f-1 1
S s
2
S r
1 α 3
− 1 23 13 2,3
= N ≡
x D r S r
2
1
b) S r 3
−
N r
2
S r
+
x ≡ N s
f
+ +
N r 1,2,3,4
N s
1 1 4
S s
− x 1
x = N ≡ S r 1 f-1 S s
D r
2 13
S
r
3 2,3,4
Figure 5.30. The joining of section trajectories under minimum
reflux for the direct split of (a) the acetone(1)-benzene(2)-
chloroform(3) mixture, and (b) the acetone(1)-benzene(2)-
chloroform(3)-toluene(4) mixture. The attraction region Reg 1 att is
2,3 2,3,4
+
shaded (x f = N , x f −1 ∈ Reg min,R or x f −1 ∈ Reg min,R ).
sep,r
sep,r
s
1 1
some trial value of (L/V) r point x f −1 turns out to be inside the rectifying region
−
+
Reg R ≡ Reg ≡ (N ⇒ N ), then calculation trajectory achieves top product
w,r att r r
point x D (i.e., set vicinity of vertex of concentration simplex). Otherwise, it does
not achieve. This allows to find exact value of (L/V) min and exact coordinates of
r
points x f −1 and x f , at which point x f −1 is at bent line, surface, or hypersurface
j
2
x f −1 ∈ Reg min,R ≡ S − N , by means of series of trial calculations (Fig. 5.31).
+
sep,r r r
i
The column trajectory, the calculation direction taken into consideration, may be
presented in the following brief form:
(n−1) 1(n−1) (n) (n) 2(2) (1)
x → S s → x ⇓⇒ x → S r → x
B f f −1 D
Reg B Reg t s N s + Reg min R Reg t r N r −
sep,r
For azeotropic mixtures there is a set of attraction regions Reg and a set of
att
separatrix min-reflux regions Reg min R (see Fig. 5.13b and 5.26b). The working
sep,r
region Reg min R is one of these. It is determined for calculated point x f −1 by means
sep,r