Page 81 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: VINOD/IYP T1: FCH
0521820928c03 CB644-Petlyuk-v1 June 11, 2004 20:12

3.4 Rule for the Checkup of Azeotropic Mixtures Separability 55

2
N B − ) 2 (

Figure 3.12. Examples of possible (x D(1) : x B(1) ,
x B(2)
12 24 x D(3) : x B(3) ) and impossible (x D(2) : x B(2) ) splits
of four-component azeotropic mixture. Thick
x B(1)
+
D x ) 3 ( ≡ N D ) 3 ( 23 lines with arrows, bond and c-lines; dotted
x B(3) crossed line, absence of bond; dotty line, sep-
x F
1 4
− aratrix; impossible product points are striked
x D(1) N
) 1 ( B out.
x D(2)
3 + + −
N ) 1 ( ;N ) 2 ( ;N
D D ) 3 ( B
As we already saw, for three- and four-component mixtures, all the operations
enumerated can be graphically implemented.

3.4.3. n-Component Mixture

At n > 4, it is necessary to use special algorithms. Determining products x D and
x B compositions for distillation without distributed components 1, 2, ... k : k + 1,
k + 2, ... n is implemented according to formulas:

k

x Di = z Fi z Fi (i = 1, 2,... k) (3.5)
1
n

(i = k + 1, k + 2,... n) (3.6)
x Bi = z Fi z Fi
k+1
−
+
Nodes N and N are defined by means of calculation of line of conjugated
D B
liquid–vapor tie-lines from point x D or line of conjugated vapor–liquid tie-lines
from point x B . In Fig. 3.12, line of conjugated vapor–liquid tie-lines from point
x B(3) is shown for four-component azeotropic mixture at separation according to
split 1 : 2,3,4. In this case, N coincides with vertex 3.
−
B
For an n-component mixture, the rule of connectedness in some cases can be
used without graphic interpretation of the concentration simplex and without
application of structural matrix (Petlyuk et al., 1977; Knight & Doherty, 1990).
+
−
+
−
Such elementary cases are the following: (1) N ≡ N , and (2) N and N are
D B D B
two vertexes of concentration simplex and at the edge (k), (k + 1) between them,
−
there is no binary azeotrope and temperature in the point N = (k + 1) is higher
B
+
than at the point N = (k). In these cases, there exists the link N → N , which
−
+
D D B
makes such a split possible. In more complicated cases with a large number of
components and azeotropes, it is necessary to use structural matrix. The structural
matrix describes the structure of the whole concentration space and checks the
possibility of separation for any feed composition of distillation column. It is