Page 213 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c06 CB644-Petlyuk-v1 June 11, 2004 20:17

6.5 Conditions of Separability in Extractive Distillation Columns 187

3 2
R
R
TheworkingtrajectoryregionsReg w,e atFig.6.9band Reg w,e atFig.6.9caretwo
1,2,4 1,3,4
dimensional. They are limited by the saddle point S m at the reversible distillation
+
−
trajectory inside concentration tetrahedron and by the node points N and N at
m m
reversible distillation trajectories in face 1-2-4 (at Fig. 6.9b) or in face 1-3-4 (at Fig.
6.9c). We note that the location of reversible distillation trajectories and of the
stationary points in these faces is similar to their location at nonsharp distillation
in the intermediate section of corresponding three-component mixtures (Fig. 6.5)
because the location of the pseudoproduct point referring these faces is similar.
The analysis carried out above (see Figs. 6.8 and 6.9) allows for a general conclu-
sion about dimensionality, structure, and evolution of trajectory bundles (regions)
of intermediate section at sharp extractive distillation for any multicomponent
mixtures.
The dimensionality of intermediate section trajectory bundle is equal to n −
m + 1, where n is total number of components, and m is summary number of
components of top product and entrainer. Pseudoproduct point x is located at

D
the continuation of the boundary element, formed by all the components of the
top product and entrainer. Reversible distillation trajectories and the stationary
points are located at the mentioned pseudoproduct boundary element and at all
boundary elements whose dimensionality is bigger by one (at m = n − 1, they are
located inside concentration simplex).
In this section, we discuss only regular extractive distillation, when heavy en-
trainer is brought in higher than cross-section of input of the separated mix-
ture. Similar analysis can also be done for indirect extractive distillation, when
light entrainer is brought in lower than cross-section of input of the separated
mixture.

6.5. Conditions of Separability in Extractive Distillation Columns and
Minimum Reflux Mode

6.5.1. Conditions of Separability in Extractive Distillation Columns

Let’s examine the conditions of sharp separation in each of the three sections
of the extractive distillation column: (1) intermediate section trajectory tear-off
j
t
t
region Reg (region, in points of which K t > K t > K ) should exist at
e i,D j,DE i,E
i=D+E
the boundary element of the concentration simplex of the mixture; (2) the top
j=E
product region Reg should exist at the boundary element of the concentra-
D
i=D
tion simplex of the mixture of top product and entrainer (D + E); (3) the bot-
j=D
tom product region Reg should exist at the boundary element of concentration
B
i=B
simplex of the mixture (F + E); and (4) sharp split region of extractive section
i: j D:E
Reg should intersect sharp split regions of top section Reg and of bottom
sh,e sh,r
i: j
section Reg .
sh,s