Page 211 - Distillation theory

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

6.4 Trajectories of Intermediate Sections of Extractive Distillation Columns 185

evolution of working trajectory bundle of intermediate section at change of two
parameter (L/V) m and E/D (for the top and bottom sections we examined in
Chapter 5, the evolution of trajectory bundles at change of unique parameter
[L/V] r ). In accordance with the structural condition, the segment α 13 -2, where
t
K 1 > K 3 > K 2 is the intermediate section trajectory tear-off segment Reg at side
e
1,2
1-2. As for the top and bottom sections, working trajectory bundle of the inter-
mediate section should be located in a sharp distillation region where the order
of the components is the same as at the trajectory tear-off region i.e. segment
3 1,3,2
t
Reg (in our case, it is region Reg ). The line K 3 = 1 divides region 132 into
e ord
1,2
two subregions, where K 3 > 1 and K 3 < 1. Location of pseudoproduct point x
D
higher or lower than the concentration triangle and corresponding to that location
of reversible distillation trajectory in the subregion K 3 > 1or K 3 < 1 depend on
the value of the parameter E/D: the first case takes place at the big values of
E/D (1 < E/D) the second case takes place at the small values E/D (ED < 1).
It follows from Eq. 6.3, where D 1 = 0 and F 1 = E. We examine the evolution of

trajectory bundle for the first case (E/D > 1). At E/D → 1, point D goes away
into infinity and reversible distillation trajectory coincides with line K 3 = 1. At
E/D =∞, point x coincides with vertex 2 and reversible distillation trajectory

D
coincides with side 2-3 (see Eq. 6.3). The parameter (L/V) m for the case under
consideration is bigger than one because (L/V) m = K 3 in the points of reversible
distillation trajectory (3 - absent component in the pseudoproduct). At (L/V) m
= 1, point S m coincides with vertex 3 and, at (L/V) m = (L/V) max , point S m co-
m
incides with reversible distillation trajectory tear-off point from side 1-2 (point
x t ). Therefore, the square, filled up with intermediate section trajectory bundle
rev,e
(region Reg R ), is maximum at (L/V) m = 1 and is equal to zero at (L/V) m =
w,e
(L/V) max .
m
We now examine the evolution of the trajectory bundle for the second case

(E/D < 1). At E/D → 1, point x goes into infinity and reversible distillation
D
trajectory coincides with the line K 3 = 1. At decrease of the parameter E/D,
point x comes nearer to vertex 1, inside concentration triangle besides with
D
reversible distillation trajectory, passing through vertex 3 and ending at side 1-2,
there is fictitious trajectory, passing through points 3 and 13. At decrease of the pa-
rameter E/D, these two trajectories are brought together and, at E/D = (E/D) min ,
they intersect each other in point of branching of reversible distillation trajecto-
ries x branch . At the smaller values of the parameter (E/D), sharp distillation in the
rev
intermediate section becomes unfeasible.
The parameter (L/V) m for the case under consideration is smaller than one.
At (L/V) m = 1, point S m coincides with vertex 3 and, at (L/V) m = (L/V) min ,it
m
coincides with reversible distillation trajectory tear-off point x t rev,e from side 1-2.
Therefore, the square, filled up with the trajectory bundle of the intermediate
section, is maximum at (L/V) m = 1 and is equal to zero at (L/V) m = (L/V) min .
m
We note that, for the top and bottom sections, the square filled up with the
trajectory bundle is also maximum at (L/V) r = 1 and (L/V) s = 1 (the mode of
infinite reflux).