Page 253 - Distillation theory

P1: JPJ/FFX P2: JMT/FFX QC: FCH/FFX T1: FCH
0521820928c07 CB644-Petlyuk-v1 June 11, 2004 20:18

7.3 Design Calculation of Two-Section Columns 227

located in the sharp split region Reg sh for the direct split). It is also important
that component 2 is the second in the value of phase equilibrium coefficient in
1
point S ≡ N (i.e., in vertex 1). Calculation of the bottom section is carried out
−
r r
by method “tray by tray” from point x B to a chosen point x f within segment
∞
[x min , x ]. This calculation is stable, because after an abrupt change of direction
f f
1
of the trajectory under calculation in the vicinity of point S it is attracted to
s
1
separatrix S − N + and to node N ≡ x ∞ (see Fig. 7.2a). The composition in
+
s s s f
point x f −1 located inside trajectory bundle of the top section is determined from
the material balance in the feed cross-section by the compositions in points x F and
x f . Then the calculation of the top section is performed from point x f−1 to point
x D ≈ N (i.e., until the condition x 1j ≥ η D is valid). The calculation of the top
−
r
section is also stable because point x f −1 is located in the region of attraction Reg att
of node N , and the calculation trajectory is attracted to this node. For azeotropic
−
r
mixtures at more minimum reflux like at minimum reflux (see Fig. 5.26b) is a set of
attraction regions Reg . The working region Reg is determined by composition
att att
x f −1 . The column’s trajectory at direct split may be put as follows:
1
x B → qS → x f ⇐⇓ x f −1 → qS r → x D .
s
Reg t sh,R Reg t Reg
B Reg [x f ] ∈ Reg [x f −1 ] ∈ Reg att r D
s sep,s
opt
To determine x f at which (n r + n s ) is minimum, it is necessary to perform
several calculations of the column at different points x f at segment [x min , x ].
∞
f
f
This algorithm was introduced in the work (Julka, 1993). The similar algorithm
can also be used at indirect separation, but calculation should be executed top-
down from point x D .
At small set concentrations of impurities (1 − η D ) and (1 − η B ) to determine
value n min = (n r + n s ) min , one does not have to make iterations by product com-
positions x B and x D (i.e., for chosen points x f and x f −1 calculation “tray by tray”
is executed once).
However, if we want to achieve full satisfaction of the distillation equation
system and to obtain precise product compositions x B and x D , it is necessary to
execute iterations by these compositions (i.e., to take into consideration the fact
that at the direct split not only the second component is an impurity one in the
top product). These iterations become more necessary the larger the set value of
(1 − η D ) at the direct split or the set value of (1 − η B ) at the indirect split.
The simplest organization of the iteration process is “simple iteration,” when
the found composition x D or x B from the previous iteration is used to determine
composition x B or x D for the following iteration at the direct or indirect separation,
respectively. Besides “simple iteration,” one can also use other more complicated
but more reliable and faster methods.

7.3.2. Intermediate Splits of Mixtures with Any Number of Components
Thenumberofintermediatesplits1, 2,... k : k + 1, k + 2 ... nequals(n−3),while
at any value of n there is only one direct split and one indirect split. Therefore, at
n > 4, intermediate splits prevail.