Page 255 - Distillation theory

P1: JPJ/FFX P2: JMT/FFX QC: FCH/FFX T1: FCH
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7.3 Design Calculation of Two-Section Columns 229

sections N r /N s :
imp
x = x f −1, k+1 + x f −1, k+2 + ··· + x f −1, n (7.3)
f −1
imp
x = x f,1 + x f,2 + ··· + x f,k (7.4)
f
In spite of the fact that points x f −1 and (x f −1 ) sh and points x f and (x f ) sh that
lin lin
correspond to them in material balance do not coincide, the values of x imp can be
f −1
sh
accepted the same as in any points of segment [x f −1 ] , and the values of x imp can
lin f
be accepted the same as in the points of segment [x f ] sh that correspond to points
lin
of segment [x f −1 ] sh in material balance.
lin
Therefore, while executing a series of trial calculations of section trajectories,
sh
some point (x f −1 ) sh at segment [x f −1 ] sh and point (x f ) sh at segment [x f ] , cor-
lin lin lin lin
responding to it in material balance, are chosen preliminarily.
imp imp
The values of x and x are determined and fixed for these points, and trial
f −1 f
calculations of section trajectories from column ends are realized further up to
imp imp
reaching at some section tray of these values of x and x . Therefore, the frac-
f −1 f
tional numbers N r and N s are determined as a result of the trial calculation itself.
Trial calculations of the top section are realized at different little concentrations
of non-key impurity components in the top product x D,k+2 , x D,k+3 ... x D,n , and trial
calculations of the bottom section are realized at different little concentrations of
non-key impurity components in the bottom product x B,1 , x B,2 ... x B,k−1 .
Design calculation comes to the search of the concentrations of these com-
ponents that would ensure validity of material balance in the feed cross-
section. Such design calculation is realized for the fixed set of points [(x f −1 ) sh −
lin
sh
sh
(x ∞ ) ]/[(x min sh − (x ∞ ) ], which determines (N r /N s ) opt , at which the total
)
f −1 lin f −1 lin f −1 lin
number of column trays is minimum.
The algorithm of design calculation includes a preliminary search for little
concentrations of non-key impurity components in separation products and sub-
sequently more precise definition of these concentrations.
The little concentrations x ◦ , x ◦ ... x ◦ at which trajectory of top section
D,k+2 D,k+3 D,n
comes to point x ◦ , where the summary concentrations of the non-key impurity
f −1
imp
components of the top product [x ◦ ] are the same as in fixed set of point
f −1 nkey
sh imp
sh
sh
)
[(x f −1 ) sh − (x ∞ ) ]/[(x min sh − (x ∞ ) ]; that is, [x ◦ ] imp = [(x f −1 ) ] are
lin f −1 lin f −1 lin f −1 lin f −1 nkey lin nkey
determined at preliminary search. The top section trajectory at quasisharp sep-
1
aration after preliminary search may be presented as follows: x ◦ D → qS →
r
2 t
qS → x ◦ . Reg Reg
r f −1 D r
Reg t qsh,R
r Reg
sep,r
The little concentrations x ◦ , x ◦ ... x ◦ at which trajectory of bottom sec-
B,1 B,2 B,k−1
tion comes to point x , where the concentrations of the non-key impurity compo-
◦
f
nents of the bottom product are the same as in point (x f ) sh corresponding to point
lin
◦ imp
(x f −1 ) sh in material balance are determined in the same way; that is, [x ] =
lin f nkey
sh imp
[(x f ) ] . The bottom section trajectory at quasisharp separation after prelim-
lin nkey
1
2
inary search may be presented as follows: x ◦ → qS → qS → x ◦ .
B s s f
Reg Reg t Reg t qsh,R
B s s Reg
sep,s