Page 254 - Distillation theory

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228 Trajectories of the Finite Columns and Their Design Calculation

Along with that, the creation of design calculation algorithms for intermediate
splits is a considerably more complicated task than that for direct and indirect
splits. For intermediate splits, it is impossible to conduct design calculation from
one end of the column to the other one.
The determination of the end coordinates of possible composition segments
in the feed cross-section [x f −1 ] sh and [x f ] sh at the assumption about linearity
lin lin
2
1
of the separatrix sharp split regions of the section Reg sh,R ≡ S − S − N and
+
sep
about sharp separation is one of the most important elements of new algorithms
of design calculation for intermediate splits (see Section 7.3.1).
The above-mentioned assumptions are valid entirely only under the condition
of absense of impurity components in the separation products (i.e., absence of
components k + 1, k + 2 ... n in the top product and of components 1, 2 ... k in
the bottom product) and also at α i = const and L r = const, V r = const, L s = const,
V s = const.
For real mixtures, at a set content of impurity components in separation prod-
ucts, the ends of segments [x f − 1 ] and [x f ] shift relatively to the ends of segments
sh
[x f −1 ] sh and [x f ] . This shifting takes place for several reasons:
lin lin
1
2
1. For real mixtures, separatrix trajectory bundles Reg sh ≡ S − S −
bound
+
N at sharp separation are curvilinear (calculations prove that this cur-
vature is not big for any mixture).
2. At the decrease of sharpness of separation (at the increase of the set content
of impurity components in separation products), segments [x f − 1 ] and [x f ]
become longer and move from separatrix sharp split regions of the section
R
2
1
Reg sh,R ≡ S − S − N deep into the working bundles Reg .
+
sep w
Therefore, the new algorithms of design calculation include the correction of
compositions in the feed cross-section x f−1 and x f compared with compositions at
sh
segments [x f −1 ] sh and [x f ] .
lin lin
The correction is realized on the basis of execution of the series of trial calcu-
lations of section trajectories by method “tray by tray” in the direction from the
feed cross-section to the ends of the column or vice versa.
Theoretic analysis proved that the algorithms employing calculation from the
feed cross-section (Petlyuk & Danilov, 2001a) can be applied only at n = 4, while
algorithms that use calculation from the ends of column can be applied at any n.
At the design calculation, the following summary concentrations of impurity
components in separation products are set (specified):
imp
x (7.1)
D = x D,k+1 + x D,k+2 +· · · + x D,n
imp
x (7.2)
B = x B,1 + x B,2 +· · · + x B,k
The distribution of non-key impurity components in the separation products
(x D,k+2 , x D,k+3 ... x D,n , x B,1 , x B,2 ... x B,k+1 ) and the numbers of trays in column
sections N r and N s are unknown.
Differentsummaryconcentrationsofimpuritycomponentsatthetraysadjacent
to the feed cross-section correspond to different ratios of tray numbers in column