Page 205 - Distillation theory

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6.3 Distillation Trajectories and Minimum Reflux Mode 179

one, should be infinite. One of the sections (the top or bottom one) remains finite
in this mode. At the increase of reflux number (i.e., of the parameter [L/V] r ) the
stationary points of three-section trajectory bundles move along reversible distil-
lation trajectories for set points of products x D and x B and of pseudoproduct x .

D
The general regularities of this movement for top and bottom sections were ex-
amined in detail in Chapter 5. The stationary points of intermediate section move
along the unique trajectory of reversible distillation. At some value of (L/V) r =
1
(L/V) , there is joining of intermediate section trajectory with the trajectory of
r
2
the first of the rest of the sections. At some greater value of (L/V) r = (L/V) ,
r
there is joining of the intermediate section trajectory with the remaining section
at infinite number of trays in these sections (N m =∞ and N r =∞ or N s =∞). The
2
found values of (L/V) are minimum for the separation in a three-section column.
r
The feed located between the intermediate and the last section, with which there
was a joining, is the control one. Along with that, the first section, with which there
2
was a joining, is finite and its joining at (L/V) with the intermediate section goes
r
on as at a reflux bigger than minimum (regularities of joining at a reflux bigger
than minimum are examined in Chapter 7).
Because in the mode of minimum reflux the intermediate section should be
infinite, its trajectory should pass though one of its stationary points S m or N .
+
m
Therefore, the following cases are feasible in minimum reflux mode: (1) point N +
m
coincides with the composition at the tray above or below the cross-section of
control feed; (2) composition point at the trays of the intermediate section in the
cross-section of control feed lies on the separatrix line, surface, or hypersurface
min,R
of point S m (i.e., in separatrix min-reflux region of intermediate section Reg
sep, int
filled of trajectory bundle S m − N ). In both cases, composition point at the tray of
+
m
the top or bottom section, adjacent to the control feed, should lie in the separatrix
2
+
min-reflux region of this section Reg min,R (S − N ).
sep
6.3.4. General Algorithm of Calculation of Minimum Reflux Mode
This develops the general algorithm of calculation of minimum reflux mode for the
columns with two feed inputs at distillation of nonideal zeotropic and azeotropic
mixtures with any number of components. The same way as for the columns with
one feed, the coordinates of stationary points of three-section trajectory bundles
are defined at the beginning at different values of the parameter (L/V) r . Besides
that, for the intermediate section proper values of the system of distillation dif-
ferential equations are determined for both stationary points from the values of
phase equilibrium coefficients. From these proper values, one finds which of the
stationary points is the saddle one S m , and states the direction of proper vectors
for the saddle point. The directions of the proper vectors obtain linear equations
describing linearized boundary elements of the working trajectory bundle of the
intermediate section. We note that, for sharp separation in the top and bottom
sections, there is no necessity to determine the proper vectors of stationary points
in order to obtain linear equations describing boundary elements of their tra-
jectory bundles, because to obtain these linear equations it is sufficient to have