Page 53 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: VINOD/IYP T1: FCH
0521820928c02 CB644-Petlyuk-v1 June 11, 2004 17:58

2.5 Trajectory Bundles Under Finite Reflux 27

2
a)

1 3 Figure 2.4. Trajectory bundles under infinite reflux for (a)
three-component ideal and (b) azeotropic mixtures. x D(1) :
x B(1) , x D(2) : x B(2) , possible splits; solid lines, trajectories; dotty
2
b) line, separatrix under infinite reflux.
x B(2)

x B(1)
x F
x
D(1)
1 x 13 3
D(2)

by the arrows). All the trajectories begin in vertex 1 and terminate in vertex 3 and
round vertex 2. At the vertexes, the tie-line length becomes equal to zero. Thus,
the vertexes are the stationary trajectory points.
If all the trajectories coming from the stationary point, in this case, such station-
ary point is called the unstable node N (vertex 1). The stationary point to which
−
the trajectories get in is called the stable node N (vertex 3). At last, the stationary
+
point that all trajectories bend around is called a saddle point S (vertex 2).
In Fig. 2.4b, another example of the trajectory bundles is shown (let’s call
the picture of trajectory bundles a distillation diagram), but already for a three-
component azeotropic mixture: acetone(1)-benzene(2)-chloroform(3).
In this case, we have two trajectory bundles, differing by their unstable nodes
and separated from each other with a specific trajectory, which begins not at the
unstable node, but in a saddle (azeotrope 13 of maximum temperature) and is
called the separatrix.
The distillation diagram illustrates the arrangement of trajectories to be the
profile of concrete column concentrations (Fig. 2.4b). It is enough to choose two
points, for example, points x D(1) and x B(1) or x D(2) and x B(2) , on the one trajectory
and to meet the requirement of the material balance (all points x D , x F , and x B
should lay within the one straight line) and to state that a part of trajectories
between points x D(1) and x B(1) or x D(2) and x B(2) serves to be a concentration
profile of possible distillation column under the infinite reflux.

2.5. Trajectory Bundles Under Finite Reflux
To return to Eqs. (2.3) and (2.5) for the rectifying section and to fix x iD and R
parameters, we obtain a number of points x ij by solving this system from the
upper tray.