Page 111 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521832772c04 CB644-Petlyuk-v1 June 11, 2004 17:49

4.3 Trajectory Bundles of Sharp Reversible Distillation 85

2

a) α
23
132
α
13
123
312 Figure 4.8. Regions of reversible distillation Reg rev
1 α 23 13 3 (shaded) and regions of component order Reg 1,2,3 , Reg 1,3,2 ,
ord
ord
and Reg 3,1,2 : (a) rectifying section, and (b) bottom section.
ord
2 Dotty line, separatrix; thin lines, α-lines; Reg 2 rev,r (region
in which component 2 is heaviest) and Reg 3 rev,s (region in
b) α which component 3 is lightest), darker shaded.
23
132
α
13
123
312
1 α 23 13 3

for which antipodal mixture the location of points in the trajectories was obtained
by means of calculation (Petlyuk et al., 1981a).
ijk
Figure 4.8 shows the regions of components order Reg ord and of reversible dis-
tillation Reg h rev,r or Reg l rev,s for this example. In all points of one trajectory in Fig.
4.7b, liquid–vapor tie-lines are directed from one and the same point of the prod-
1,2,3 1,3,2
uct x B located at side 2-3 (for the regions of components order Reg and Reg
ord ord
forming common region of reversible distillation Reg 1 of the bottom section in
rev,s
which the lightest component is component 1− lighter shaded in Fig. 4.8b) or at
3,1,2
side 1-2 (for the region of components order Reg ≡ Reg 3 − darker shaded
ord rev,s
in Fig. 4.8b). In all the points of one trajectory in Fig. 4.7a, liquid–vapor tie-lines
are directed to one and the same point of the product x D located at side 1-2 (for
1,2,3
the region of components order Reg ord ≡ Reg 3 rev,r − lighter shaded in Fig. 4.8a)
1,3,2 3,1,2
or at side 1-3 (for the regions of components order Reg ord and Reg ord forming
common region of reversible distillation Reg 2 rev,r − darker shaded in Fig. 4.8a).
Therefore, each trajectory in Figs. 4.7a,b is a line of stationarity for the point of
the product of sharp distillation x D and x B , located at the corresponding side
of the concentration triangle. Moreover, in Fig 4.7a, all lines of stationarity consist
of two parts, one of which goes from point x D at the side of the concentration
(2)
triangle Reg ≡ 1-3 (i.e., they are true trajectories of reversible distillation). At
D
Fig. 4.7b, only a number of stationarity lines go from the points of the products x B
located at some segment of side 2-3 adjacent to vertex 2. Only these stationarity
lines are true trajectories of reversible distillation, and this segment of side 2-3 is
(2)
a segment of feasible points of the bottom product Reg . The rest of stationarity
B
lines do not reach that side of the concentration triangle where the corresponding
product points are located. Therefore, these stationarity lines are fictitious trajec-
tories of reversible distillation. They all begin and end in the points of components