Page 308 - Distillation theory

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282 Synthesis of Separation Flowsheets

8.4.1. Possible Product Segments at the Edges of Concentration Simplex

In Chapter 5, we examine structural conditions of trajectory tear-off for the top
and bottom sections. We now examine these conditions in more detail for multi-
component mixtures. We examine edge 1-2 of five-component mixture 1,2,3,4,5 as
an example. For trajectory tear-off from edge 1-2 into the concentration pentahe-
dron (for obtaining the mixture 1, 2 as product of the five-component distillation)
it is necessary that these trajectories could tear-off into each of adjacent with this
edge faces 1-2-3, 1-2-4 and 1-2-5 (that the mixture 1, 2 could be the product of the
distillation of 1, 2, 3 mixture, 1, 2, 4 mixture, and 1, 2, 5 mixture). Figure 8.8 shows
such a case for the top section at separation of a hypothetical mixture. This graph
shows curves x t2 → x rev for the mentioned faces at reversible distillation. The way
D2
to obtain these curves is described in Chapter 4.
In this example, the tear-off into face 1-2-4 is possible from all points of edge 1-
2, into face 1-2-3 it is possible from the points of segment [0 – max x 1−2−3 ], and into
t2
face 1-2-5 it is possible from the points of segment [min x 1−2−5 – 1]. Therefore,
t2
tear-off from edge 1-2 into pentahedron is possible only from the points of segment

Figure 8.8. Possible overhead product (mixture 1,2) concentrations
x D,2 of the component 2 for constituent mixtures 1,2,3; 1,2,4; 1,2,5 as
function of tear-off point compositions x t on the edge 1-2 of the con-
r,2
centration simplex for the five-component mixture. Segment possible
3,4,5 3,4,5
(2)
t
top product Reg D (solid) and tear-off segment Reg (hatched) on the
r
1,2 1,2 4
(t)
edge 1-2 for the five-component mixture separation; Reg r = [0 – 1],
3 1,2 4
5 3 (2) (2)
1−2−3
t
t
Reg = [x 1−2−5 – 1], Reg = [0 – x 1−2−3 ], Reg D = [0 – x max,D ], Reg D =
r
r
max
min
1,2 1,2 1,2 1,2
5
(2)
[0 – 1], Reg D = [0 – 1].
1,2