Page 312 - Distillation theory

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286 Synthesis of Separation Flowsheets

j j
(1) (1)
2. Determination of the possible product points Reg D and Reg B in the ver-
i i
texes of the concentration simplex (they are nodes N − and N + of the
concentration simplex).
3. Determination of the coordinates of the ends of the possible product seg-
j j
(2) (2)
ments Reg and Reg at the edges of the concentration simplex (see
D B
i i
Section 8.4.1).
4. Determination of the coordinates of the ends of the boundary elements
j j
possible product regions Reg bound,D and Reg bound,B at the edges of the con-
i i j j
(k) (k)
centration simplex for the possible product regions Reg and Reg at the
D
B
i i
(3)
(4)
two-dimensional faces C , three-dimensional hyperfaces C , etc., up to
(n − 1)-component hyperfaces C (n−1) (i.e., vertexes of these regions).
8.4.3. Possible Sharp Splits in Columns with One Feed
Thesplitsthatmeetthefollowingtwoconditionsarefeasible:(1)pointsofproducts
and of feeding lie in one straight line and (2) points of products belong to possible
j j
product composition regions x D ∈ Reg D and x B ∈ Reg B . Therefore, to determine
i i
possible splits, it is necessary to check these conditions.
For splits without distributed components, there is a correspondence be-
j j
(k) (k)
tween each possible product region Reg or Reg containing k components
D B
j i j i
(n−k) (n−k)
and a possible product region Reg or Reg containing (n − k) compo-
B D
i i
nents that is complementary to it (i.e., these elements taken together contain all
components). Therefore, to determine feasible splits, one looks over those bound-
(k)
ary elements of concentration simplexC , which contain possible product regions
j j
(k) (k)
Reg and Reg , and checks which of them complement each other. Each pair
D B
i i
determines one possible split. If the product points for the set composition of
j j
(k) (n−k)
feeding get into possible product regions (i.e., x D ∈ Reg and x B ∈ Reg ),
D B
i i
then this split is feasible without any recycle flows. If they do not get there, then
this split is feasible if recycle flows of separation products of the unit are available,
because these flows move the feed point into the concentration simplex. The value
of necessary recycle flow rate is proportional to the length of the segment between
the product point without recycle and the boundary of possible product region.
The segments have to be taken at the secants passing through vertexes of the
concentration simplex. The smallest of these segments corresponds to the com-
ponent the required recycle flow rate of which is the smallest for the split under
consideration. To check if product point gets into possible product composition
region, one has to divide this region into simplexes, number of vertexes of which