Page 191 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c05 CB644-Petlyuk-v1 June 11, 2004 20:15

5.9 Questions 165

2
product: (n − k). Separatrix min-reflux region of the section Reg min,R ≡ S − N +
sep
that is the most remote from product point has the dimensionality smaller by one
than the dimensionality of separatrix sharp region of the section. In the mode of
minimum reflux at separation without distributed components, the composition
2
points in the feed cross-section belong to these boundary elements S − N and
+
r
r
2
S − N (x f −1 ∈ Reg min,R , x f ∈ Reg min,R ) and, at separation with one distributed
+
sep,s
s
sep,r
s
component, the composition point in feed cross-section in one of the sections be-
1
2
longs to trajectory bundle S − S − N and, in the other section, it belongs to
+
2
the boundary element of this bundle S − N (x f −1 ∈ Reg sh,R , x f ∈ Reg min,R or
+
sep,r sep,s
x f −1 ∈ Reg min,R , x f ∈ Reg sh,R ).
sep,r
sep,s
2
1
Stationary points of trajectory bundles S − S − N + are located at reversible
distillation trajectories in the boundary elements of concentration simplex or in
the α-lines, α-surfaces, and α-hypersurfaces. Their coordinates can be calculated
1
2
for each value of parameter L/V. Trajectory bundles of the sections S − S − N +
2
and their boundary elements S − N can be accepted to be linear for practical
+
purposes. This calculates minimum reflux mode for any mixtures and any splits
with sufficient precision. Found values (L/V) min can also be used for quasisharp
separation at sufficient purity of the products.
Phase equilibrium coefficients field of each concrete nonideal or azeotropic
mixture determines boundaries of various regions at the boundaries of concentra-
i, j,k
tionsimplexandinsideit(ofcomponentorderregionsReg ord ,ofsharpsplitregions
i: j t
Reg , of trajectory tear-off regions Reg , of possible product regions Reg D and
sh
Reg B , of tangential pinch regions Reg tang , and of pitchfork regions Reg pitch , etc.).
These regions are polygons, polyhedrons, or hyperpolyhedrons with curvilinear
boundaries, vertexes of which are located at edges of concentration simplex. Coor-
dinates of these vertexes can be determined by helping to calculate values of phase
equilibrium coefficients of the components at edges of concentration simplex.
This solves the task of determination of possible splits for any mixture and
synthesizes its separation flowsheet.
At quasisharp separation, possible product composition regions Reg D and
Reg B grow at the decrease of purity of the products. Boundaries found for sharp
separation deliberately ensure possible splits for quasisharp separation, but, if it
is necessary, the widened boundaries for the set purity can be found.
5.9. Questions
1. Can the top product of the column contain components 4, 5, and 6 if in face 4-
5-6 there is component order region Reg 56432 ? Can the bottom product contain
ord
components 3 and 4 if at the edge there is segment Reg 15243 ?
ord
2. Is it possible to separate mixture at split 2,5,4: 5,1,3 if in face 2-5-4 there is com-
ponent order region Reg 45231 and in face 5-1-3 there is region Reg 42135 ?
ord ord
3. Will tangential pinch arise if the top product contains components 4, 5, and 6, tear-
off point belongs to region Reg 56432 , and in the vicinity of tear-off point component
ord
3 has a phase equilibrium coefficient that is smaller than in tear-off point itself?