Page 174 - Distillation theory

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

148 Distillation Trajectories and Conditions of Mixture Separability

examination the first tear-off point max x t1 and by the closest second tear-off
rev
t2
point min x , then the point under examination is possible product point and
rev
j
(k) t1 t2
mentioned segment is trajectory tear-off segment Reg t ≡ [max x , min x ].
rev
rev
i
j
(k)
At marked in such a way trajectory tear-off segments Reg , Eqs. (5.13) ÷ (5.16)
t
i
are valid.
Let’s note that besides the mentioned cases distillation trajectory tear-off at
finite reflux from k-component boundary element to (k + 2)- component bound-
ary element, if there is α-hypersurface which indexes dont include components of
k-component boundary element under examination.
All the possible product points in the boundary elements form possible product
j j
(k) (k)
region Reg or Reg :at k = 1, it is vertex of simplex; at k = 2 it is segment,
D B
i i
in the face (k = 3) it is polygon, in the hyperface (k > 3) it is polihedron or
hyperpolyhedron.
The definition of components concentrations in the boundary points of possi-
j j
(k) (k)
ble product compositions regions Reg or Reg (in the ends of the segments,
D B
i i
in the vertexes of the polygons, of the polyhedrons or hyperpolyhedrons) is main
step of the algorithm of azeotropic mixtures separation flowsheets synthesis that is
described in Chapter 8. To define these concentration, Eqs. (4.19) and (4.20) con-
necting concentrations in product points and in reversible distillation trajectory
tear-off points are used.
If the product point of sharp distillation is located in possible product compo-
j j
(k) (k)
sition region (x D ∈ Reg or x B ∈ Reg ) and if the value of the parameter L/V
D B
i i
lies inside the interval of the values of the parameter L/V, for which distillation
trajectory tear-off from the boundary product element of concentration simplex is
feasible((L/V) min < L/V < (L/V) max ), then rectifying or stripping bundle appears
inside this simplex Reg R or Reg R .
w,r w,s
The stationary points of this bundle are located both in the boundary elements
of simplex and inside it, at reversible distillation trajectories. The number of such
stationary points of the bundle is equal to the difference between the number of
the components of the mixture being separated n and the number of the com-
ponents of section product k plus one. Stationary points of the bundle of top or
bottom section are one unstable node N (it exists inside the simplex only in the
−
product point, if product is a pure component or an azeotrope); one stable node
N (it is located at the boundary element, containing one component more than
+
the product if K < n − 1); the rest of the stationary points of the bundle are sad-
1
dle points S.The first (in the course of the trajectory) saddle point (S ) is located
at the product boundary element (if product is pure component or azeotrope,
1
−
then the saddle point S coincides with the unstable node N and with product
2
point). The second saddle point (S ) is located at the boundary element, con-
taining product components and one additional component, closest to product