Page 186 - Distillation theory

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

160 Distillation Trajectories and Conditions of Mixture Separability

Different types of joining of section trajectories at different component dis-
tribution coefficients reflect the fact that split with one distributed component
1, 2,... k − 1, k : k, k + 1,... n occupies intermediate position between two splits
without distributed components: 1, 2, ... k − 1: k, k + 1, ... n and 1, 2, ... k − 1,
k : k + 1, ... n. Number and location of stationary points for rectifying minimum
2
+
reflux bundle S − N for the split with one distributed component is the same as
r r
for split 1, 2, ... k − 1, k : k + 1, ... n and, for stripping minimum reflux bundle
2
+
S − N , it is the same as for split 1, 2, ... k − 1: k, k + 1, ... n.
s
s
At relatively small content of the distributed component k in top product,
joining of section trajectories goes on at type, characteristic for splits 1, 2, ... k −
2
+
1: k, k + 1, ... n (i.e., point x f lies in bundle S − N ) and at big content joining
s
s
goes on at type, characteristic for split 1, 2, ... k − 1, k : k + 1, ... n, (and point
2
x f −1 lies in bundle S − N ).
+
r
r
At some intermediate (“boundary”) content of the component k in top product
joining of section trajectories goes on simultaneously at two mentioned types.
The algorithm of calculation of minimum reflux mode for splits with distributed
component includes the same stages as for intermediate splits without distributed
components.
The value of (L/V) min , at which there is intersection of linearized bundles
r
2
2
2
1
2
1
+
+
+
+
S − N and S − S − N or S − N and S − S − N (i.e., the smallest value
r r s s s s s r r r
1 2 + 1 2
of [L/V] r , at which there is intersection of bundles S − S − N and S − S −
r r r s s
+
N , is determined at the first stage). The point of intersection can be located
s
2
2
1
2
+
+
both inside bundles S − N and S − S − N , and inside bundles S − N and
+
r r s s s s s
1
2
+
S − S − N , which determines the type of joining of sections trajectories in the
r r r
mode of minimum reflux (see Fig. 5.35a,b).
The coordinates of points x f −1 and x f are defined at the second stage in accor-
dance with determined at the first stage type of joining of sections trajectories.
2
If, for example, point x f −1 lies in bundle S − N r + and point x f lies in bundle
r
1
2
S − S − N , then point x f −1 can be found as intersection point of linear man-
+
s
s
2
2
2
1
+
+
ifolds S − N and x F − S − S − N and point x f can be found as intersection
s
r
s
r
s
2
2
1
+
point of linear manifolds S − S − N and x F − S − N . In other respects, the
+
s
s
r
s
r
second stage of search for (L/V) r min for splits with distributed components remains
the same as for splits without distributed components.
Nonlinearity of separatrix trajectory bundles is taken into consideration only
at the third stage, if it is necessary to determine precisely the value of (L/V) min .
r
Usually to solve practical tasks, it is sufficient to confine oneself to the first two
stages of the algorithm.
Figure 5.35 is carried out according to the results of calculation of (L/V) min
r
for equimolar mixture pentane(1)-hexane(2)-heptane(3)-octane(4) were made at
separation of it with distributed component at split 1,2 : 2,3,4 at different distribu-
tion coefficients of component 2 between products. This figure shows the location
2
1
+
of rectifying plane S − S − N and of bottom section trajectory in minimum
r r r
reflux mode at several characteristic values of distribution coefficient of compo-
nent 2: (1) at joining “at the type of direct split” (1: 2,3,4) (Fig. 5.35b; x D2 = 0.1, x f ≡
+
N s , zone of constant concentrations is located in feed cross-section in bottom