Page 231 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c06 CB644-Petlyuk-v1 June 11, 2004 20:17

6.8 Calculation of Minimum Reflux Mode for Distillation Complexes 205

withdrawals flow rates of pseudoproducts in the first two-section column, and for
the complex in Fig. 6.13a, it is this ratio in the first three two-section columns. The
preferable split is thermodynamically optimal for two-section columns themselves
with distributed components, but such split leads to nonbalancing of vapor and
liquid flows in the next columns of the complex (i.e., to the modes of the reflux big-
ger than minimum in separate columns). It was shown in the work (Christiansen &
Scogestad, 1997) for the complex at Fig. 6.12d that preferable split in the first col-
umn and separation leading to balancing of flows in the next two columns maintain
close to each other expenditures of energy for separation, but the preferable split
leads to smaller expenditures. Therefore, it is possible to use the preferable split as
optimal. This calculates withdrawals flow rates of pseudoproducts and minimum
flows of vapor and liquid in the first column of the complex (and for the complex in
Fig. 6.13a also in the other columns with distributed components). Compositions
of liquid and vapor at the ends of the first column should correspond to trajectory
t
t
tear-off points x (S r ) and x (S s ) from boundary elements of concentration sim-
r s
plex of the mixture under separation. The transition to the subsequent columns
in the course of separation and, finally, to the last product column is carried out
after that. This transition is realized in the same way as it is for the columns with
side strippings. The calculation of section trajectories at the preferable split in the
minimum reflux mode is carried out most easily, compared with the calculation
of sections trajectories for other splits, because in this case the minimum value
of parameter L/V does not have to be found by means of scanning (it is equal
to the ratio of flows in feed cross-section at sharp reversible distillation and it is
defined at Eq. [5.6], where K j is the phase equilibrium coefficient in the feed point
of the component absent in top product). Section trajectories in this case should
be calculated in the direction from column ends to the feed cross-section using
the method “tray by tray” (Fig. 5.6a).
We examined above Petlyuk columns with preferable split in each column –
1,2 . . . n – 1 : 2,3 . . . n. Along with such sequence one can use in practice sequences,
where each product contains several components. The example of such separation
given in the work (Amminudin et al., 2001) is the separation of the mixture of
light hydrocarbons consisting of nine components into three products: propane
fraction, butane fraction, and pentane fraction. In these case, the split of the
following type is used in the first column: 1,2, . . k,... l : k, k + 1,... l,... n (i.e.,
components k, k + 1, . . . l are distributed ones). So far, we examined only splits with
one distributed component or with (n − 2) distributed components (the preferable
split). The split 1,2 . . . k,... l : k, k + 1, . . . l,... n has more than one and less than
(n − 2) distributed components. The main difficulty in the calculation of minimum
reflux mode for such splits consists of the fact that distribution coefficients of the
distributed components cannot be arbitrary. In order that sections trajectories
in minimum reflux mode join each other product points should belong to some
regions at the boundary elements of concentration simplex. In the general case,
the boundaries of these regions are unknown. However, for zeotropic mixtures,
separation product compositions can be determined at the set requirements to
the quality of the products with the help of the Underwood equation system