Page 201 - Distillation theory

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

6.3 Distillation Trajectories and Minimum Reflux Mode 175

of such columns at separation of mixtures with constant relative volatilities and
molar flows, the Underwood method (Barnes, Hanson, & King, 1972; Nikolaides &
Malone, 1987) was used.
For nonideal three-component mixtures, the methods of calculation of mini-
mum reflux mode was developed in the works (Glanz & Stichlmair, 1997; Levy &
Doherty, 1986). The simplified method that was offered before for the columns
with one feed (Stichlmair, Offers, & Potthof, 1993) was developed in the work
(Glanz & Stichlmair, 1997).
It follows from general thermodynamic considerations that at one and the same
product compositions the column with several feed flows of different composition
should require less energy for separation than the column with one feed flow
formed by mixing all the feed flows. It follows from the fact that summary entropy
of all feed flows should be smaller than that of the mixed flow because the mixing
of flows of different composition increases the entropy and the separation of flows
decreases it. Therefore, the minimum reflux number for the column with several
feed inputs should be smaller than that for the column with one mixed feed flow
(i.e., it is unprofitable to mix flows before their separation).
In Chapter 5, to develop a general algorithm of calculation of minimum reflux
mode for columns with one feed, we had to understand the location of reversible
distillation trajectories and the structure of top and bottom section trajectory
bundles.
As in that case, to develop a general algorithm of calculation of minimum reflux
mode for columns with several feed inputs, we need to understand the location
of reversible distillation trajectories of intermediate sections and the structure of
trajectory bundles for these sections.

6.3.1. Location of Reversible Distillation Trajectories of Intermediate Sections

Locations of reversible distillation trajectories depends on position of pseudo-
product point (i.e., on compositions and on flow rates of feeds and of separa-
tion products, as is seen from Eq. [6.3]). Difference from the top and bottom
sections appears, when the pseudoproduct point of the intermediate section is
located outside the concentration simplex (i.e., if concentrations of some com-
ponents x Di obtained from Eq. [6.3], are smaller than zero or bigger than one),
which in particular takes place, if concentration of admixture components in sep-
aration products are small components (i.e., at sharp separation in the whole
column). The location of reversible distillation trajectories of the intermediate
sections at x < 0or x > 1 differs in principle from location of ones for top
Di Di
and bottom sections, as is seen from Fig. 6.3 for ideal three-component mixture
(K 1 > K 2 > K 3 ) and from Fig. 6.4 for ideal four-component mixture (K 1 > K 2 >
K 3 > K 4 ).
As far as pseudoproduct point x and liquid-vapor tie-line in all points of
D
reversible distillation trajectory should lie at one straight line, pseudoproduct
point x at Fig. 6.3, can lie behind side 2-3 or side 1-2 and at Fig. 6.4, they can lie

D
behind face 1-2-3 or face 2-3-4.