Page 118 - Distillation theory

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0521832772c04 CB644-Petlyuk-v1 June 11, 2004 17:49

92 Trajectories of Thermodynamically Reversible Distillation

Therefore, an infinitesimal amount of heat should be drawn off in each cross-
section of the top section and should be brought in in each cross-section of the
bottom section. For azeotropic mixtures, the phase equilibrium coefficients field
is of complicated character, which leads to nonmonotony of the liquid and vapor
flow rates changing along the sections trajectories (i.e., to the necessity of input
or output of heat in various cross-sections of the section). Such character of the
flow rates changing at reversible distillation influences on the conditions of mini-
mum reflux mode in adiabatic columns, which results in a number of cases in the
phenomenon of “tangential pinch” (see Chapter 5).

4.4. Diagrams of Three-Component Mixture Reversible Distillation
Locations of trajectories bundles Reg , of node points of these bundles N rev , and
rev
(2) (2)
of possible product segments Reg and Reg B can be shown in diagrams of three-
D
component azeotropic mixtures sharp reversible distillation for various types of
such mixtures (Fig. 4.11).
Along with the diagrams of open evaporation (see Chapter 3), these diagrams
contain a great deal of information necessary to design separation units.
The location of trajectory bundles and possible product composition segments
at reversible distillation of three-component mixtures determines the location of
trajectory bundles, and of possible product composition regions of multicompo-
nent mixtures and the locations of trajectory bundles of real adiabatic columns.

4.4.1. Calculation of Reversible Distillation Trajectories
Diagrams of reversible distillation of various types of three-component mixtures
can be obtained in various ways with the help of the model of phase equilibrium
describing these types of mixtures. It is possible to calculate the trajectory conse-
quently for each chosen product point using Eq. (4.6) ÷ (4.13) and increasing step
by step the concentration of the component that is absent in the product, after the
definition of trajectory tear-off point with the help of Eqs. (4.19) and (4.20). The
iteration procedure for such calculation was proposed by Koehler et al. (1991)
and further improved by Petlyuk & Danilov (2001).
0
Let’s consider, for example, that some point x on the trajectory of reversible
i
distillation for given product point x D . Further concentration of the heaviest com-
0
ponent is increased x h = x + . Concentrations of the rest of components are
h
0
defined by normalizing x i = x /(1 + ). In a new point, K i (x i ) and L/V = K n (x n )
i
are calculated. New values x i for i = 1, 2 ... (n − 1) and the corresponding new
values K i and L/V are defined with the help of Eq. (4.6). Such procedure goes
on until concentrations x i stop changing. To ensure convergence of the iteration
process, the procedure illustrated graphically in Fig. 4.12 is used. After the fi-
nal definition of point x i at reversible distillation trajectory, the next increase of
concentration of the heaviest component is to be done. Such a method of calcu-
lation for reversible distillation trajectories is good for mixtures with any number