Page 115 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
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4.3 Trajectory Bundles of Sharp Reversible Distillation 89

distillation column trajectory may be briefly described as follows:

(2) t(2) (3) t(2) (2)
x → x ← x
D → x rev,r F ← x rev,s B .
Reg D Reg t rev,r Reg rev,rs Reg t rev,s Reg B

If the feed point lies on the α-line, α-surface, or α-hypersurface, then the liquid–
vapor tie-line of feeding is directed to some (n − 2)-component boundary element
or from some (n − 2)-component boundary element. If, along with that, the liquid–
vapor tie-line is directed to the possible product composition region at this bound-
ary element or from this region, then the product of reversible distillation section
can contain n − 2 components. For example, if the feed point in Fig. 4.10c lies on
the α 23 -line within the true bundle of bottom section trajectories then the liquid–
vapor tie-line of feeding is directed to vertex 1 [i.e., the component 1 = Reg can
D
be a product of the section (the product contains n − 2 components)].
The general rule: if the phase equilibrium coefficients of k light or heavy com-
ponents are equal to each other in the feed point, then the section product can
contain (n − k) components.
We previously examined the process of reversible distillation for a given feed
point. Below we examine trajectories of reversible distillation sections for given
product points located at any k-component boundary elements C k of the concen-
tration simplex (x D ∈ C k or x B ∈ C k ).If k < (n − 1), then in the general case such
trajectories should consist of two parts: the part located in the same k-component
boundary element where the product point lies and the part located at some
(k+ 1)-component boundary element C k+ 1 adjacent to it. Along with that, the
(k)
product point should belong to the possible product composition region Reg or
D
(k)
Reg for the examined (k)-component boundary element, and the boundaries of
B
this region can be defined with the help of Eqs. (4.19) and (4.20).
Such an approach on the basis of product points will be necessary at the analysis
of the location of adiabatic sections trajectories bundles (at finite reflux) which
products consist less (n − 1) components (see Chapter 5).

4.3.5. Liquid and Vapor Flow Rates Changing along the Reversible
Distillation Trajectories
Besides the location of reversible distillation trajectories in the concentration
simplex, the character of the liquid and vapor flow rates changing is of great
importance. In accordance with the formulas [Eqs. (4.11) and (4.13)], the ratio
of liquid and vapor flow rates in each cross-section in the top section should
be equal to the phase equilibrium coefficient of the heaviest component and in
the bottom section to that of the lightest component. For ideal mixtures, these
phase equilibrium coefficients should change monotonously along the sections
trajectories, which leads to maximum liquid and vapor flow rates in the feed cross-
section (see Figs. 4.3 and 4.6).