Page 176 - Distillation theory

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150 Distillation Trajectories and Conditions of Mixture Separability

1
At nonsharp separation tear-off point S is absent because it is located out-
side the concentration simplex. However, for practical purposes, it is expedient to
examine the separation, close to sharp one, which assumes the content of ad-
mixture components in products to be small (quasisharp separation). With this
1
2
approach, one can examine the same stationary points S , S ... N , as for the
+
corresponding absolutely sharp separation, bearing in mind, that trajectories of
quasisharp process go not through the stationary points themselves, but close to
them (through quasistationary points). That allows to use the theory of sharp
separation trajectories bundles for the solution of practical tasks, for which distil-
lation process cannot be absolutely sharp (i.e., besides product components, each
product contains also admixture components).
Section trajectory bundle in its general form may be put in brief as follows:

(k+1) (k+1)
(k) 1(k) S r +(k+1) (k) 1(k) S s +(k+1)
x → S ⇒ N , or x → S ⇒ N .
D r r B s s
Reg Reg t Reg Reg 1
D r B s
5.6. Conditions of Section Trajectories Joining and Methods of
Minimum Reflux Calculating

5.6.1. Two Models of Feed Tray

So the distillation process in two-section column may be feasible, it is neces-
sary that sections trajectories are joined with each other (i.e., that there is ma-
terial balance between sections flows at the plates above and below feed cross-
section).
The mixture of two flows of liquid goes into the plate, located below feed cross-
section: the liquid part of feeding and of liquid, following down from top section
bottom plate (Fig. 5.29a). Therefore, between liquid leaving top section and liquid
going into bottom section, there is a leap of concentrations in accordance with the
equation of material balance in feed cross-section:

L r x f −1 + L F x F = L s x f , (5.18)

where x f −1 and x f should belong to trajectory bundles of top and bottom sections
R
correspondingly (x f −1 ∈ Reg R and x f ∈ Reg w,s ). Hereinafter, we use the following
w,r
⇓
symbol for a leap of concentrations in the feed cross-section: x f −1 ⇒ x f .
The simplified model of feed tray, based on the assumption that feed plate
is common for both sections and that the process of mixing and the process of
equilibrium achievement go on simultaneously (Fig. 5.29b), is used in a number
of works (Levy et al., 1985; Julka & Doherty, 1990). According to this model,
the composition x f can be determined from the equations of both sections (i.e.,
point x f should lie at the intersection of two sections trajectories) (x f ∈ Reg R •
w,r
Reg R ).
w,s