Page 105 - Distillation theory

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4.2 Essence of Reversible Distillation Process and Its Peculiarities 79

of feed input and in the ends of the column where the flows from condenser
and reboiler are brought in); (2) there is a loss of pressure because of hydraulic
resistance of contact devices at the plates of the column; and (3) heat is brought
and removed in reboilers and condensers at nonzero temperature differences.
The real process thermodynamic efficiency of distillations equals to
η = S dist /( S dist + S ir ) (4.5)

In the case of real process, the thermodynamic efficiency is quite low; in air
separation units, it is equal to 18%; in crude units, it is equal to 12%; and in units
for ethylene and propylene production, it is equal to 5% (Haselden, 1958).

4.2.2. Location of Reversible Distillation Trajectories
The main peculiarity of thermodynamically reversible distillation process consists
of the fact that flows of two different phases (vapor and liquid) found in any cross-
section are in equilibrium, and flows found in the feed cross-section are of the
same composition as feed flows.
Usingtheequationofmaterialbalanceandofphaseequilibriumforanarbitrary
cross-section of the upper section, we get

(4.6)
Vy i = Lx i + Dy Di
(4.7)
y i = K i x i
Similarly, for the lower section,
(4.8)
Lx i = Vy i + Bx Bi
It follows from Eq. (4.6) that the points of the upper section x i , y i , y Di lie in
one straight line in the concentration simplex.
Similarly, it follows from Eq. (4.8) that points x i , y i , x Bi of the lower section are
also colinear. Equations (4.6) and (4.8) are simultaneously valid for the feed cross-
section. Therefore, points x Fi , y Fi , y Di , and x Bi should belong to the same straight
line (x fi = x Fi , y fi = y Fi , where x fi , y fi are concentrations of the component i in
the feed cross-section and x Fi , y Fi are concentrations in the feed). The validity of
Eqs. (4.6) and (4.8) leads to the conclusion: the product points in the concentration
simplex should lie on the prolongation of liquid–vapor tie-lines in each cross-
section of the column (Fig. 4.1). The reversible distillation trajectory is the locus of
the points where the straight lines passing through product points are tangent to the
residue curves because liquid–vapor tie-lines are tangent to these curves.

y D
y
Figure 4.1. Location of reversible section trajectories and
y = y f liquid–vapor tie-lines in arbitrary tray cross-section illus-
F
x = x f
F
x trating that extended tie-lines pass through product points
x x B and y D . x and y, composition in arbitrary tray cross-
section (little circles).
x B
y