Page 80 - Applied Process Design For Chemical And Petrochemical Plants Volume II

Distillation 69

not an operable condition. Knowledge of the minimum tributed, (b) no split key components exist, (c) total molal
reflux ratio aids considerably in establishing an economi- overflow rates and relative volatilities are constant. This
cal and practical operating ratio. Ratios of 1.2 to 2.0 times method provides good agreement with the detailed
the minimum are often in the economical range for method of Underwood.
hydrocarbon chemical systems. However, it is well to rec- Yaws [124] et al. provide an estimating technique for
ognize that high reflux rates increase column size (but recovery of each component in the distillate and bottoms
reduce number of trays required), reboiler size, steam from multicomponent distillation using short-cut equa-
rate, condenser size and coolant rate. tions and involving the specification of the recovery of
For adjacent key systems, all components lighter than each component in the distillate, the recovery of the heavy
the light key appear only in the overhead, and all compo- key component in the bottoms, and the relative volatility
nents heavier than the heavy key appear only in the bot- of the light key component. The results compare very well
toms, and the keys each appear in the overhead and bot- with plate-to-plate calculations, Figure 8-46, for a wide
toms in accordance with specifications. range of recoveries of 0.05 to 99.93% in the distillate.
For a split key system the lights and heavies distribute The distribution of components for the distillate and
the same as for adjacent key systems. However, the com- the bottoms is given by the Hengstebeck-Geddes equation
ponent(s) between the keys also distribute to overhead [124, 125, 1261:
and bottoms.
At minimum reflux, the regions in which the number of log (di/bi) = A + B log ~i (8- 124)
trays approaches infinity (called the pinch zones and where di = mols of component i in distillate
region of constant compositions) are: bi = mols of component i in bottoms
ai = relative volatility of component i
1. Binary system: pinch zone adjacent to feed plate A, B = correlation constants
2. Multicomponent:
a. Three components with no component lighter A material balance for the i component in the feed is:
than light key: pinch zone in stripping section adja- (8- 123)
cent to feed plate. fi = di + bi
b.Three components with no component heavier Then the quantity of component i in the distillate can be
than heavy key: pinch zone in rectifying section expressed as a mol fraction recovered, or di/fi. Likewise,
adjacent to feed plate. the mol fraction of component i recovered in the bottoms
c. Three components mixture: pinch zones may be is bi/fi, or 1 - di/fi. Substituting into Equation 8-124:
above and below feed plate.
d. Greater than four components: pinch zones
appear in rectifying and stripping sections.

For systems with one sidestream drawoff, either above
or below the feed, Tsuo et al. [lo21 propose a method for
recognizing that the minimum reflux ratio is greater for a
column with sidestream drawoff. At the sidestream the
operating line has an inflection. For multifeed distillation
systems, the minimum reflux is determined by factoring
together the separate effect of each feed [ 1031.
Lesi [ 1051 proposes a detailed graphical procedure for
figuring multicomponent minimum reflux by a graphical
extension of a McCable-Thiele diagram, assuming infinite
plates or eqcilibrium stages. In this traditional model the
concentration in the distillate of the components heavier
than the heavy key component are assumed to be zero,
and the heaky key component reaches its maximum con-
centration a+, the upper pinch point (see Figures 8-23 and Relative volatility. a,
8-23). Therefore, this assumption is that only the heavy
and light keys are present at the upper pinch point, simi- Figure 8-46. Yaws short-cut method compared to plate-to-plate cal-
culations. Used by permission, Yaws, C. L. et ai. Hydrocarbon Pro-
lar in concept to the handling of a binary mixture [106]. cessing, V. 58, No. 2 (1979) p. 99. Gulf Publishing Co., all rights
The method assumes (a) only the key components are dis- resewed.