Page 33 - Applied Process Design For Chemical And Petrochemical Plants Volume II

22 Applied Process Design for Chemical and Petrochemical Plants

energy in the form of reboiler heat and condenser coolant Because the feed tray is essentially non-effective it is sug-
to maintain a total reflux condition with no feed, no over- gested that an additional theoretical tray be added to
head and no bottoms products or withdrawals. allow for this. This can be conveniently solved by the
The conditions of total liquid reflux in a column also nornographs [21] of Figures 8-16 and 17. If the minimum
represent the minimum number of plates required for a number of trays in the rectifying section are needed, they
given separation. Under such conditions the column has can be calculated by the Fenske equation substituting the
zero production of product, and infinite heat require- limits of xF1 for XBh and XBl, and the stripping section can
ments, and L,/V, = 1.0 as shown in Figure 8-15. This is the be calculated by difference.
limiting condition for the number of trays and is a conve From Fenske’s equation, the minimum number of equi-
nient measure of the complexity or difficulty of separation. librium stages at total reflux is related to their bottoms (B)
and distillate or overhead (D) compositions using the
Fenske Equation: Overall Minimum Total Trays with average relative volatility, see Equation 8-29.
Total Condenser To solve for the component split [loo] in distillate or
bottoms:
(”) = (“) Sm

(8 - 29) (aLK-m (8-32)
\--min , -I x~ D X~~ D
log Q avg.
This includes the bottoms reboiler as a tray in the system. where S, = total number of calculated theoretical trays
See tabulation below. at total reflux, from Equation &30
Nmin includes only the required trays in the column Xlk = XLK = liquid mol fraction of light key
itself, and not the reboiler. xa = xm = liquid mol fraction of heavy key
lk - hk = LK - HK= average relative volatility of column (top to
bottom)
aavg = (alk/hk)
D refers to overhead distillate
B refers to bottoms Because a column cannot operate at total reflux and
produce net product from the column, a reflux ratio of
about 1.1 to 1.5 times the minimum reflux will usually give
(8 - 30) practical results. Be aware that as the reflux ratio comes
down approaching the minimum, the number of theoret-
This applies to any pair of components. My experience ical and then corresponding actua2 trays must increase.
suggests adding +1 theoretical tray for the reboiler, thus
making the total theoretical trays perhaps a bit conservative. Relative Volatility
But, they must be included when converting to actual trays
using the selected or calculated tray efficiency: Relative volatility is the volatility separation factor in a
vapor-liquid system, i.e., the volatility of one component
S,+ 1 =N,h (8 - 31) divided by the volatility of the other. It is the tendency for
one component in a liquid mixture to separate upon dis-
For a condition of overall total trays allowance is to be tillation from the other. The term is expressed as the ratio
made for feed tray effect, then add one more theoretical tray to of vapor pressure of the more volatile to the less volatile in
the total. As demonstrated in the tabulation to follow,
allowance should be made for the reboiler and condenser. the liquid mixture, and therefore a1,2 is always equal to 1.0
or greater. a1,2 means the relationship of the more volatile
Total Partial or low boiler to the less volatile or high boiler at a constant
Condenser Reboiler Condenser Total specific temperature. The greater the value of a, the easier
will be the desired separation. Relative volatility can be cal-
Nmin +I 0 +O Nm+l culated between any two components in a mixture, binary
+1 +O Nm+2 or multicomponent. One of the substances is chosen as the
Nmin +O +1 +1 N,+2 reference to which the other component is compared.
Definition of Relative Volatility: Relative Volatility of
Note that the approach recommended here is not in
agreement with Van Winkle [74], because he assumes the Component 1 with respect to component 2.
reboiler and partial condenser are included in the overall Q1,2 = (p1 XZ)/(PZ Xl) = (y1 X2)/(Y2 x1) (8 - 33)
calculation for NmiW
Various average values of a for use in these calculations where 1,2, etc. are component identification
are suggested in the following section on “Relative Volatility.” p = partial pressure of a component