Page 208 - Separation process principles 2

5.4 Multicomponent Vapor-Liquid Cascades 173

Distillate For either an enricher or exhauster, +A and +E are given,
from above, by (5-48) and (5-50), respectively, or from
Figure 5.9.
To couple the enriching and exhausting cascades, a feed
stage is employed for which the absorption factor is related
to the streams leaving the feed stage by
top plate
Feed -91 For the distillation column of Figure 5.14, (5-62), (5-64),
Enriching
cascade
Enricher
bottom plate
'F 'BE
f Feed plate and (5-65) are combined to eliminate IF and VF. The result is
'TX 'F Exhauster
-- -
top plate
Exhausting
cascade To apply (5-66) for the calculation of component split ra-
tios, bid, it is necessary to establish values of absorption fac-
w : ; s t e r
bottom plate tors AF and Ac, and the stripping factor SB. Average values
u~ 'AX
for factors AE, Ax, SE, and Sx for each conlponent are also
Reboiler I
required for the two cascades to determine the correspond-
ing + values. To establish these values, it is necessary to
b
estimate temperatures and molar vapor and liquid, V and L,
Bottoms
flow rates. An approximate method for making these esti-
Figure 5.14 Countercurrent distillation cascade.
mates is given in the following example.
by making the following substitutions, which are obtained
from material balance and equilibrium considerations. For
each component in the feed,
The hydrocarbon gas of Example 5.3 is distilled at 400 psia
UTE = 1c + d (5-56) (2.76 MPa), to separate ethane from propane, for the conditions
VF = BE + d (5-57) shown in Figure 5.15. Estimate the distillate and bottoms composi-
tions using (5-66). This example is best solved by using a spread-
and
sheet computer program.
lc = dAc (5-58)
where SOLUTION I
LC
Ac = - (for a partial condenser) (5-59) Assume a feed stage temperature equal to the feed temperature, #
DKc 105°F. Toestimate the condenser and reboiler temperatures, assume a I
L c perfect split for the specified distillate rate of 530 lbmolh, with all
Ac = - (for a total condenser) (5-60)
D methane and ethane going to the distillate and all propane and heav- I
ier going to the bottoms. Thus the preliminary material balance is
The resulting enricher recovery equations for each species are 1
I
lbmolih
/
Assumed Assumed
Component Feed, f Distillate, d Bottoms, b ?

c I 160 160 0 11

where the additional subscript E on + refers to the enricher.
The recovery equations for the exhauster are obtained in
a similar manner, as
VTX SB+AX
-- - - 1 (5-63)
b +sx
For these assumed products, applying procedures in Section 4.4, 1
a distillate temperature of 12°F is obtained from a dew-point calcu- I
lation and a bottoms temperature of 165°F from a bubble-point
where calculation. Average temperatures of (12 + 105)/2 = 59°F and I ~
(105 + 165)/2 = 135°F are estimated for the enriching and
SB = KBVB/B
exhausting cascades, respectively. Assuming that total molar flow I I
for a partial reboiler, and additional subscript X on + denotes rates are constant in each cascade, the following vapor and liquid I
an exhauster. flow-rate estimates are obtained by working down from the top of II
1