Page 250 - Separation process principles 2

6.6 Tray Diameter, Pressure Drop, and Mass Transfer 215

EXAMPLE 6.4

Assume that the column diameter for the absorption operation of
Example 6.1 is 3 ft. If the overall stage efficiency, E,, is 30% for the
Downcomer absorption of ethyl alcohol, estimate the average Murphree vapor
efficiency, EMV, and the possible range of the Murphree vapor-point
efficiency, Eov.

SOLUTION
For Example 6.1, the system is dilute in ethyl alcohol, the main
Column wall
component undergoing mass transfer. Therefore, the equilibrium
and operating lines are essentially straight, and (6-37) can be ap-
Figure 6.20 Oldershaw column. plied. From the data of Example 6.1, A = KV/L = 0.57(180)/
\ 151.5 = 0.68.
Solving (6-37) for EMv, using E, = 0.30,

and shown schematically in Figure 6.20. Oldershaw columns
are typically 1 to 2 in. in diameter and can be assembled with
For a 3-ft-diameter column, the degree of liquid mixing proba-
almost any number of sieve plates, usually containing 0.035-
bly lies intermediate between complete mixing and plug flow. From
to 0.043-in. holes with a hole area of approximately 10%.
(6-3 1) for the former case, Eov = EMv = 0.34. From a rearrange-
A detailed study by Fair, Null, and Bolles [23] showed that
ment of (6-32) for the latter case, Eov = In(1 + AEMV)/A =
overall plate efficiencies of Oldershaw columns operated In[l + 0.68(0.34)]/0.68 = 0.3 1. Therefore, Eovlies in the range of
over a pressure range of 3 to 165 psia are in conservative 31% to 34%, probably closer to 34% for complete mixing. How-
agreement with distillation data obtained from sieve-tray, ever, the differences between E,, EMV, and EoV for this example are
pilot-plant and industrial-size columns ranging in size from almost negligible.
18 in. to 4 ft in diameter when operated in the range of 40%
to 90% of flooding. It may be assumed that similar agree-
ment might be realized for absorption and stripping. 6.6 TRAY DIAMETER, PRESSURE DROP,
It is believed that the small-diameter Oldershaw column
AND MASS TRANSFER
achieves essentially complete mixing of liquid on each tray,
thus permitting the measurement of a point efficiency. As In the trayed tower shown in Figure 6.21, vapor flows verti-
discussed above, somewhat larger efficiencies may be ob- cally upward, contacting liquid in crossflow on each tray.
served in much-larger-diameter columns due to incomplete When trays are designed properly, a stable operation is
liquid mixing, which results in a higher Murphree tray effi- achieved wherein (1) vapor flows only through the perfora-
ciency and, therefore, higher overall plate efficiency. tions or open regions of the tray between the downcomers,
Fair et al. [23] recommend the following conservative (2) liquid flows from tray to tray only by means of the down-
scale-up procedure for the Oldershaw column: comers, (3) liquid neither weeps through the tray perfora-
tions nor is carried by the vapor as entrainment to the tray
1. Determine the flooding point.
above, and (4) vapor is neither carried (occluded) down by
2. Establish operation at about 60% of flooding (but the liquid in the downcomer to the tray below nor allowed to
40 to 90% seems acceptable). bubble up through the liquid in the downcomer. Tray design
3. Run the system to find a combination of plates and includes the determination of tray diameter and the division
flow rates that gives the desired degree of separation. of the tray cross-sectional area, A, as shown in Figure 6.21,
into active vapor bubbling area, A,, and liquid downcomer
4. Assume that the commercial column will require the
area, Ad. With the tray diameter fixed, vapor pressure drop
same number of plates for the same ratio of liquid to
and mass-transfer coefficients can be estimated.
vapor molar flow rates.
If reliable vapor-liquid equilibrium data are available, they
Tray Diameter
can be used with the Oldershaw data to determine the overall
column efficiency, E,. Then (6-37) and (6-34) can be used to For a given liquid flow rate, as shown in Figure 6.22 for a
estimate the average point efficiency. For the commercial-size sieve-tray column, a maximum vapor flow rate exists
column, the Murphree vapor efficiency can be determined beyond which incipient column flooding occurs because of
from the Oldershaw column point efficiency using (6-34), backup of liquid in the downcomer. This condition, if sus-
which takes into account incomplete liquid mixing. In gen- tained, leads to carryout of liquid with the overhead vapor
eral, the tray efficiency of the commercial column, depending leaving the column. Downcomerffooding takes place when,
on the length of the liquid flow path, will be higher than for the in the absence of entrainment, liquid backup is caused by
Oldershaw column at the same percentage of flooding. downcomers of inadequate cross-sectional area, Ad, to carry