1401
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1948
,
.
assumed feed-tray temperatures indicated this t o be correct. However, the curve of total trays against feedtray temperature is very flat over the range of 195 ’ to 205 F. At this reflux ratio, the optimum feed-tray tempere ture does not have to be determined accurately. At reflux ratios close to the minimum the determination of optimum feed-tray temperature is very critical. It was found also that a t fzed-tray temperatures more than 10 F. outside of this optimum range, several extra trays will be required.
TABLE 111. FEED-TRAY LOCATION
___-_ Number Fractionating
of Theoretical Trays---Stripping Total Calcd. Actual Calcd. Actual Calcd. Botual No.n R RAf rM rT 8.92 16.15 16.17 8.93 7.22 7.25 9 3.00 1.127 0.958 0.530 0.692 16.75 16.77 6.70 6.95 1.638 0.530 1.279 10.07 9.80 B 0.74 0.500 9.32 19.37 19.38 9.14 0.705 0,530 0.643 10.23 10.06 C 4.00 2.51 16.65 16.66 6.27 6.43 0.705 0.530 0.654 10.38 10.23 II 3.50 2.48 16.70 16.70 ‘6.93 7.09 9.61 9.77 0.530 0.613 0.650 E 2.85 4.05 16.45 16.43 7.20 7.21 9.25 9.24 0.311 0.530 0,382 F 7.38 4.60 14.26 14.30 7.20 7.10 7.06 7 . 2 0 0,707 1.010 G 1 78 0.913 1.30 Balance of cas@ based on liquid feed a t a Case F based on vapor feed a t feed-plate temperature. feed-plate temperature.
Case
1’
CONCLUSION
The columns of r , and ~ TT in this table also indicate the wide variation of the ratio of the key components in the feed-tray liquid between minimum reflux and total reflux. According to the previous method of Gilliland (2),the optimum feed tray in cases A t o E would be that on which the ratio of the keys in the liquid was less than 0.75 and would require that this ratio be greater than 0.75 on the tray above the feed a t all reflux ratios. Thus, considerable error would result from the application 01 this criterion, particularly in the region close to minimum reflux. The previous method (8) applies exactly at total reflux and reasonably well at reflux ratios close to total reflux, The method of Underwood (8) gives essentially the same results as that of Gilliland and would include the same objections. APPLICATION OF EQUATIONS
As a sample calculation, the present empirical method can be applied to the multicomponent tray calculations of Jenny (23). The calculation of minimum reflux ratio for this case was demonstrated in a previous article ( 7 ) . At the feed tray, the following relative volatilities of the components were obtained (7) : XF 0.26 0.09 0.25 0.17 0.11 0.12
ff
20.6
5.0 2.0 1 .o 0.44 0.21
It was previously determined that the pseudo feed line intersects the binary equilibrium curve at 0.470, thus
v
= 0.66
1 = 0.34 (1
aD(l
-
aD)XD = (2.0
- 2.0 X
0 6612.0 X 0.25
- 1)(0.25 + 0.17)(1 - 0.26 -
- 0 4410.11 f 0.21(1 - 0.21)0.12]
[0.44(1
0.09)
-0,0275
XA2= rrA
-1
-
(2 0 1)20 34 ( 0 . 2 5 + 0 17)(1 0 11 - 0 12)1-c
-
0 262 +
-1
XAZ
=
+
2,.0(0.25 0.17)(1
20.6 L O . 6 IM =
7
=
-2 0 - 1.0O
- 0.11 - 0.12) -
5.0 2.0 0.092] 26z + 5.0 - 1.0
0.887
1
- 0 0275 + 0.0058 - 0.0717
1,040
=
LITERATURE CITED
(1) Badger, W. H., and McCahe, W. H., “Elements of Chemical Engineering,’’ New York, McGraw-Hill Book Go., 1931. (2) Gilliland, E. R., IND. ENG.CHEM., 32,918 (1940). (3) Jenny, F. J., T r a n s . Am.Inst. Chem. Engrs., 3 5 , 6 3 5 (1939). (4) Jenny, F. J., and Cicalese, M. J., IND. ENG.CHEM., 37, 956 (1945). (5) Murphree, E. V., Ibid., 1 7 , 7 4 7 , 9 6 0 (1925). (6) Scheihel, E. G., Ibid., 38, 397 (1946). (7) Soheihel,E. G., a n d Montross, C. F.,Ibid., 38, 268 (1946). (8) Underwood, A. J. V., T r a n s . Inst. Chem. Eng. ( L o n d o n ) , 10,112 (1932).
RECEIVED April 25, 1947. 09*
=
0 0058
(2.0 - 1)0.66
F a x
The empirical equations previously presented give the ratio of the light to heavy key in the optimum feed-tray liquid. The equations have been developed for the range of conditions usually encountered in practice. Without doubt they have limitations in extreme cases for feeds consisting of less than 10% key components and particularly ,when the relative volatilities of all the components in this feed are very close (within 10%). The accuracy of the equations was found t o be within the reliability with which the optimum feed tray could be located by a series of tray calculations a t different feed-tray locations. The method is particularly applicable to tray calculations by the Jenny method (9) of assuming a feed-tray temperature and calculating the feed-tray liquid composition. By the use of these equations, the ratio of the keys in the optimum feed tray can be calculated directly. A comparison with the ratio a t the asspmed feed-tray temperature will indicate immediately whether the optimum feed tray occurs close to the assumed temperature or at a higher or lorver temperature. I t is thus possible to assume a second feed-tray temperature which will be closer to the optimum value. A final set of complete tray calculations can then be made Ft the optimum feed-tray temperature to determine accurately the trays required above and below the feed. The present method eliminates the tedious trial and error procedure of carrying out tray-to-tray calculations using different feed-tray locations to determine which location requires the smallest number of total trays for the desired separation.
Heat Transfer-Correction =
0.0717
0 978
+ O 1.5 x 5 (0 978 - 1.040) = 1.000
Thus, the calculated optimum ratio of the key components in the feed-tray liquid is 1.000 and the ratio of the keys in the feed-tray liquid a t 205’ F. has been calculated by Jenny as 0.872. This indicates that the assumed feed-tray temperature ia too high and another trial a t 200” F. will give the desired o timum ratio. Accurate tray calculations on this separation a t Jfferent
In the article “Heat Transfer with Extended Surface. Determination of the Local Heat Transfer Coefficient from the Average ENG.CHEM.,40, 1098-1101 Coefficient,” by C. F. Bonilla [IND. (1948)1, the expression tan h should be replaced by tanh, or hgperbolic tangent, twice in Equation 4,and in Equations 5 and 6, and undyr example a. In the following article, “Heat Transfer with Extended Surface. No Mixing Parallel to the Extended Surface,” by W. E. Dunn, Jr., and C. F. Bonilla, the same misprint is present in Equation 3, three lines under Equation 3, and in example 6. The symbol ta 2 in examples a and b, and in the definition of T in the nomenclature, should have a bar over it to indicate that it is the average temperature of the fluid leaving.
*
