The over-all plate efficiency in commercial petroleum columns treating gasoline or light naphthas under efficient operating conditions is close to 100 per cent. With close plate spacing or short path of reflux on plates, the efficiency is decreased to about 80 per cent. In lower sections of petroleum columns, or when operating on less volatile fractions, the plate efficiency is progressivelyreduced. With poor operating conditions, such as large quantities of water on plates, the plate efficiency is seriously limited and may be reduced to about 15 per cent. The graphical method of computing the number of equilibrium plates required to separate complex mixtures, such as petroleum, is convenient and reliable when limited to a section containing not more than six or eight equilibrium plates, and may be used in conjunction with over-all plate efficiencies to compute the number of actual plates required in a petroleum fractionating column.
DESIGN OF SIDNEY CHARLES SINGER, JR., ROY RUSSELL WILSON,1 AND GEORGE GRANGER BROWN University of Michigan, Ann Arbor, Mich.
DIS?
I
a 2 4 3 Y 4
t
L 5 6
0
.IO
.PO
30 .40 .SO .BO ,70 .BO MOL FRACTION IN LIQUID
.PO
FIGURE1. UNDERWOOD’S LIQUID COMPOBITIONS FOR
HERE sharp separation between components is required, as is usually the case in gas and gasoline fractionation, a procedure similar to that previously described (4) is recommended for computing the number of equilibrium plates, or a more complete procedure (96)may be used, when time permits, for checking an assumed operation. In cases where less sharp separation between adjacent components, or a smaller number of plates between products, is required, as in current commercial practice in petroleum fractionation, the procedure to be described offers the advantage of greater simplicity. The graphical method of McCabe and Thiele (19) is most satisfactory for its intended application to binary mixtures when the reflux ratio may be assumed to be constant. Attempts to apply an equivalent graphical procedure to complex mixtures have not been successful. Fenske (6) and Garton and Huntington (9) have assumed that the fractionation between two cut components in the complex mixture is the same as though the two cut components alone were present in the same proportion, and that the reflux ratio of all components for the complex mixture is equivalent to the same reflux ratio for the two cut components alone for the equivalent binary mixture. This simplification is valid only for total reflux or for an infinite number of plates (3,28), and is generally unreliable. Obryadchikov (91) and Peters and Obryadchikov (23) used a single equilibrium curve based on the composition of the feed to a fractionating column to compute, by a graphical method similar to that of McCabe and Thiele (I@, the number of plates required to separate the feed into overhead and bottom fractions containing certain percentages boiling below (or above) a chosen cut temperature. Adjustments in the slope of the operating lines were made a t each plate for the changes in reflux ratio, and apparently satisfactory results were obtained by a somewhat obscure procedure, using Engler
TOTAL REFLUXPROBLEM
distillation data. Attempts to apply the method, as described, to an entire column on the basis of either A. s.T. M. or so-called true-boiling-point distillation analyses have been unsuccessful. The difficulty lies in the attempted use for all plates of a single equilibrium curve based on the feed composition, which can express accurately the equilibrium conditions only for a mixture of the same composition as the feed. Since the shape of the equilibrium curve depends upon the compoeition of the material (IS), which differs from plate to plate throughout the column and is a t no point therein the same as the feed, successful application of this method requires the use of equilibrium curves depending upon the composition on the plates where the equilibrium is supposed to exist and n o t upon the composition of the feed.
Application to Underwood’sData For example, the solution given by Underwood (28) for the fractionation of a mixture of five components may be correctly solved by a simple graphical procedure only if the proper equilibrium curve is used for each equilibrium plate. The conditions of this problem as solved by Underwood are given in Table I, and the compositions on plates 1 through 6, as computed by Underwood, are plotted in Figure 1. TABLE I. SPECIFICATIONS FOR UNDERWOOD’S PROBLEM (28) Mole Fraction in: Component Feed Overhead Bottom Hexane 0.3100 0.6360 Heptane 0.2600 0.4600 0.00126 Octane 0.1870 0.00406 0.4370 Nonane 0.1260 0.2960 Deaane 0.1120 0.2660 M oles/mole of overhead 1.7310 i.0000 0.7310 Total pressure = 14.7 Ib./sq. in.; column operated at total reflux ( L / V = 1).
...
... ...
824
FRACTIONATING COLUMNS 111. Plate Efficiency and Number of Plates for Petroleum, Columns2 Figure 2 is a plot, or graphical solution, of the composition on each of plates 1 through 6 according to the conditions set up in Table I, using the equilibrium curve for each plate as determined by Raoult’s law from the known composition and temperature of the vapor rising from that plate. Since the column is operated with total reflux (L/V = l),the composition of the liquid overflowing from any plate is the same as that of the vapor rising to that plate. The composition of the overhead vapor is given in Table I. By means of the equations (IS),
.($) and y where X =
=
=
1
Kx
5 when Raoult’s law is used
p = vapor pressure of a particular component at equi-
P
5
librium temp. total pressure of equilibrium
the temperature of the top plate and the composition of the liquid overflowing from that plate are determined. The numbered points in Figure 2 refer to the composition on the plate of that number for a particular cut temperature. The plain numbers (toward the upper right-hand corner) indicate the combined mole fraction of hexane plus heptane as a single component, while the primed numbers (toward the lower left-hand corner) indicate the mole fraction of hexane. The cut in the former case is made between heptane and octane, and in the latter between hexane and heptane; i. e., the two arbitrary components of the equivalent binary mixture are, in the first case, octane and all more volatile material; and in the second instance, hexane and all less volatile material. By the use of the two series of steps, one representing the cut between octane and more volatile material (hexane and heptane) and the other between hexane and less volatile material (heptane and octane), the entire composition on each plate is represented by Figure 2 in a manner similar to that used by McCabe and Thiele for binary mixtures. The equilibrium curve for plate 2 only is drawn in its entirety, but it is clear that reliable results could not be obtained if any one of the six equilibrium curves were used to represent the conditions on all plates. When the correct equilibrium curve is used for each plate, the graphical principle of McCabe and Thiele, with all of its conveniences can be applied with accurate results to the fractionation of complex mixtures. But the difficulties in constructing a separate equilibrium curve from the composition of the vapor or liquid for each plate rob the method of all its conveniences. Over a limited number of pIates such as a short fractionat1 Present
ing column or a section of a tall column, including usually not more than about six or eight equilibrium plates, it was found that the equilibrium curves for the materials on the intermediate plates are usually intermediate to, and lie within the area bounded by, the equilibrium curves for the first and last plates of the section. It was also found that such intermediate curves may be located with sufficient accuracy in this intermediate zone by proportional spacing of the abscissas (or ordinates), according to the number of intermediate plates. This procedure was applied to a second problem set up by Underwood (28) in which the feed, overhead, and bottoms are of the same composition as given in Table I, but the reflux ratio ( L / V ) is 0.75. Underwood also computed the cornposition of the liquid on plate 6, which will be used as the lower terminal plate. The proposed binary mixture method is illustrated in Figure 3 in which the graphical solution is given for the mole fraction of hexane on the various plates in solid lines. The number of equilibrium plates required for this separation between hexane and the less volatile material (heptane and octane) as computed by the graphical method is six, the same as computed by Underwood. The number of equilibrium plates required for the separa-
o
.IO .20
.JO .40 .so .60 a o MOL FRACTION IN LIQUID
.eo
so
PLOT OF PLATE-TO-PLATE CALCULATIONS UNDERWOOD’S TOTALREFLUXPROBLEM
FIGURE 2.
I,OO
FOR
Plain numbers refer t o equilibrium plate compositions for hexane plus heptane, as a single component. Prlmed numbers refer to equilibrium plate compositions for hexane.
address, Standard Oil Company, Casper, Wyo.
* Part I appeared in January, 1934, and Part I1 in April, 1935. a25
VOL. 28, NO. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
826
FOR UNDERWOOD’S EXAMPLES (38’ TABLE11. VAPORAND LIQUIDCOMPOSITIONS
Method 1 P Underwood’s calculation for total.reflux ( L / V = 1.0). Method 2 = Hausbrand late-to-plate calculation for total reflux ( L / V = 1.0). Method 3 = graphical cayculation for total reflux ( L / V = l.O),using empirical curves of Figure 4. Method 1A = Underwood‘s calculation for internal reflux ( L / V ) of 0.75. Method 2A = graphical calciilation for internal reflux ratio ( L / V ) of 0.75. Method 3A = graphical calculation for internal reflux ratio ( L / V ) of 0.75,using empirical curves of Figure 4. Compoc Mole Fraction of Component nent Method 11 21 YZ 22 YJ 28 Y4 24 Y6 xs Ye C7H16 1 0 9960 0 9860 0 9670 0 9175 0.8310 0.6820 CsHir 2 0’9960 0’9860 0:9860 019650 0:9650 0:9175 0:9i75 0.8300 0:8300 0.6830 0:6830 3 0:9960 0:9925 0,9925 0,9815 0.9815 0.9600 0.9600 0.9200 0.9200 0.8465 0.8465 cs&b 1 0.5325 0.3360 0.1850 0.0930 0.0400 0.1500 2 0.6325 o 3325 0’33i5 0.2040 o:ioio o.0980 o:oiio 0.0410 o:oiio 0.0185 o:bi85 3 0.5325 0:3525 0:3525 o.2060 o.2060 0.1115 0.1115 o.0580 0.0580 0.0310 0.0310 CiHis 1A 0,9960 0.9860 c~H~, ZA 0.9960 0,9860 o:g880 o:gGo o : g j & o:biis o:iLio o:iiio o:ibb4 o:iiis o:i(ii5 CIH14 1-4 0,5325 2~ 0.5325 0:3325 o:&io o:i3g5 o:iioo o:iSio o:iibs 0:ibi5 o:iiio 0:iii5 o:iioo 3.4 0.5325 0.3530 0,3980 0,2400 0.3125 0.1790 0.2670 0.15oo 0.2450 0.1300 0.2300
+ +
MOL FRACTION IN LIQUID
FIGURE 3. APPLICATIONOF GRAPHICAL METEODTO UNDERWOOD’S DATA FOR REFLUX RATIO( L / V )OF 0.75 Determination of number of equilibrium plates needed to obtain same fractionation as that indicated by Underwood’s six computed equilibrium plates
Xb u; 27 YS 0.4985 . . . . . . . . . . . 0.4975 0.7245 0,7245 0:5535 0:5535 0.0040 . . . . . . . . . . . . 0.0060 0.0195 o:oi95 o:oiio o:oiio 0.7010 ........... 0.6725 . . . . . . . . . . . 0.0910 . . . . . . . . . . . . 0.0910 o.1200 o:iiOo o:iiio ....
....
column, and in the same manner as the more reliable equilibrium curves computed ( I S ) from the actual composition of the liquid or vapor leaving the plate. For example, the graphical solution of Underwood’s problem for a reflux ratio ( L / V ) of 0.75 was made on Figure 4 (dotted lines) for the separation of hexane from the less volatile material (heptane and octane). Since the slope of the distillation curve of the material present on plate 6, according to Underwood’s computations, would be zero if computed from the temperatures of the 10 and 70 per cent points, the slope was taken as between the initial and end points, or 102 O F. per 100 per cent, or 1.02’ F. per per cent. Both the overhead product and liquid on plate 6 have such slopes of 1.02; hence the one curve serves both the terminal and intermediate conditions. It may be suggested that, because of the diEculty of properly interpolating for equilibrium curves of materials having distillation-curve slopes of less than 1.0, the curve for a slope of 1.0 be used for all fractions having slopes of 1.0 or less. The dotted lines on Figure 4 suggest a difficulty that is sometimes experienced with these empirical curves. The operating line intersects the equilibrium curve at or before the point where the desired lower terminal composition is reached, because the equilibrium curves represent only approximately the terminal plate materials. Consequently the result of the determination in this instance is somewhat in doubt, approximately seven or eight plates being indicated as
tion between octane and the more volatile components (heptane and hexane) as computed by the graphical method indicated by dotted lines in Figure 3 is about 1.5plates more than computed by Underwood. The discrepancy in the latter case i s due to the angularity of the curves when so few components are present, which may cause the equilibrium curve for intermediate plates to lie outside the area between the equilibrium curves for the terminal plates. Table I1 gives results obtained by the graphical procedure when using the correct equilibrium curve for each plate. The small discrepancy is caused by inaccuracies of graphical methods in the corners of the diagram.
Application of Empirical Curves I n instances where a minimum of data is available or where accuracy can be sacrificed for rapidity, the equilibrium curves may be estimated from the slope of the analytical distillation by an empirical relationship (13). Although these “empirical” curves, plotted in Figure 4,were originally based on the weight fraction of the feed material for an equilibrium vaporization, they may be used on a mole fraction basis when applied to the vapor or liquid in a section of a petroleum
O V I o .IO
I
I
I
I
I
I
I
1
.20 .30 .40 s o .eo . i o .eo .go WEIGHT FRACTION I N LIQUIO A T t D F .
I LOO
FIGURE 4. EMPIRICAL EQUILIBRIUM CURVES OF
KATZAND BROWN
Numbers on the curves refer t o tpe slope of the socalled true-boiling-poinq dis4111atlon curves, in ’ F. per per cent. Dotted line8 indicate ,app)ication of the curves to the graphlcal determlnatlon of the number of equilibrium plates required for the problem set up by Underwood (88) for reflux ratlo ( L / V )of 0.75
JULY, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
821
TABLE 111. TESTDATAFOR UNIT1
I
I
FINAL CONDENSER
, UNCONDENJED
C,"S
GAS SEPARATOR
2 LBS.PER 5 9 . IN. GAGE PRESSURE
BOTTOMS
4 2 5 -F.
DIAGRAM OF UNIT1 FIGURE 5. FLOW
UNDER
TEST
necessary to accomplish the desired separation, as against six computed by the more accurate methods.
Application to Petroleum Columns
Stream Crude Residuum Naphtha feed Bottoms Distillate Liquid on: Plate 1 Plate 2 Plate 3 Plate 5 Plate 9 Plate 13 Plate 16 Plate 19 Plate 21 Plate 23 Plate 25 Plate 26 Plate 28 Plate 30 Steam
Gravity A. P. I: 31.1 19.8 44.9 33.7 51.6 42.3 41.8 40.8 40.3 39.9 39.5 39.4 39.2 38.5 37.6 35.5 35.0 34.2 35.2
..
-Temp., F.Liquid Vapor 614 566 ... 572 ... 425 ... ... 330
...
363 397 414 423 436 440 441 447
359
4ii
Quantity/Hr. 209 bbl. 107 bbl. 102 bbl. 335 bbl. 68.4 bbl.
... ... ...
... ... ...
...
...
485 481
455 467 492 527
.. , ... ...
455
444
...
...
... ...
...
... ...
...
...
... 630 Ib.
Gage Pressure Lb./Sq. Ih.
.. .. .. .. ..
6.5
.. .. ..
.. 18:o
.. .. ..
L/V for use in this analysis was obtained by averaging the L/V ratios found for plates 2, 3, and 4 by the plate-to-plate calculations. Using this average value of 0.568 for the slope, the operating line was laid off, passing through the point (zl, yz) for the arbitrarily selected cut temperature, and the number of equilibrium plates required was stepped off as previously described. The two operating lines in Figure 9 represent the two cut temperatures of 425' and 390" F. Similar oDerating lines were laid off for each cut temperature shown in f a b l e Vrand the required number of equili'brium plates was stepped off to obtain the same separation as in the case of the four equilibrium plates of the plate-to-plate calculation. The
The practical value of any method can be determined only by successful application to commercial operations. Complete test data were obtained on a commercial column, designated as unit 1, operating on a naphtha fraction of a California &de. Figure 5 gives a diagrammatic flow sheet of this unit under test;. This fractionatTABLEIV. COMPUTATION OF VAPOR-LIQUID EQUILIBRIUM ing column is 8 feet 7 inches in diameter and conON PLATE 5 OF UNIT1 tains thirty plates spaced 12 inches apart. Vapors Mole Fraction Vapor -Mole FractionAv. Atm. Pressure ( 2 ) in Vapor in Liquid were supplied from an evaporator in which the Ax 13. P. at 425O F. K*Ax At/ Y crude was separated into 51 per cent residuum and .:;".' F. Mm. Hg 49 per cent vapor feed which entered the column 160 0 0 0.02 202 10,550 0.1690 0.1663 between plates 25 and 26, and was fractionated 228 o.02 0.166 into an overhead product and bottoms. Reflux for 0.02 250 6,200 0.09R4 0.0969 0.263 theseparation was furnished by passing the cold 265 0.04 0.02 282 4,290 0.0680 0.0670 293 0.06 0.330 crude through a partial condenser located in the 0.02 305 3,255 0.0516 0.0509 vapor space above plate 1. 317 0.08 0.381 0.04 335 2,273 0.0721 0.0710 The operating test data are presented in Figures 353 0.12 0.452 0.04 365 1,600 0.0508 0.0500 6 and 7, and Table 111. The molecular weights 374 o.16 0.502 were determined from published data (7, 18), as 0.06 383 1,265 0.0602 0.0593 390 0.22 0.661 were the specific, sensible, and latent heats (8, 14, 0.06 395 1,100 0.0524 0.0515 399 0.28 0.613 30,Sl). 0.06 402 992 0.0473 0.0465 The usual equations ($9) employed in making 406 0.34 0.669 0.06 409 930 0.0443 0.0435 the Hausbrand type ( l a ) of plate-to-plate com414 0.40 0.713 0.06 422 775 0.0369 0.0363 putation were applied to the experimentally deter424 0.46 0.749 mined composition of the liquid overflowing from 0.06 425 760 0.0362 0.0366 0.785 plate 1 to compute the composition and quantity 426 0.52 0.06 429 730 0.0348 0.0342 430 0.58 0.819 of the vapor rising from plate 2 rather than at0.06 433 695 0.0330 0.0324 tempting to use the undetermined composition of 436 0.64 0.851 0.06 439 648 0.0308 0.0303 the stream from the reflux condenser as a starting 441 0.70 0.882 0.06 442 605 0.0288 0.0283 point. The composition and temperature of the 445 o,76 0.910 liquid on equilibrium plate 2 was next computed 0.06 447 575 0.0273 0.0268 0.927 by the application of a corrected Raoult's law (1) 449 o.82 0.04 449 655 0.0176 0.0173 450 0.86 0.944 to the composition of the vapor rising from plate 550 0.0173 0.0170 0.04 450 2, in the manner shown in Table IV (IS). This 450 0.90 0.961 0.04 451 545 0.0171 0.0168 procedure was then repeated for equilibrium plates 452 o.94 0.978 0.04 456 516 0.0162 0.0159 3, 4, and 5. The results of these calculations are 0.994 465 o.98 given as method 1 in Table V and in Figure 8. 0.02 474 400 0.0063 0.0062 1.000 The graphical method was then applied to 492 l.O0 the same problem, using identical vapor-liquid Total 1.0184 1.0000 equilibrium data for equilibrium plates 2 and * K = 0.88 p / ~ :P = 1110 mm. H g . 5, as illustrated in Figure 9. The value of
.
VOL. 28, NO. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
828
TABLEV. EQUILIBRIUM PLATESAND PLATEEFFICIENCY IN UPPERSECTION OF UNIT 1 Method 1 = plate-to-plate calculation for 4 equilibrium plates (Raoult's law correction factor = 0.88). Average reflux ratio ( L / V ) = 0.568 for following methods: Method 2 = graphical calculation using same terminal plates as found b y method 1 (Raoult's law correction factor = 0.88). Method 2A = graphical calculation from aotual plate 2 through actual plate 5 Raoult's law correotion faotor = 0.88). graphical calculation from actual plate 2 through actual plate 5 !Raoult's law unmodified). Method 2B Method 3 = graphical calculation from actual plate 2 through actual plate 5, using empirical curves of Figure 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 No. of Plates &&brium to Equal XI Of with cut Mole Fraction of Arbitrary Component Method Actual Actual Temo. Method XI YZ xz wa xa y4 X4 US 26 18 Xd 17 1 2s 21
-
F. 445
18
Eq,uilibNq.. Plate rium E5Pletea ciency
%
0
1
0.9895 0.9926 0.9655 0.9791 0.9191 0.9023 0.7369 0.8478 0.6318 0.7600 2 0.9895 0.9926 0.9655 0.9790 0.9185 0.9520 0.8340 0.9040 0.7310 0:8i60 0:62iO 4:97 2A 0.9926 . . . . 0.9810 0.9566 0.9200 .... 0.8790 . . . . .... . 0.7600 2B 0.9926 0.9815 0.9600 0.9275 .... 0.8880 . . . . .... 0.7600 1 0.9385 0.9629 0.8623 0.9199 0.7610 0.8622 0.6535 0.7988 0.5429 . . . . . . . . . . . . 0.6950 2 0.9385 0.9829 0.8623 0.9190 0.7515 0.8560 0.6370 0.7910 0.5310 . . . . . . . . .... 3:kS .... 2A 0.9629 0.9195 0.8640 0.8075 . . . . . . . . . . . . . . . . 0.6950 2B 0.9629 0.9200 0.8650 0.8100 . . . . . . . . . . . . . . . . 0.6950 3 .... 0,9629 0,9120 .... 0.8380 . . . . . . . . . . . . . . . . . . . . .... 0.6950 1 0.9125 0.9416 0.7975 0.8768 0.6658 0.7994 0.5372 0.7253 0.4241 . . . . .... 0.4900 0.9125 0.9416 0.7975 0.8765 0.6645 0,8010 0.5385 0.7295 0.4280 0.6670 2 . . . . 4:i7 0.8025 2-4 0.9416 .... 0.8750 0.7340 . . . . . . . . .... .... . 0.4900 0.8050 2B 0.8755 0.9416 0.7375 . . . . . . . . . . . . .... . 0.4900 0.7710 3 ..,. 0.9416 .... 0.8640 .... .... .. 0.4900 1 .... .... 0.9057 0.9194 0.7408 0.8264 0.5671 0.7247 0.4178 0.6385 0.3042 . . . . 0.4000 0.9057 0.9194 0.7408 0.8270 0.5755 0.7325 0.4245 0.6460 0.3150 0.5670 . . . . 2 . . . . 4.09 0.7300 2A 0.9194 0,8255 0.6480 . . . . . . . . . . . . .... 0.4000 0.7350 2B 0.9194 . . . . 0.8270 0.6510 . . . . . . . . . . . . .... 0.4000 1 .... .... 0.8953 0.9075 0.7153 0.8059 0.5317 0.6986 0.3819 0.6119 0.2823 . . . . 0.3380 0.8953 0.9075 0.7153 0.8065 0.5375 0.7045 0.3835 0.6175 0.2815 0.5600 . . . . 2 . . . . .4:io 0.7060 2A 0.9075 .... 0.8070 0.6205 . . . . . . . . .... .... 0.3380 0.7080 .... 0.6245 . . . . . . . . . . . . 2B 0.9075 . . . . 0.8070 .... 0.3380 .... 3 0.9075 . . . . 0.7850 . . . . 0.6700 .... 0.3380 1 0.8151 0.8540 0.6157 0.7416 0.4399 0.6378 0.3091 0.5620 0.2208 . . . . .... .... 0.2400 0.8151 0.8540 0.6157 0.7415 0.4305 0.6370 0.2995 0.5620 0.2208 . . . . 2 .... 4:60 0.7375 0.6350 2A 0.8540 0.5600 . . . . . . . . .... 0:24bO 0.6390 2B . . . . 0.8540 . . . . 0.7415 0.5640 . . . . . . . . .... 0.2400 1 0.6615 0.7639 0.4578 0,6490 0,3159 0.5631 0.2250 0.5101 0.1700 . . . . . . . . .... 0.2180 .... 2 0.6615 0.7639 0.4578 0.6480 0,3070 0.5620 0.2220 0.5125 0.1715 0.4860 . . . . 4:i9 2A 0.7639 0.6490 0.5640 .... 0.5130 . . . . . . . . . . . . .... 0,2180 2B 0.7639 0.6500 0.5660 .... 0.5135 . . . . . . . . . . . . .... . . 0.2180 3 0.7639 . . . . 0.6230 0.5550 0.5400 . . . . . . . . . . . . . . . . 0.2180 1 0.5512 0.6728 0.3312 0,5478 0,2074 0.4728 0.1423 0.4343 0.1090 . . . . . . . . .... 0.1320 2 0.5512 0.6728 0.3312 0.5470 0,2050 0.4755 0.1435 0.4410 0.1140.0.4250 . . . . . . . . 4:64 2A 0.6728 . . . . 0.5485 0.4750 0.4425 . . . . . . . . . . . . , . , . 0.1320 .... 2B ,0.6728 .... 0.5520 . . . . 0.4785 . . . . 0.4400 . . . . . . . . . . . . . . 0.1320 Operating line intersected equilibrium curve before reaching necessary X L 3 1 0.3628 0.5420 0.2010 0.4507 0.1306 0.4048 0.0973 0.3845 0.0802 . . . . 0.0930 2 0.3628 0.5420 0.2010 0.4515 0.1300 0.4115 0.1030 0.3965 0.0895 0.3880 0:0825 O:i840 5: L9 2A 0.5420 . . . . 0,4500 0,4070 0.3920 . . . . . . . . . . . . . . . . O.'d9iO 2B 0.5420 . . . . 0.4510 ..... 0,4085 0.3905 . . . . . . . . . . . . . . . . 0.0930 Operating line intersected equilibrium curve before reaching necessary X6 3 1 0.1972 0.3909 0.0962 0,3339 0.0864 0,3115 0.0533 0.3030 0.0465 . . . . -0.0650 2 0.1972 0.3909 0.0962 0.3350 0.0875 0.3180 0.0575 0.3130 0.0520 0.3090 0:0485 0:iOiO 6:60 2A 0,3909 .... 0.3335 0,3155 0.3120 . . . . . . . . . . . . . . . . 0.0650 2B . . . . 0,3909 . . . . 0.3345 . . . . 0,3175 . . . . 0.3120 . . . . . . . . . . . . . . . . 0.0850
.... ....
440
425
415
405
....
390
300
::::
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.... ....
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.... ....
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340
.... ....
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....
a60
.... ....
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394
19
..
.... ....
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....
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....
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....
0.8996
3.0s
76
0.8995 0.9025 0.8690
4:SO 4.63 2.88
iii
0.8690 0.8720 0,8975 0.7620
2193 2.87 2.20 3.60
73
72 55 88
0.7620 0.7650 0.7850 0.7070
3:fi9 3.59 2.85 3.21
90 90 71 80
0:iOiO 0.7095 0.6645
3:iS 3.18 3.39
82 80 85
0.'6645 0.6655 0.6780 0.5835
3:49 3.61 2.94 3.72
87 88 74 93
0.5835 0.6875 0.5620
3:69 3.69 3.02
92 92 75
O:i6iO 0.5680 0.5530 0.4625
3104 2.98 3.12 3.27
76 76 78 82
O:i6i5 0.4800
3:iS 2.98
Sb
0.4010
3.19
80
0.4010 0.4185
3:iO 2.77
05 69
0.3410
1.88
47
o:iiio
I:&
47 40
....
....
....
....
....
0.3520
116
72
..
..
.. ..
.
1.59
I
..
76
*.
..
-___
compositions of the individual streams so computed are intemperatures with fractions less than 0.08 or 0.10 in the dicated under method 2 of Table V. The number of plates liquid on the lower terminal plate should not be used for redetermined by this method, necessary to give the same fracliable results. The average of the results of this graphical tionation as indicated by the four equilibrium plates of the procedure (method 2, Table V), omitting the obviously ind a t e - t o d a t e analvsis are indicated in Table V, column 15. correct values of the 445", 340°, and 300" F. cuts for these A comparison of the composition of reasons, indicates 4.12 plates required each stream as obtained by these two to accomplish the same fractionation procedures, methods 1 and 2 , indias obtained by 4 plates as computed cates good agreement in all but a few by the p l a t e - t o - p l a t e procedure (method 1, Table V). cases a t the extreme corners of the equilibrium curves. This difficulty Another comparison of equilibrium encountered in the upper corner is plates was made in the lower section of the same column. In this case due in part to the high sensitivity to small changes in the vapor composithe plate-to-plate computations were tion, and in part to the difficulty in begun with the liquid leaving plate making sufficiently accurate geomet19 (Figure 7) and continued for three rical construction in the small diequilibrium plates. The procedure mensions of the corner. Similar for calculating t h e v a p o r-1 i q u id errors are also introduced in the lower equilibria was somewhat modified corner. from that followed in the upper section of the column. I n this inA study of Table V indicates that cut temperatures with fractions of stance the equilibrium plate tempera27 2 5 23 21 I O I7 15 13 I1 9 7 5 3 I more than 0.97 or 0.98 in the material ture was approximated and Raoult's PLATE NUMBER rising from the top terminal plate law was applied, provisions being FIGURE6. OPERATINGCONDITIONS FOR should not be used. Similarly, cut made for arbitrarily introducing on USIT 1 UNDER TEST
INDUSTRIAL AND ENGINEERING CHEMISTRY
JULY, 1936
700
829
1
I
650
400
600
I
I
A"
550 500
'.L I
4 50
300
Y
u ~
'
400
+
350
W
L
n.
Y
I
Y
* 203
300
a
5 250
w 200 I50
100
100 50
500
0 0
IO
20
40 .LO SO .70 MOL FRACTION DISTILLED
.30
.80
.SO
1.00
FIGURE7. TRUE-BOILING-POINT DISTILLATION ANALYSES FOR UNIT1 Compoaitions.for overhead distillate and liquid leaving plates 1, 5, 19, and 25
each plate a proportional part of the heavier component present in the liquid from actual plate 25, but not appearing in the analysis of the liquid on plate 19. The results of the computation ape given as method 1 in Table VI and in Figure 10. The graphical method was applied to the identical equilibrium data ae were used in these plate-to-plate computations for the lower section of the column, with the results given as method 2 in Table VI. The cut temperature of 555" F. gave excellent agreement with the plate-to-plate calculations, although representing more than 0,98 of the vapor rising from the upper terminal plate. The cut temperature of 400' F. represents less than 0.10 of the liquid on the lower terminal plate, and, for the reasons stated, is not expected to give reliable results. Excluding the cut temperature of 400" F., the graphical method indicates an average of 2.70 equilibrium plates for the same fractionation as calculated for 3 equilibrium plates by the plate-to-plate method. The graphical calculations presented for the determination of the number of equilibrium plates required to effect a given
400
LL
,300 w
a 3 Q Y
a
xW
I- 200
IO0
0
20
.30
.40 S O .BO .70 MOL FRACTION DISTILLE"
.SO
J O
1.00
FIGURE8. DISTILLATION CURVESFOR VAPORSAND LIQUIDS IN UPPERSECTION OF UNIT1 AS CALCULATED BY PLATE-TO-PLATE METHOD (Abovs) Computed vapors rising from equilibrium p l a h 2, 3, 4, and 5 (Below) Computed liquids leaving equilibrium plates 2,3, 4, and 6
* TABLEVI.
.IO
COMPARISON OF EQUILIBRIUM PLATESIN LOWER SECTION OF UNIT1
Method 1 = Hausbrand's plate-to-plate calculation for 3 equilibrium plates. Method 2 = graphioal calaulation for aame terminal plates a8 used in method 1 (average L / V E 0.515). c Mole Fraction of Arbitrary Component cut Temp. Method zi 2/2 21 va XI %I4 24 Plates ' F. 3.00 0.9962 0,9925 0.9466 0.9725 0.8482 0.9231 0.6315 555 1 2.95 2 0.9962 0.9925 0.9466 0.9715 0.8500 0.9225 0.6270 3.00 488 1 0.9390 0.9677 0.8570 0,9264 0.7116 0.8539 0.4639 2.85 2 0.9390 0.9677 0.8570 0.9260 0.7000 0.8445 0.4495 3.00 1 0.8480 0.9199 0.7462 0.8694 0.6014 0.7981 0.3799 475 2 2.75 0.8480 0.9199 0.7462 0.8670 0.5625 0.7725 0.3460 3.00 460 1 0.6585 0.8202 0.5588 0.7730 0.4494 0.7211 0.2832 2.60 2 0.6585 0.8202 0.5588 0.7685 0.4545 0.6895 0.2460 3.00 452 1 0.4986 0.7352 0,4180 0.6996 0.3144 0.6518 0.2067 2.70 2 0.4986 0.7352 0.4180 0.6945 0.3030 0.6350 0.1900 3.00 439 1 0,3002 0,6295 0.2601 0.6171 0.2112 0.5982 0.1531 2.35 2 0,3002 0.8295 0.2601 0.6085 0.2030 0.5785 0.1365 3.00 0,1694 0.5236 0.1446 0.5194 0.1207 0.5136 0.0921 400 1 2 0,1694 0,5235 0.1446 0.5100 0.1130 0,4945 0.0820 1.65 Average, method 1 (excluding 400" F. cut) 3.00 Average, method 2 (excluding 400' F.cut) 2.70
. 9~:::-
separation agree within about =t10 per cent with the plate-to-plate computations. The equilibrium curves for the material on the top and bottom plates Of a short section Of any '01umn may be used as the limits for the equilibria on intermediate plates, and these equilibria on intermediate plates may be estimated in the manner described. However. there is a limitation in selecting the cut temperatures to be used, because of the limitations of accuracy with which drawinge and analyses can be made.
Plate Efficiency The matter of plate efficiency has been investigated from two distinctly different approaches, the average individual plate efficiency (WO), and the over-all plate efficiency. The former is derived from a consideration of the individual plate efficiency of each plate in a column. The latter is the quotient of the total number of
INDUSTRIAL AND ENGINEERING CHEMISTRY
830
TABLEVII. SUMMARY OF PLATE EFFICIENCIES AT UPPER SECTION OF UNITl a Av. No. Av. Equilib- Plate rium EffiCut Temp. Method Plates ciency Included in Av. % F. 1. Plate-to-plate calcn. for plates 2 through 5 (Raoult’a 3.28 82 440,425,415,405, law correction factor = 0.88) 394,390,360 2A. Graphical c a l m for plates 2 through 5 (Raoult’s 3.35 84 440,425,415,405, law Correction factor = 0.88) 394,390,360 3.26 82 440,425,415,405, 2B. Graphical ca!cn. for plates 2 through 5 (Raoult’s law unmodified) 394,390,360 3. Graphical calcn. for plates 2 through 5,using em2.78 70 440,425,405.390 pirical curves of Fig. 1 a
Average reflux ratio ( L / V ) = 0.568.
TABLEVIII. PLATEEFFICIENCY IN BOTTOM OF UNIT 15 Method 1 = graphical calculation for plates 19 through 25 (Raoult’s law correction factor = 0.88). Method 2 = graphical calculation for plates 19 through 25, using empirical curves of Figure 4. --Mole Fraction of Arbitrary Component-2/26, in eauilibrium No. with Equilib- Plate cut Actual actual rium EffiTemp. Method 11s 2/20 2/21 ll22 526 $25 Plates ciency F. % 520, 1 0.9800 0.9820 0.9490 0.8760 0.6650 0.9400 2.13 36 2 0.9800 0.9820 0.9560 0.9000 0.6650 0.9280 2.49 42 2.40 40 490 1 0.9350 0.9510 0.9080 0.8190 0.5070 0.8720 2 0.9350 0.9510 0.8900 0.7820 0.5070 0.8650 2.23 37 476 1 0.8740 0.9000 0,8435 0.7605 0.4250 0.8280 2.19 37 2 0.8740 0.9000 0.7970 0.6700 0.4250 0.8220 1.76 29 464 1 0.7300 0.7800 0.7090 0.5960 0.3210 0.7620 1.25 21 2 0.7300 0.7800 0,6350 0.5325 0.3210 0.7500 1.21 20 1 0.5980 0.6850 . , . , . ... 0,2590 0.7180
