April, 1946
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
their reaction with 30-50y0 sodium hydroxide solution. The remainder of the scales consisted of calcium carbonate and magnesium hydroxide. These laboratory data led to the actual treatments of the following nine heat exchange units with sodium hydroxide solutions in order to remove the scale high in ca!cium sulfate: one 1500-gallon locomotive boiler for a steel company, one 500-gdlon crane boiler for a steel company, one 6000-gallon vertical tube boiler for a tool company, three 6000-gallon Wickes -4-type boilers for a sugar refinery, two 6000-gallon boilers for a coal tar refinery, and one $0,000-gallon brine evaporator for a chemical company. $11 the units except the brine evaporator were first treated with 30-50% sodium hydroxide and then treated with approximately 5% hydrochloric acid to help dissolve any of the reaction products. All the treatments were 85-100% successful; that is, 85-100% of the scale in the boiler was removed. Considerable quantities of the scale disintegrated and fell t o the bottom of the units, however, and, although not completely reacted, was readily removed. TREATMENT OF BRINE EVAPORATOR
The 50,000-gallon brine evaporator was a cone-bottom evaporator (Figure 3) consisting of a steel shell and containing 4100 IO-foot copper tubes (2 inches i.d.) rolled into steel tube sheets (Figure 4). Its capacity was 7000 cubic feet or approximately 50,000 gallons. Analysis of four samples of scale showed 100% to inch thick. The amount of scale calcium sulfate, from was estimated to be 100,000 pounds. Turbining this evaporator had never been very satisfactory. The hard scale and the relatively soft copper tubes were not the best combination. The scale had a tendency t o divert the turbine tool off its course through the side of the tube. METHODOF TREATIXG. The evaporator was filled t o its operating level with 48-50% sodium hydroxide and kept a t 230" F.,(llOo C.) for a total of 5 days with constant circulation. The first stage of the treatment lasted 3 days. During this time the caustic concentration dropped from 49.6 to 47.6%. The sodium hydroxide was drained from the evaporator and pumpecl into settling tanks. The evaporator was then filled with water,
397
brough6 to a boil, and washed thoroughly. Inspection showed that thescale was approximately half gone (Figure 4). The evaporator was refilled with 46.0% sodium hydroxide and kept at 230' F. for another two days. During this stage the caustic concentration had dropped to 45.4%; it was then increased to 48.2% by evaporating under vacuum some of the water from the .solution and replenishing with 50% sodium hydroxide. The 48.2% caustic dropped t o 46.9% a t the end of the treatment. The second stage was stopped 6 hours before its scheduled 2clay run because of the following observations: A large increase occurred in the amount of sludge in the samples. The amperage .on the circulating pump increased from 170 to 270 amperes due to the heavier liquid being pumped. A temperature difference was noticed above and below the tubes. This difference was due to poor circulation. On inspection the evaporator was pronounced 90% clean (Figure 4). During the first stage the solids in the sodium hydroxide solution had increased from 0 t o 15.1% by weight. During the second stage they had increased from 6.9 to 20.9%, or 14.0%. The scale from the evaporator a t the end of first stage was 100% calcium sulfate; at the end of the second stage, it was made up of 85% calcium hydroxide, 10% calcium carbonate, and 5% sodium sulfate. CALCULATIONS. The amount of solids in the drain solutions was 98,500 pounds in the first stage and 92,000 in the second, or a total of 190,500 pounds of solids formed. Since calcium sulfate formed about twice its weight of insoluble reaction products, about 95,000 pounds of calcium sulfate were removed from this evaporator. Therefore it was found that the efficiency of the evaporator increabed 4045%, and the rate of steam condensation increased from 55,000-60,000 to 85,000 pounds of rondensate per hour. LITERATURE CITED
(1) Brock, James, U. S. Patent 89,121 (April 20, 1869). (2) Burgess, Hugh,Ibid., 168,222 (Sept. 28, 1875). (3) Hers, W., 2.anorg. Chem., 71, 206-8 (1911). (4) Riley, James, U. S. Patent 182,774 (Oct. 3, 1876). PRESENTED on the program of the Division of Industrial and Engineering CHEMICAL SOCIETY. Chemistry of the 1945 Meeting-in-Print, AMERICAN
Multicomponent Tray Calculations Based on Equilibrium Curve of Key Components EDWARD G . SCHEIBEL' Polytechnic I n s t i t u t e of Brooklyn, N . Y .
PREVIOUS paper (IO)presented an equation for calculating the minimum reflux ratio in multicomponent distillation. In the design of fractionating towers to effect a given separation, it IS then necessary t o carry out a set of tray calculations to determine the total trays and the feed tray location a t a reflux ratio greater than the minimum. The first rigorous method of multicomponent tray calculations involved a matching of the components a t the feed tray by a trial-and-error process. Jenny (7') proposed a method whereby this trial and error can be eliminated. The method consists of estimating a feed tray temperature and determining the liquid and vapor compositions a t this temperature. The calculations can then be made down the column until the bottom product 1
Present address, Hoffmann-La Roche, Ino., Nutley, N. J.
composition is matched and up the column until the overhead composition is obtained. Thjs method is more direct in that all the heavier components become negligible several trays above the feed and all the lighter components become negligible several trays below the feed. Thus, the triakand-error method of metching is eliminated. The uncertainty in the method lies in the choice of the feed tray temperature since, if the temperature is too high or too low, a larger number of trays will be required. At reflux ratios close to the minimum, a feed tray temperature must be estimated very accurately, but at reflux ratios generally used in practice, the effect of feed tray temperature on the number of trays is quite small, and little difficulty will be encountered if the temperature is estimated according to the empirical method described by Jenny (7).
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INDUSTRIAL AND ENGINEERING CHEMISTRY
A graphical method is presented for tray calculations on
Vol. 38, No. 4
to apply than previous methods i n that i t requires only the equilibrium curve for the key components, and the graphical tray calculations are made by the RlcCabe-Thiele method. The total trays by this method agree with the rigorous tray calculations with an accuracy of about 5 % . and the feed tray is located with an accuracy satinfactor! for all practical purposes.
multicomponent systems. The method is based on a pseudo reflux ratio which gives the same number of trays for the binary system of the key components as the actual multicomponent calculatious. This pseudo reflux ratio is calculated from a general correlation of the results of a large number of tray c.alrulations. This method is simpler
Smith (11) described a shorter but more approximate method for determining the number of trays required for a multicomponent distillation. The method is based on assuming average vaporization equilibrium constants for the fractionating and stripping sections of the column. These constants were chosen a t a calculated average temperahre; however, all the component’s do not have their average equilibrium constants at the same temperature, and, therefore, the method is not compIetc.Iy accurat’e. Another method lor making tray calculations, somewhat similar to the method of Jenny, was applied by Hummel (6) to the case of a separation in the presence of a comporicrit with a volatility intermediate between the key components. Recently another simplified method (8) was proposcd f o i , estimating the number of trays required a t any reflux ratio when a set of calculations are available a t another reflux ratio. Thv method is based on B tn-o-component equilibrium curve, rombining all components lighter than the light key with the light key and all components heavier than the heavy kry with tht, heavy key. To apply this method, :i sCt of tray culculntioiih must first be made. Several correlations (W, 6 ) have becn proposed for estimxtiny the total number of trays required a t given reflux ratios bawd on the minimum reflux rat,io and trays at total reflux. In the tours(' of the present n-ork, about one hundred sets of tray calculntions were studied and a general correlation similar to that of Gilliland ( 6 ) wis attempted. The same function of the torn1 tr:iys
was used; however, a somewhat better correlation was obtaiiii 11 when a slight correction was made for the composition and ~ 1 1 dition of the feed. The function of rrflux ratio that gavc this best results was:
+ n)
( R - Rm),/(R
The general correlations give only the total trays rcyuiitvl i l i the column and do not provide any clue as to the feed tray IO(:Ition. This is of equal importance because improper loeatioii OI this tray ~ ~ 1 essentially 11 neutralize the effect of somc of thc t i n \ and make the separatioii appear more difficult.
THE previous paper (10) introduced the concept of a i ) ~ ( ~ u t I ~ i minimum reflux as a basis for determining the minimum I Y + ~ U X ratio for a multicomponent distillation. It is possiblc t o r o i i sider n pseudo reflux ratio as that reflux ratio which gives,. 1 1 1 1 , same number of total trays on a binary distillation curve :IC (I(&termined by the tray calculations a t a given reflux ratio O J I t h e actual multiromponent system. It can be seen from the E’c.iiske equation ( 4 ) a t total reflux that t,he number of trays requircd in the muhicomponent separation is the same as in a hinar:. system )Then the overhead and bottom compositions are b a w l 011 the key components alone. The empirical correlation of 1he tray calculations indiw ti.that the relation betwecn thc pseudo reflux ratio and the actiwl roflux ratio is given by the followirig relation:
‘+ R-
?? 5‘
8
where I?’ R
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- R:,, = R’ ___
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pseudo reflux ratio actual reflux ratio RC,= pseudo minimum reflux ratio R, = actual minimum reflux ratio x, = intersection of operating lines a t pseudo minimum reflux = trays required in actual multiconi1)onent calculations =trays required at pseudo reflux ratio on binary system A:,,, = trays required at total reflux in multicomponent systcms = trays ri’quired at total rc.flux in hiiiur\system = =
A\’
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THEOR€T/CAL TRAYS R€QU/REP 7.5 FRACTiONAT/NG TRAYS 8.5 STR/PP/NG TRAYS 16.0 rorAL T . Ars
.429
.30 . 4 0 ‘ .jO .6b .7b .80 MOLE FRACTION OF LlGHT K€Y / N L/QU/D Figure 1
-
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.90
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When the operating lines, correspondirlg to the pseudo reflux ratio thus calculated, have been drawn on the binary equilibrium curve for the keys, the stripping and fractionating trays are accurately determined as well as the total trayx The agreement in some cases is within the accurary of the graphical construction. It has been found by accurate tray calculations that the optimum feed tray in any distillation is that which properly s t r a d d w
I N D U S T R 1 A L , A N D E N G I N E E R I N G C H E M I S T.R Y
April, 1946
399
optimum feed tray. The trays determined graphically above and below this feed tray were found to agree very well with those Relative Product Composition determined by the analytical method of tray calculations. case Feed Composition Volatilities Based on Keys No. X, X, Xc X D a d a B n C aD Overhead Bottoms Tables I and I1 give the comparison between the fractionating trays and stripping trays determined by actual tray calculations A 0.30 0.30 0.40 ,. 4 2 1 .. 0 . 9 8 0 0.010 B 0.72 0 . 1 2 0.16 4. 2 1 ,.‘ 0.985 0.010 and by the graphical method. The illustrative cases in Table I C .. 0.30 0.40 0:30 , . 2 1 0 . 5 0.990 0.017 are based on total liquid feed a t the feed tray temperature, with D .. 0 . 3 0 0 . 4 0 0 . 3 0 .. 2 1 0 . 5 0 . 9 8 5 0.070 E . , 00 .. 31 02 00 .. 14 60 00 .. 3702 .. the exception of case F which is total vapor feed at the feed Fa ,. 22 11 00 .. 55 00 .. 99 99 10 00 .. 00 15 74 G 0:30 0 . 2 0 0 . 2 0 0.30 4 2 1 0 . 5 0.975 0.025 tray temperature. I n Table I the feed composition was varied t o contain Up to 72% Of a third composition. Numel’ouS other Case F is based on vapor feed at the feed late temperature and the balance of the cases are based on liquid feed at &e feed plate temperature. cases with components of different relative volatilities were also checked with reliable results. The agreement between TABLE11. COMPARISON O F GRAPISICAL METHODWITH ACTUAL TRAY CALCULATIONS the total trays required is generally No. of Theoretical Trays within 5%, and the feed tray location Case Fractionating Stripping Total determined graphically will function as Calcd. Graph. Calcd. Graph. Calcd. Graph. NO. si Rm R&, R R’ well in the tower as that determined by 8.5 7.3 7.5 ‘ 8 . 9 16.2 16.0 A 0 , 5 0 0 1.127 1 . 8 8 3 . 0 0 4 . 4 0 the rigorous method of calculation. 10.7 1 1 . 0 ’ 19.5 8.8 9.4 20.4 B 0.726 0.500 1.25 0 . 7 4 1.68 C 0,429 2.51 2.28 4.00 3.66 10.1 10.4 9.3 8.3 19.4 18.7 Table 111shows the agreement between 10.2 6.4 6.2 D 0.429 2 . 4 8 2.25 3.50 3.19 10.2 16.6 16.4 E 0,429 4.05 2.28 5.85 3.37 9.9 11.0 6.8 6.7 16.7 17.7 the graphical method given in this paper F 11 46 .. 34 11 56 .. 73 with the results of tray calculations on 77 .. 23 86 .. 68 79 .. 20 79 .. 15 G 00 ..26215 0 40 .. 6901 3 41 ..3’ 74 771. 3. 78 8 61 ..8626 different systems reported in the literature (9). I n the calculations the feed tray was deOF GRAPHICAL SOLUTION WITH TRAY CALCULATIONS OF ROBINSON TABLE111. COMPARISON termined to, the nearest tray, AND GILLILAND (9) and no attempt was made to No. of Theoretical Trays establish the exact optimum Page Fractionating Stripping Total Problem No. (9) zi Rm RA R R’ Calcd. Graph. Calcd. Graph. Calcd. Graph. point for introduction of the feed. . There :s no doubt that Benzenetoluene, etc. 139 0 . 6 6 7 0 . 9 7 5 0 . 9 9 0 2 . 0 1.974 7 7.0 9 9.5 16 16.5 the feed tray location deterPhenol-cresol, 158 0.700 4 . 6 9 5.35 10.0 9.17 13 13.5 13 12.8 26 26.3 etc. 167 . . . . . , . . . 7 . 0 6.40 16 17.3 18 17.3 34 34.6 mined graphically will function Gasoline stabiliaer 175 0.695 0.886 0 , 8 2 2 2 . 0 2 . 2 0 3 3.3 8 8.7 11 12.0 equally well with that given in the actual tray calculations. The last case in Table I11 involved a split key, and in calculating the minimum reflux ratio the original assumption of the intersection of the operating lines. At total reflux the Robinson and Gilliland that 20Y0 of this key would pass overhead optimum feed tray liquid would be ane half tray below the feed composition and the vapor would be one half tray above the was employed as described in the previous article. This case also involved subcooled liquid feed, and the agreement between feed composition. The concept is based on 100% tray efficiency, and this value is frequently approached in petroleum fractionatthe calculated and graphically determined trays demonstrates the broad application of this method. ing towers. Only at small tray efficiencies does the optimum I n Table I11 the total trays and the feed tray location deterfeed tray liquid a t total reflux approach the feed composition. mined graphically agree with the actual tray calculations to Thus the optimum feed tray composition at total reflux, assum-, irig 100% tray efficiency, is calculated as follows: within a theoretical tray in almost all cases. The time required for application of the graphical method is only a small fraction XT of the time required t o carry out the actual tray calculations, -XI q - G 1 and the results are sufficiently reliable for all practical engineering purposes. .For cases where the differences in latent heats over the column are sufficient to produce appreciable curvature of the operating line, the same technique of locating the pseudo operating lines where q = concentration of light key based on keys for the McCabe-Thiele method may be applied to the Ponchon = XB/(.XB X c ) method with equally reliable results. xT = concentratlon of light key in optimum feed tray a t total reflux X B = concentration of light key in feed BIBLIOGRAPHY X C = concentration of heavy key in feed CYB = relative volatility of key components Badger, W. H., and McCabe, W. H., “Elements of Chernica Engineering”, New York, McGraw-Hill Book Co., 1931, Brown, G. G., and Martin, H. V., Trans. Am. Inat. Chem. The only feed tray possible a t minimum reflux occurs a t the Engrs., 35, 679 (1939). intersection of the operating lines; thus the optimum feed tray Colburn, A. P., Ibzd., 37,805 (1941). must vary between this point and the calculated point a t total reFenske, M. P., IND.FNQ.CHEM.,24,482 (1932). Gilliland, E. R., Ibid., 32, 1220 (1940). flux. It can be found by very accurate calculations on binary Hummel, H. H., Trans. Am. Inst. Chem. Engrs., 40,445 (1944). systems that the optimum feed tray variation is linear on the Jenny, F. J., Ibid., 35,635 (1939). conventional McCabe-Thiele diagram ( I ) . I n Figure 1, which Jenny, F. J., and Cicalese, M. J., ICND. ENQ.CHEM.,37, 956 represents the graphical tray calculations for case A in Table I, (1945). Robinson, C. S., and Gilliland, E. R., “Elements of Fractional the locus of the optimum feed tray is given by the heavy dashed Distillation”, New York, McGraw-Hill Book Co., 1939. line between xi and XT. The operating line? are determined Scheibel, E. G., and Montross, C. F., IND.ENG.CHEM.,38, 2 8 from the calculated pseudo reflux ratio, and the trays are stepped (1946). off by the conventional McCabe-Thiele method ( I ) starting a t the Smith, R. L., Trans. Am. Inst. Chem. Engrs., 37,333 (1941). OF ILLUSTRATXVE CASES TABLE I. DESCRIPTION
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