March, 1935
INDUSTRIAL AND ENGINEERING CHEMISTRY 28 T = 320 f 2 413.5 - 320) 8.6 = 320 34 = 354’ K.
+
which checks closely enough, and the total number of theoretical plates in addition to the still is 8.6 which compares well with the 8.5 obtained by Lewis and Cope and by Lewis and Matheson. The application of E:quation 7A to C4- Cbnow will give the concentration of zspif it is desired; likewise all the other undetermined terminal concentrations can be easily obtained in a similar manner. The main advantages of the method are (1) i t is rapid and (2) it allows the concentrations and number of plates to be estimated directly
265
C = component = actual number of plates in column exclusive of the still a = relative volatility P = total pressure D = vaporpressure ,9 is defined by Equations 5A and 5B
t
Suhscripts: n = section above feed rn = section below feed f = feed plate p = product w = bottoms or still t = top plnte T = total pressure 1 , 2 , 3 , etc., = components; that is, CI signifiesmethane LITERATURE C I T E D
Brown and Souders, Trans. -4m.Inst. C h m . Engrs., 30, 488 NOMENCLATURE
x = mole fraction in liquid y = mole fraction in vapor y * = equilibrium mole fraction in vapor o0‘ == moles of overflow moles of overflow below feed plate P = moles of distillate F = moles of feed vV’ == moles of vapor moles of vapor belox feed plate W = moles of bottoms f = fugacity K = equilibrium constant = (y*/s)
(19341.
Brown, Souders, and Heder, Ibid. 30, 457 (19343. Brown, Souders, and Nylantl, ISD. ENQ.CHEJI.,24, 522 (1932). Carey, Griswold, M c l d a m s , and Lewis, Trans. Am. Inst.Chem. Engrs., 30,504 (1034). Fenske, I N D . ENG.CHEhf., 24, 482 (1932). Lewis, Trans. A m . I n s t . .l.li?zing M e t . Engru., 107, 11 jlH84!. Lewis and Cope, IND. ESG.C H E X . ,2 4 , 4 9 8 (1932). Lewis and Kay, Oil Gas J . , 32, No. 4 5 , 4 0 , 114 (1934). Lewis and Matheson, IND. EKQ.C H E Y . 24, , 494 (1932). McCabe and Thiele, I b i d . , 17, 605 (1925). Underwood, Trans I n s f . C’hem. Engrs. (London), 10, 112 (19:+2). RECEIVED December 20, 1934
Entrainment in Plate Columns T. K. SHERWOOD AND F. J. JENNY. Massachusetts Institute of Technology, Cambridge, Mass.
I
.
Chillas and Weir ( 3 ) report N THE design of plate colNew data are presented o n entrainment in a data on entrainment of water umns for absorption or disbubble-cap column, using air and water. The by air in a large column with tillation, t h e height or results show clearly the effect of gas velocity, plates 41 cm. apart. Holbrook number of plates is determined plate spacing, and liquid level. An effect of and Baker (4)report data on Iiy the separation req,uired, the entrainment of h o t w a t e r b y “slot celocity” as well as superficial velocity is operating conditions, and the exsteam in a two-cap laboratory p e c t e d p l a t e efficiency. The erident. * column. A s h r a f , C u b b a g e , cross section of the column may An analysis of the effect of entrainment on a n d H u n t i n g t o n (2) r e p o r t in some cases be fixed by the recolumn performance is presented, including data on the entrainment of hyquirement of numerous overflow treatments of the eSfect of enirainment on both d r o c a r b o n oils by air and by pipes to take care of a Large reflux natural gas in three laboratory or liquid rate, but more frefractionation eficiency and Ihe appearance of and semi-plant-scale column& quently the cross section must be color in the distillate. Sample calculations show and one commercial absorber. made only large enough so that the effect oj’ entrainment of less than 0.1 mole t h e a l l o w a b l e v a p o r or gas Souders and Brown (6) express liquid per mole mpor to be negligible in most the allowable vapor velocity as velocity is not exceeded. From ordinary cases. the point of view of cost, cross W C [di(di d2)1”’ (1) section and height are of roughly the same importance, and itwould seem evident that intorma- where W = allownble mass velocity, as weight of vapor flowing per unit time per unit of total cross section tion on “allowable” vapor velocities is of just as much practical d? = vapor density importance as data on plate efficiencies and methods of caldl = liquid tlengity culating the required number of plates. C = a constant dependent on plate spacing, surface The allowable vapor velocity may be determined by variouc tension of liquid on plate, etc. factors; the two of most obvious importance are (a) the excessive pressure drop across each plate a t high vapor veloci- A plot is given of C vs. plate spacing, and the effect of liquid ties, and the danger of “priming,” and (b) the effect of en- surface tension on the location of this curve is indicated. The trainment of liquid from one plate to the next 011 the separa- values of C plotted were obtained from performance data on tion accomplished by each plate, or on the appearance of non- a number of full-scale fractionating columns operating at volatile color in the distillate. Under the first heading rela- “approximately the maximum vapor load compatible with tively few published data on pressure drop in plate columns satisfactory product.” S o explanation is given as to what are available. Under the second heading, several inveetiga- happened in these columns when these vapor rates were extions of entrainment have been published recently, ceeded.
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266
INDUSTRIAL AND ENGINEERING CHEMISTRY
Apparently only Underwood (7) and Souders and Brown exhibited curiosity as t o the quantitative effect of entrainment on the performance of a fractionating column. Underwood's treatment is inadequate; Souders and Brown derive a relation between plate efficiency and the amount of entrainment, but a factor, f (the ratio of the concentration of the dry vapor leaving a given plate t o the equilibrium concentration corresponding to the liquid on the same plate), is involved which is itself a function of plate efficiency, entrainment, liquid composition, etc. Exp e r i m e n t a l data are necessary, but quantitative data on the amount of liquid e n t r a i n e d are of little value UPPER PLATE w i t h o u t a sound m e t h o d of calcuLOWER lating the effect of PLATE a specified amount of entrainment on the performance of MANOMETEL a g i v e n column, CONNECTIONS' with respect t o the f r a c t i o n a t i o n of v o l a t i l e components and with respect to separation of a n o n v o l a t i l e impurity. The 1 U present paper preFIGURE 1. GENERALLAYOUT OF APs e n t s ( a ) t h e rePARATUS sults of an experimental study of the effect of various factors on entrainment of water by air in a bubble-cap column and (b) a n analysis of the relation between entrainment and column performance, both for fractionation and for separation of nonvolatile impurities.
EXPERIMENTAL STUDY The experimental ap aratus consisted of a 46-cm., two-plate, bubble-cap column wit{ drainage connections to each plate, but no overflow pipes. Air was supplied beneath the lower plate, the air rate being obtained by a 7.64-cm. orifice in the 10.0-cm. supply line. The entrainment from lower to upper plate was measured by a technic which has been employed by several investigators-namely, by titrating the dissolved salt appearing in the upper plate as a result of entrainment of the salt solution placed on the lower plate. The salt used was sodium hydroxide, and the solution was titrated with a standard acid solution. At the beginning of each run the lower plate was covered to the desired depth with a 0.15 to 0.25 N sodium hydroxide solution, and the upper plate was covered with water. The solution on both plates was titrated both before and after the run. I t was found that the concentration on the lower plate increased slightly; this change was especially noticeable on warm days when considerable evaporation would be expected. Before each run it was necessary to carry out a blank titration of the water on the to plate, since it was difficult to wash out all traces of caustic l e i after the previous test. Equal volumes of solution from both plates were used in the titrations against the same standard acid. The number of cubic centimeters of liquid entrained from the lower plate was calculated as the ratio of the net acid required for the solution from the upper plate t o the average titration of the solution from the lower plate, multiplied by the volume of solution on the upper plate at the end of the run. Measurement of the total solution on the upper plate before and after the test gave an independent measurement of the entrainment, but the checks obtained were poor because there was a loss due t o evaporation, and because the second calculation involved the subtraction of two relatively large numbers. The results reported are consequently based on the titration method. Loss of caustic by entrainment from the upper plate was believed to be small because the solution on this plate was relatively dilute and
Vol. 27, No. 3
because the distance from the upper plate to the top of the apparatus was sufficiently great to minimize entrainment. The general assembly is shown in Figure 1, and details of cap, slots, and plate are given in Figure 2 . The caps used were of the common simple-notch type having thirty-three slots The caps were supported 0.63 cm. above the plate by e:ft extending this distance below the rim of the caps. The upper plate formed the bottom of a vertical cylinder forming the inner shell. This cylinder was slightly smaller in diameter than the outer shell and could be moved vertically to vary the distance between upper and lower plates. The upper plate was fitted with seven caps, placed as shown in Figure 2. The lower plate was operated with all seven caps, as shown, in series A to H, with the central cap only (No. 4) in series K I,, M, N, and with four caps (1, 4, 5, 6) in series PA and PB. i n the runs of series K, L, M, I9 the column diameter was varied by placing a cylinder, open at the ends, in a vertical position between the plates and concentric with cap 4 which was the only one in operation. The liquid level on the plate was observed by a gage glass shown in Figure 1. The reading by this glass was checked periodically against measurements within the column. The liquid levels reported are those existin with air flowing, and were somewhat higher than with no air fowing. The static pressure drop across the lower plate was measured by a manometer attached as indicated by Figure 1. The tests were made during the months of June to September, and the air temperature was taken as constant a t 26' C. in the orifice calculation. No means of calibrating the orifice was at hand, so that the orifice coefficient was taken from the charts of Spitz glass ( 1 ) after placing the downstream pressure tap at the indicated vena contracta. The experimental data are given in Table I. The principal variables were the air rate, the liquid level on the plate, the plate spacing, and the cap arrangement on the plate. Entrainment was measured as each of these items was varied independently of the others. Air rate and plate spacing were varied over a rather wide range, and the liquid level over the tops of the slots was varied about threefold, but the study of the effect of the arrangement of the caps on the plates was somewhat limited. Figure 3 shows the data of series A t o H i n which t h e plate spacing was varied from 23 to 76 cm. (9 to 30 inches), using a liquid level of 4.5 cm. (1.9 cm. above the tops of the slots). Entrainm e n t is plotted as grams liquid per gram of a i r ( p o u n d s p e r pound) os. the superficial air flow as grams air per minute per sq. cm. of c o l u m n c r o s s section. The result is a family of curves, the e n t r a i n m e n t for the l a r g e s t plate spacing being only about one per cent of that for the smallest plate spacing. The indication is that each curve is S-shaped on the semi-logarithmic coordinates used; only t h e u p p e r portion of each curve is comparable in shape to the results of Holbrook and Baker who gave curves concave d o w n w a r d s FIGURE2. DETAILSOF BUBBLE when plotted in a simiCAP, SLOTS,AND ARRANGEMENT lar way. It is possible OF CAPSON PLATE
*
INDUSTRIAL AND ENGIKEERING
March, 1935
267
CHEMISTRY
TABLEI. EXPERIMENTAL DATA PRESBURE RUN
PRESSURE
DROI,
NO.
COLUMP OF LIQCID SPACINQ DIAM. Caps LEVEL PLlTE
ACROSS
AIR RATE
PLATE
ENTRAINMEKT
RUN
Super-
A3 A4 .4 5 A6 A7 A8 A9 A10 All BA1 BA2 B.43 BA4 BA5 BA6 B.47 BAS BAS BAlO BAll Bh12 BA13 B.414 BA15
Cm. 23 23 23 23 23 23 23 23 23 23 23 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5
Cm. 45.7 45.7 45.2 45.j 45.7 45.7 45.2 45.i 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 4~. 5 .. 7 45.7 45.7 45.2 45.) 45.1 45.l 45.7
BB1 BB2 BB3 BB4 BB5 BB6 BB7 BB8 BB9 BRlO BBll BB12 BB13 BB14 BB15 BBl6 BB17 BB18 c1 c2 c3 c4 c5 C6 c7 C8 c9 c10 c11 c12 C13 C14
30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 30.5 38 38 38 38 38 38 38 38 38 38 38 38 38 38
45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.i 45.7 45.7 45.7 45.7 45.2 45. t 45.7 45.z 45.r 45.7 45.2 45.t 45.7
D1 D2 D3 D4 D5 D6 D7 D8 D9 D 10 D11 El E2 E3 E4 E5 E6 E7 E8 E9 F1 F2 F3 F4
46 46 46 46 46 46 46 46 46 46 46 53 53 53 53 53 53 53 53 53 61 61 61 61
45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.7 45.1 45.,
.I 1 A2
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
; 2 i
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
Cm. 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5
3.8 3.8 3.8 3.8 3.8 3.8 3.2 3.2 3.2 3.2 3.2 4.5 4.5 5.1 5.1 5.1 5.1 4.5
G./min./ ficial G. liquid/ sq. cm. ft./sec. Cm./l%O g. air 2.03 0.00048 1.37 0.64 0.96 2.34 0,00049 2.06 1.24 2.3!3 0,00078 2.67 1.40 2.54 0,0016 3.01 2.76 0.0043 3.18 1.48 1.68 2.85 0,019 3.61 1.97 4.23 2.82 0.044 5.11 2.38 3.61 0.071 2.80 4.06 0,092 6.02 1.58 3.40 2.92 O.OL2 2.20 3.30 0.008 4.72 1.27 0.59 2.03 0,00028 1.87 0,00030 0.87 2.Od 2.96 0.00053 1.38 2.41 3.60 1.67 2.41 0.006 0.0013 3.25 1 . 5 0 2.411 2.58 1.20 2.82 0,00036 0.0135 4.06 1 . 8 9 2.8CI 4.76 2.22 2.92 0.0187 n . 030 5.51 2.56 3.5fi 6.62 0,042 3.08 4.5i 4.71 2.19 2.54 0.0175 n 049 6.88 3.2 4.07 5.16 2.4 3.17 0.020 6.12 2.85 3.81 0.032 5.42 0.0247 2.52 3.17 1.80 3.82 4.75 5.57 4.30 6.71 3.96 4.39 5.16 7.01 6.02 5.10 5.98 3.59 4.30 5.16 6.45 3.44
0.84 1.78 2.21 2.59 2.0 3.12 1.84 2.04 2.4 3.26 2.8 2.37 2.78 1.67 2.0 2.4 3.0 1.6
1.78 2.3!3 2.62 2.80 2.74 3.1 1.9 1.9 2.44 2.87 2.67 3.0 3.3 3.3 3.5 3.55 3.81 2.67
0,00016 0.0049 0.0141 0.0202 0,0093 0.028 0.0023 0.005 0,0097 0.018 0.014 0,0208 0.031 0.0051 0.0141 0,022 0,038 0,0034
F5 F6 F7 F8 G1 G2 G3 G4 G5 G6 G7 G8 H1 H2 H3 H4 H5 H6 K1 K2 K3 I
