766
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
Vol. 39, No. 6
NOMENCLATURE
/
=
/.
= 7' = /'., = = P = (I =
lioiliug p i i i i i t t i t lo\ver boiliiig compoiiriit, . ('. tmiling point of higher boiling conipoiirnt, ' C:. ;ti)acilute boiling point of the mistiir~c~. ' I i i i d , nim. Hg i ~ l n t i v rw h t i l i t y
COMPARISON of RECTIFICATION and DESORPTION in PACKED COLUMNS Donald
W. Deed', P. W . Schutz',
and Thomas
C O L U M B I A UNIVERSITY, N E W Y O R K , N. Y.
HE unit opelutioii \I-hich coirsictc ~ i bi,iugi~ig i :I strearii t ~ liilf uid and a stream of gas countercurreiitlg into direct contact to allow spontaneous interphase transfer of their constituents :inti of enthalpy is called "rectification" if the in(-oiriing liquid i y .U}Iplied by condensing part of the gas leaving, or if the iiicoriiing ga? is produced by reboiling part of the liquid leaviiig. 111most c i t l i c ~ r circumstances the term '~at~sorptioii," in it> grneralizeti seiiw, iaccepted. The character of the effect- inilurrd anti t h e typec ( i t equipment found useful ai'e indepentieiit i i f the soui'ce- u i t lit. fluid stream>. So also, presumably, x h o i i l ~ tt)e the rehtiiriih :iinciiig the parameters u i performance i'iJrniula~,tlitx I)riipei'tie.> oi tlic streams, and t h e operating varialiles. Ho\vevc>r,e*tiniate+ F ~ . i i i i i published data o r rectification ( 2 , 4,16) uI'tlir height.. i i f iiidiyidual and ovrr-:iIl liquid-film trail-frr unit> liavc led to v:iItic~sermiiigly a t variance with the re-ulta fi.cini atjrorptioii trst-, liirt 11 az,to magnitude and manner of v:~riatioii \\-it11 tlir licluiii, rate,. Sii illogical a situation aeemed t o require iiivrstigatioii. To avoid poahihle rnisi~~ter~ii~rtatiori iJwau-1' (if i l [ i i , r s r t : > i i i t >
T
1
I'reaent addresb, > t ~ i i ~ d x nOI! I l l c ~ v t ~ l o p i i t c ~I 'io~t1i i p
. nereased.
,x
I
B. Drew
June 1947
INDUSTRIAL AND ENGINEERING CHEMISTRY
Rectification experiments with isopropanol-water mixtures and experiment: on the desorption of oxygen and of carbon dioxide from water into air were performed in a 6-inch column packed with 47 inches of half-inch ceramic Raschig rings. The desorption results lor liquid rates above 1000 lb./(hr.)(sq. lt.) checked closely those of Sherwood and Holloway. A t lower liquid rates, values OF (H.T.U.)L for desorption of carbon dioxide were found to be a function of the liquid distributor. Most of the desorption data at low liquid rates gave values of (H.T.U.)L somewhat above an extrapolation of Sherwood and Holloway's work, but a few runs, made with 2 feet of
767
packing and modified operation of the liquid distributor, gave results following their curve down to a l i q u i d rate of 300 lb,/(hr.) (sq. ft.). In the dilute isopropanol range, values of (H.T.U.)L were obtainable from the rectification data. When these values were converted to the system carbon dioxide-water (at 95' C.), the results were found to agree approximately with the values experimentally observed for that system. These experimentally observed values averaged about 0.6 foot over the range of liquid rates common to both the rectification and desorption sets of experiments-that is, 130 to 460 Ib./(hr.)(sq. ft.).
that' as little of the diffu,-ing matter as one please< completely t h r ~ ~ u git; h (b; for suc~lr a layer tLe ratio of the differenre in potential tietween a:->- usual iiieati across it to the t1iffei~t~nc.e potential in the xtreatn anti that a t the interface i h a function of such quailtities a> Reynolds numbers, physical property ratios, and velatire location i t i the apparatul. If, as in this paper, binary mixtures only are considered and mole iraction is chosen t o measure the potential, the general equation for the rate of rlow of component A from the main hod? of the gas to the interface i >
.d
where p, pi
lz -
e
=
niolc iracstion- of coniponent .I in main h o d - arid a t interfacp, rvspectively
=
ll'd
=
mass t,rati4csi, i.oi,firic.rit
(w.4
+
uClnL= logarithmic.
a
I(:B
nii'wil ot i z - y i atitl
(2
F,
II ss
For equimolar couiiter-diffusim r . 4 = - ~ P B ) the , condition approached in rectification, the equation become? /['.I
=
/.'&,(y - !/'
1
IHOT WATER
(21
This may be found hy taking tltt> limit o i Eyuation 1 as e approaches infinity. Another important s p e h l case, t h a t of z = 1, ior which tlir simplification is obvious. orcuri when one coniponent only is transferred. For all finite value- of z, Equation 2 approxiniate~Equation 1 Tvlien and y simultaneously hecmw Pufficiently ~ m d l . The rate of flow of c o i ~ p o n e ; ~i~from t the iiiterface into the main hrxiy of thp liciuid can PXpressed similarly :
T
AIR ORIFICE
5 =SAMPLING POINT TTTHERMOMETER V s VENT
T 1 :
S
Figure 1 .
Diagram of Apparatus
Vol. 39, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
768
For the general case Equation 1 i, used, and the le-ult
I-in. coupling
F o r the r w e integral is
iii
\\-liic.h ir
1
= -IC,.?,
Equation 2 i- u-rd. and t h e
The integi,ali have usually i ~ e e givc,n ~i iri tliih ~ I J I , I I I tiecau~wit lias tieen expected that t h e group F,n 'G 11 ~ v o u l dva1'y little over tlir lieiglit of tlie column and could hc $1-sunied constant a t the value of its average. Tlie reciprocal of tlii-. prijup linq the dimensions of length and is called the height of a ga+-filni ti,uisfer unit, H;,,. Either member of tlie equation ma>*be regarded a? exprwsiiig the iiuiiiber of gas-film transfer units. -Y.,,. Analogoucly, there arc' i i i use:
I
I
I
M
I
Figure
2.
Reflux
I
Distributor
1 +, = 1 I ,
- iil,
I;
I
14)
DATA FOR ABSORPTION
The equation holds for liquid rates from 400 to a- high as 32,000
June 1947
INDUSTRIAL AND ENGINEERING CHEMISTRY
FOR Htc T.IRI,E;I. EQYATIOSS
FOR
Source of Orer-all Data IS 1
. ~ J I \ ~ o s I . A - ~ ~ - . ~ T E RAT - A IRoo11 R T E M P E R . ~ T L - R E , OBTAISEUFROJI ISDIRECT I).IT.A o s .I\IM~SI.I ABSORPTIOS, BY SI-BTRICTIOS OF LIQL-ID FIIXRESIST.IY~E
Itnnge of L
Range of G 5 2 - 170
Recalculated by:
440
(14,
-
Liquid F i l m D a t a Range Source of L of dntn 400-3L'.000 115)
Packing Sire & Type 3-in tile [I
f 3 1,
100--1000
500
( 31
800-31',000
if51
(1%;
100-1100
1800-1s.000
(12,
3000-20,000
(211'
o-in ~ I I I E ~
{ l - i n r!rix~ 1,lL ?-in ring4 , 1-in r i n g j , l - i n , saddles
yq+
CONES
6' B R A Y
PIPE
EDGE
Ld
vAma Figure 3 .
SAMPLER
POSITION Of
COLUMN
Liquid and Vapor Samplers
llolstnd arid rc~-~vorkers ( 1 11, de-orbing oxygen from water, confirmed the result. of Shern-ood and Hollon-ny for 1-inch rings arid 3-inch cingl~-qiiraltile for liquid rates from 3000 t o 32,000 l b . / ( l i r . ) ( q . it.). Their values of H!r, for 1-inch saddles n-ere 20% higher thaii tlio-e found by Sherwood and H o l l o ~ a y . They also extended the data to include various grid packings and tile. The oxygen desorption runs carried out in the present work agreed with tlie P l i e r ~ ~ o oaiid d Hollon-ay curve a t 25' C. xithin 57, (Figure 41. Tlie temperature coefficient of those authors was rrproduced nithiii tlie precision of the data. Shervood and Hollon-ay estimated t h e reliability of their own data a t *loyo. Their technique v a s tluplicated as nearly as possible. The carbon dioside dewrption runs of t h e present work \\-ere made primarily in an endeavor t o extend the data to liquid rates belon- those of Sliern-ood ancl Holloii-a!-. However, a t liquor rate< above 1000 Ib. /(hr.)(sq. ft.! e-.entia1 agreement was found. T ~ I R E C T D.iT.4 FOR H , G . Direct methods of finding Hi(, ini,lude vaporization of pure liquids, a h o r p t i o n of ammonia in :ieid, and abwrptioii of wlfur dioxide iii caustic. Slier~rocid aiid Hollon.ay reviewed such i\-ork ancl shoired t h a t a fair agreement exists, although some uncertainties remain t o tie resolred. Their Figure 3 (14, page 29) s h o w data for three packings, including some obtained by an indirect method ( w i n g values of oi-er-all coefficients for ammonia in water). T h e d a t a of.Hollot\-ay for vaporization of water into air showed t h a t Htc varied ~ i t Go.3'i'LI h '3. I n one oi Holl6i~-ay'sseries of texts with l'/Z-inch rings, G x-aried from 20 t o 1830 a t an L of 390 t o 410; in another, L varied from lG8 t o G l O O ivhen G n-as 230. Assuming a variation of H ~ G n-ith L - * / 3 ,a line iva? drawn for 1I '.-inch rings and 3-inch spiral file; its equation,
H~~ =
SAMPLERS IN
1.1~0.3!~1/3=0.~j(~/~)1'3
(16)
Equation for H ! G 0 . 1 5 GO.' 0 . 4 7 Gu.'D) 0 . 2 8 GO.?? I 0 . 2 3 GJ.28'
E 5 t d . Liquid F i l m Reii-tiince,
U o l e E'ractiun I s v p r u y a r d Liquid \-apor beloa belou packine packing Reflu,
:j5ii 37 " :38" :3 9 40"
0.404 0.108 0.16i 0.0108 0.212
0.486 0.181 0.244 0,0520 0.274
0.682 0,680 0.681 0.340 0 67.5
1 0 k%h 1
49.5
41a 41h 42 4:1 44'
0.0077
0.0064 0.0030 0.0061 0.413 0.366 0,0288 0.0261 0.0210 0.0218 0,0037
0.0494 0.0433 0.0039 0.0468 0,482 0.490 0.277 0,270 0.259 0.225 0.0412
0.534 0.469 0.465 0.51H 0.671 0.670
0.8b5 0.866 1 0 899 0.916 0 706
42,s 40i 48.3 497 567 516
0,660
0.61b 0 53i 0 ,3 4 ~ 0.490 0 869
497 560
0.0042 0.0012 0.370 0.439 0.339
0.0635 0.0136 0.503 0,503 0.458
0.0175 0.005 0.0105 0.0251 0 029 0 0608 0.0404 0.026 0.249 0.318 0.260 0 426 0 395 0,307 0.048 0.0253 0.0155 0.012
0.141 0.040% 0.0589 0.236 0.275
0.226 0.294 0.660 0.678 0.673 0,530 0.611 0.508 0.561 0,442
0.391 0.329 0.260 0,500 0,506
0.600 0.493 0.414 0.62i 0.653
0.484 0.537 0.522 0.485 0.317
0.65; 0.66i 0,660 0.647 0.638
0.589 0.568 0.559
582 599 601 574 551
0.252
0,456 0,335 0.270
0.430 0,467 0 469
586 615 580
1i 11, I
45'' 46" 47 48" 49 50
51
52
58 54 55
5b 5i
58 59
60
61" 62" 63'' 64 66
66 67" 68" 69
70" i1"
72" 73 (1
0.174 0.140
0,570 0.408 0,445 0.354
Irlterllal
Reflux Ratin.
t(J1)
I. .V ' G ,ir
G
1
I
(4. 724
0.918 0.664 0.858 0,836
0.753 0,911 0.833 0,559 0.342 0.343 0.331 0.338 0.339 0.475 0.491 0.579
367 345 2i7 3i2
top
L
:36i
H1oc mR\
Fr.
HlOL
I' 321 256 213 242 391
0.40 4.92 3 52 14 0 3.02
0.4 0.36 0 32 3 88 0.43
0 44 0 69
272 262 358 328 459 XI5
9.50 11.0 11.9 9.96 0.39 0.38
1.51 2.08 2.70 1.65 0 48 0 33
0.76 0.70 0 8 0.76 0 67 0 43
219 219 148 209
:(,09 2.95 i .48 7.44
0.44 1.29 4.28 3 16
0.42 0 79 0.82 0 95
-4\-.
550 560 489 403 459 408 487 465
345 2ii 30i 495 37.5 352 483 448 520 366 306 301 192 275 424
330
13.9
3.40
291 421 280 418 389
242 336 243 373 330
16.i 15.6 0.36 0 0 .. 3 49 1
6.80 4.12 0 42 0 .35 0.39
0.49 0 .. 4571 0
413 413 372 577 502
311 376 309 323 172
228 266 227 235 131
7.71 8.55 10.0 4.92 6.50
1.6i 0.89 1.72 1 38 3.i3
0.92 0.63 0.88 0.89 1.03
514 524 538 517 584
177
131 132 140 144 234 234 309 313 275 224 192 227 223
1.32 4 00 7.49 0.32 0 35 0.36 0.40 0.34 0 35 2.50 6 67 11.6 14.1
0.90 2.78 4.40 0.45 0.31 0.20 0.32 0.41 0.50 0.61 3.07 5.70 7.70
0.80 1.06 0.96 0.46 0.31 0 22 0 39 0.51 0.62 0.62 0.97 0.93 0.95
174
182 175 277 287 347 355 327 309 253
287
2i3
0.79
0.93 0.87
0.72
0 77
0 63
little to increase the reliability of prediction. Rough values of H ~ cao L 'tic estimated by valid indirecat methods only for tlvo of t,lir tcms reported by Scheibel and Othnier (fS)-that is, absorpin water from air of methyl isobutyl ketone and of methyl n-amyl ketone. I n these caser-:the gas-film re-istance appearb til have varied only from 1t o 20y0 (if the total, and a rough estimate of t h e gas-film resiatance subtracted from the measured over-;all r r s k t m c e might give fair values of individual liquid-film resist nnces Tlie values of H L Lt h u i obtained are from twn t o S I X times tliose estimated by an extrapolation of Allen's data, as reported by Sherwood and Hollon-ay (1.5) for 3/8-inch ceramic. rings. Sclieihel and Othmer uned 10-mm. glass rings. The comparison is uncertain because of doubt as to the value of diffusirity to he used i n Pherwvood and Hollo\\-ay'sequation.
.Analyses are average values for t w o sets o i samples.
Sonit. data of Icowalke, Hougen, a,nd Wat-.on ( 8 ) a t a. liquid rate of L = 150, as recalculated by Sherwood and Holloimy ( I h ) , have been omitted in Table I because the liquid-film data of Holloway had t o be extrapolated t o liquid rates belon- the experimental range; t h e values of H ~ so G obtained are substantially independriit of ga.3 rate. The equations for individual gas-film transfer coefficient actually published by Dlvyer and Dodge (3)included L ab a variat+e; their justification is doubtful because tlie basis v x a a n extrapolation of the Sherwood and Hollonay liquid-film d a t a belon. t h e experimental range. Tariations of H ~ xGi t h Don-ers of I, from -0.20 t o -0.39 were indicated by their equatioiib. There is sonit: question about t h e validity of the equatiunh t ( i i . H l o given for the first tu-o sets of data in Talilc I, becaure i i i neither case is there any certainty that the liquid diitrihutors and othrr equipment details were ~ c ' that h the Shern-nod and H d l o -
~
Fr.
difficulty by measuring both liquid-film and over-all data n i the sanie apparatus. Severtheless, Molstad found i t nrcessary t o repeat some of t h e liquid-film measurements w t i i B different location of one typr of diitrihutor, after finding difficulties in teits of ammonia absorption. His ovrr-all rrwlta for the small packiilg,. ~ w r ethus reduced t o gas-filn. values by tlie use of liquid-filii! (lata obtained from tests witt: a location of the distribut(1slightly different from t h a t enlployed in the over-all measurcments. However, the difference in location was judged tcl he unimportant. The exponents given by bloljtad for the effect of L are average values over the elitire range of liquid rates; actually the rffect of L thus indicated was too small at low liquid rates. This class u! indirect data gives results n-hirh are not wholly inccirlit x i t h those ohtained tJy t methods, but they do
~
1. 0
i LL
0.6
f s I
0.6
0.4 1
HOLLOWAY DATA
J
CO2 DESORPTION
LlOUlD RATE L, LB.(HR.)(SQ.FT.) Figure
6. Comparison of Rectification with Desorption
Lines drawn for Sherwood and Holloway correlation, extrapolated to low liquid rates and for carbon dioxide desorption data.
INDUSTRIAL AND ENGINEERING CHEMISTRY
lune 1947
D A T A FOR RECTIFICATION
The p i e m i t experimental result, o11 isopropanol-water are given in Table I1 and s h o m graphically in Figures 5 , 6, and 7. T h r rangec of variable. were a. follon.: Liquid twlon. packing, r = 0.0012 t.> 0 5 92 4 .>.I 6 -" 3 (I
:R
:iS :i!>
42 49 4:< 4:4
4:; 44 44 44 4i -1 ,i 4J 46 4 ti 46 47
--
(j
-_ --, >
':
ive, i n d i c ~ ~ t i oofn :iii increase in H:L nt very lox p t e r rateb.
foot.
Compariwn of the data for alcohol at. lo!+- cuncentratioi~r{vith thohe for carbon dioxide-water h l i o ~ at h a t the liquor rate:: E(ii, the rectification runs n-ere largely lielox what proved to he B 5t:Ltile range for the distributor when operating with\\-ater; also it w:is iniposiihle under the conditions of rectification to return reflux tii tllv column a t it rate as high as 2000 111. :(hr.) (sq. Et.), so t h a t preHu-11ing was impossible. Considerable spatter of the points is tlicrefore not surprising. Because t h e importance of ensuring \vel1 wetted packing Tvas known, the packing xas al~vay::\\-ell fliiodcd
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1947
0 2 :30 5 55 10 5 2 19 0:3 s2 1
0 685 0 868 1 100 1 335 1.59; 1 607 1 597 1 301 1 137
45 1
58 5 100
'
60 59 58 56 54 51 49
3 6 5
9 2
5 i 4G 9 45 3
18 17 13 9 5 4 6 8
0 35
7 73
"direct" absorption-desorptio~itechniques for measuring 2lll and H t o separately, especially HG. As a matter of fact, until more reliable direct data on H t c are available, it does riot appear possible to $ho\i- conclusively from published data t h a t the additive reFistance forniula for packed colunins is in genrral empirically vnlid. There is some reason, theoretically, for holding it suspect.
25
5 3 9 3 0 11 85
" 1-iscosity a n d den-iry e r t r n p o l a t e d i r i l n i values f o u n d esperinrentally at "0' , 2 5 O , 47.4", and 6 4 . 4 * C . 1\Iolal diffusivity e-tiinated froin d a t a of J.eiiionde ( I O ) a t 16' C , u-ing t h e Stokes-Einutein relation t h a t D r u is proiit'rtionnl T O t h e absoliite t e i i i p e r a t u r e .
M o r e :I .erieh of iuns was started. In the carbon dioxide {vork, ~vlierehigh n-ater rate.: were readily attainable h y opening tlie \ Y : i t e r vnlve, many oi the runs, even of t h e earlier series, n-ei'e ni:itle after recent flushing of the distributor a t sufficiently high i.:ttes to induce >table'flow. The authors believe thic may account for the lesser spatter arid generaliy loner position. of the i,:irt!oii dioxide-n-ater points. Within the experimental uiicertiiiiity tlir H ! Lfor dewrhing isopropanol from dilute aqueou tion- into cte:ini seems t o be e-sentially the same as t h a t for de-orl)ing rnrlion dioside from dilute squeoui holutions into air, 1!1~)vitleclthat the allowance for differing phy-ical properties iiitlicated by the Sliern-ood and Hollo\r-ay forniula is duly made. It is impo.cihle t o tect the data of Furrias and Taylor (4)or of Duncnn, Iioffolt, and WtliroTv 12) from thi.; point of vien-, becnuie tlieir column. :tnd di-trihutor.s lvere not calihrnted v i t h a n y teni in tlie range cii flo\\- rate- used. treating 1rrtific~:itioiid:ita may he uced t o sci'ure rough value- ( i t H,,,, the height of the gay-film ti.an-fer iiirit from the high c~oiii~entratii!ii iso~~r~)~):inol-\r-ntel. runs. Figure i c h i ! \ \ - - H,,,,, pliittctl agwin.t ,\ .G I / I,.,, where
APPARATUS AND PROCEDURE
Thc column n-a? of 6-inch brass pipe, 8.125 inchw iii inside diameter, a n d 0.201 square foot in internal cross section. The packed section had 60.5cc free volume. The perforated plates above and below packing each contained eighty-seven holes of 31!~-inchdiameter, giving 5 5 2 free area. The packed height n-as 47 inches, except for t,helast eight runs on carbon diosidc dcsorption perforniccl by Jones (:) when a 24-inch hright n-a.~uwd. Vapor ~ v a qsupplicd from a 40-gallon coppe~.kettle hcatcd by coil and jacket. For reflus heating, hot water from a stcamjacketed kettle Tvas pumped t.hrough a coil heater a t - a high rate. The t,eniperature of the hot water was not appreciably higher than the hoiling point of the rcflus. Reflux ~ 3 returned s to the column at about 10" F. belon- it bubble point. Piping froni tile tvater main t o t h e reflus line wa . galvanized i r , m ; all o t h e r pipc in contact n-ith solutions was brass. T h e four-point liquid distributor was a d j u s t d , licfore insta1l:ition, to gire equal f l o m from each of the 118-inch pipes: the distributor %vasnot changed during the rectification and desorption tests, until the last eight runs made by Jones, hen 2 feet of 114inch brass pipe Ivere added in loxvering tlie distrihutor. Copper coil condensers and ccolcrs were uqed on tht, vapor ant1 liquid samplers below the packing; vapor was withdran-n wing a leveling bottle and a gas sample bottle connected to tlir top of the vapor sample bottle. T h e samplers Tvere 3j4-inthbe lo^ thcl parking support, plate. Thc liquid sampler was insulnted n-ith a ]/:inch layer of cement. Each sampler was purged inimediatrly before each sample \vas n-ithdrann. ACKNOWLEDGMENT
T h e author.; ackiiowledge the courte.y and :.ooperntion of h. H. R:idacch of The Cooper 1-nion, who kinilly permitted tlir experiments reported here t o lie carried out i n t l e unit operation. lahoixt tri,y of that inst it ut ion. NOMENCLATURE (1
~Iicrc'
=
rlopc ~i equilit!~~iuni c v r ~ - eat y
Tliic i; tlie ,saiiir kind of :iver:ige that n-a.. u-ed ljy Furii:i> atid T:iylcii, (4,.Fi,oiii I.-urP drop through one tray, the clear liquid depths over weir., arid tlie height the clear liquid rises in the downflows (6,1 1 , 16. 1 6 ) . Tliisituation is in part due t o the complexity of the design factoi.- u i d to the many different types of tray layouts and cap shapes in m i n i inon use Tvhich exhibit, satisfactory efficiencies. Some of the mow unusual factors affecting the efficiency were recently described ( 5 ) .
T
TRAY FEATURES
.liter the tou-er diameter, tray qpacing, and cap design have heen deterniined by methods described in the literature, the tray layout has t o be selected t o give satisfactory over-all effirieiicie. and tower vapor pressure drop under floiving conditions at the design vapor and liquid loads. A well designed tr:ty should linve. as far as possible, the folloiving features:
B a ~ . i s cor~ ability to maintain satisfactory efficiency under flowing conditions when operating with design loads of vapor and liquid. The tray spacing, toner diameter, and cap design are mainly determined from design vapor flow rates. T h e flow of liquid across the tray has a profound influence on t h e over-all efficiency for reasons ot,lierthan the liquid concentration gradirnt and is onc ors that determine the layout. Halancc is frctabilitg," b u t here this: tcrm is rcwsi,vcd to d i s Lture. .4 well balanced t r a y will niaintain good efficiency under steady flowing conditions. FLEXIBILITY or ability t o maintain satisfactory efficiency ur1tii.r conditions n-hvrc either vapor or liquid rates are greater or l i , h i than design rates.
.\t high vaiior vibliii.ities in u\c~*>> of maximuin vapoi &.sign ratths, tlie i n c w a w in entrainment and decrease in local efficiency tlue t o insufficient. contact (vapors jetting from the slots) will ad\-er.sel,v a,fft,ct the ovcr-all efficiency (1). At very low vapor loads poor vapor-liquid rotitact is attainpd as a result, of vapor tieing piiorly c l i h h u t r d over the tray--that is, channeling ( 2 I ; also thrt vapor flow will pulsate i.9) which adwrsely affects t h e local and over-all t.fficiencies. A flexible t,ray should maintain good efficiency by maintaining p i m l vapor arid liquid distritlut ion at high and loiv lcrad~. STIBILITY or ability t 1 1 rnaintain satisfactory i:tFicitm.y iiri(1t:r flow or unsteady state conditions. ~*haiiging rying vapor ratrs havt1 lxwt ohservcd by the writ t ' t o decrease t h r over-all cfficienry from a n esprct of vapor vclority produc t o 3OC& An ai~cc~lrration t,ioiial head term in Bernoulli's q u a t i o n , arid similarly tion produces a negative head term. A n accc~lrratingvapor rate in a bubble toxer, if great enough t:vt:n though of very short durat,ion, will blow the liquid a,way from the cap: i n consequtwe of the following decelrrating vapor rate, the liquid ruhhes t)ar!i to thil space it originally occupied around the cap. T h e monit~ntum
