I I III I I I I I IIIIII I I 126 236 THS AN INVESTIGATION OF THE EFFECT OF VISCOSITY UPON THE PLATE EFFICIENCY IN A BUBBLE-TRAY TOWER Thmis for the Degree a! M. S. MICHIGAN STATE COLLEGE Robert Asa Smi‘I-h I949 AN INVESTIGATICH CF THE EFFECT OF VISCOSITY UPON THE PLATE EFFICIENCY IR A BUBBLE-TRAY TOHER By Robert Asa Smith A THESIS Submitted to the School of Graduate Studies of Eichigan State College of Agriculture and Apylied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIEECE Department of Chemical Engineering 1949 ACKKOHLEDGEHEE The author is deeply appreciative of the valuable advice and guidance of Professor Jc W. Donnell. Appreciea tion is also expressed to Dr. C. M. Casper for his advice, and to ur. W. B. Clippingcr for his assistance in the mechanical aspects of the problem. TABLE OF COHTENTS HISTORY EQUIEEEHT PROCEDURE DAIA DISCUSSION COECLUSIOHS CALCULATIONS HOEEECLATURE BIBLIOGRAPL Page HISTORY In 1943 Brickemer and Bradford presented a correlau ticn.beteeen viscosity and plate efficiency in the‘grgnz sections 9.3 the American Institute 3; ghemicel Engineered” They pointed out that the tray efficiency of fractionating columns is a function of many things. Some of these are temperature, pressure, tray design, column.loed, physical prcperties of the liquid. etc. When all other things are constant, such as in columns of similar design or for similar purposes, the efficiency may then.be a function of the physic- al properties of the liquid. It is obvious that the efficiency would not be a func- tion of Just any one physical property, but of many. It is desired in this problem, then, to study the effect of liquid viscosity upon the efficiency of a bubble-tray tower. AA water solution of a soluble cellulose gun was metered on to the top tray of the tower. The effect of the gum use to vary the liquid viscosity in the tower. By analyzing various liquid end vapor samples from the tower. the efficiencies and viseosities were determined. The results obtained by Drickamer and Bradford were drawn from test date on 54 refinery fractionating columns and dealt wholly with hydrocarbons. They checked their re- sulting curve against data on 80 commercial columns taken from the literature. The literature data used was also from hydrocarbon columns, except for four points. Two of these 2 points were Beer Stills. one an hectic Acid-deter tower, and the othur on average :f five tests on commercial Alcohol» tater t were. Their results ere shown in figures (1) and (e). The curve is of the form 3 n 0.17 - 0.616.10510 (zrhq for efficiencies (E) of frecticneting colunns using hydrocuro halter and Sherwoed have also deelt slightly with this problem.(10) Qhoy suggested e general equation for nurphrec efficiencies for gas absorption, tching into account the effect of viscosity. They no une thet Although it is highly probable that the indivio duel 36s and liquid film coefficients are diff- erent functions of viscosity, the present dets con be correlated fairly well by assuming both liquid end 598 film coefficients to be inversely preportionel to viscosity to the 0.68 poser. Their equation is where [3.9 h]- __ {3-50 I o.svo/n¢ei a 0.68 "0.33 Efficien ice estimated by this equation u re s.nsrinr of Sufi different iron the experiments. results. The storage deviation use 32%. The equation severed values of EEV from 0.0095 to 0.75. n from 0.70 to 22. n1 from 1.05 to 1.8". gee rates from 0.70 to 3.4 pound mole per hour per square inch of PERCENT TRAY EFFICIENCY ‘00 90 H4; +r 4b— —-0— 4%- .- .4»... *— 60 59 - —— ——1L—— -—<> r— -——-4L—~———~4>— ‘ . 1 P. L AHO 80 To $\. ’ l i I 1 30 - .4}. __ .4}. 20 ._.._4)... _-- -~ \\\.\\ \\ Q} ~.\..\\ ‘ x o \ x ' \t .Clll x. -114 i...— Figure 6. CM) feeding system, showing the storage‘ tank and pressure source. !; KT 9.. i [#3, - 4 . . > ‘ Figure 7. Sampling apparatus. showing the valves. union: and cooling coil. Figure 8. Viecoeimeter, showing the stirrer, heaters and controller. Photograrhy by Ruby, (clear and Author. IRiCSBULE It was previaus 13 stEf tafl thtt tEe a; stem neceasarg to feed the CEO solutiona 1333 the t3' of the towEr was net 3 r gal r 1:3: t of the t330r uiHit but 333 tag 3 3333013 - 13 far this varo :3. The C"C eel: aticns 3Ecre fed into the toner thrc" h 3h3t w33 ier.crly a 33’3”".Etcr 3611. This 3011 was 13 the 73333 83306 abeve tfie tsp (Eétiw .) tray and aircctlJ telan the rcflax 13133. It 333 felt 3333 t! e efh fact a: the refl u: liquid flowing down ever tfie CEO solution 3330 t 6 p031 of linuié b03135 the weir we 315 C333 9 Eddbnti‘l¢ 13‘ 30 crfcct 313135. A be 316 of $33. 3383 35 32 ex €02. 333 333a 33 3 33033330 auurcc for the feaéing 339303. The 33333336 13 the $603133 t33}: 33a }:c;t tetEpen 5 3: Ed ? pcic. The 31603 aldwet r teca atock W a aixefi in ELc kettle to 3 cor re.Er*tion of 33;i 34m 'cly 53 6 33301. by weight. The 931331033 were t3 orcuEhlJ rifle“ t3 100130313 ti: n tc so- aure ufliffirmity of tha feed: A yrwblem tExnt 533 £53113 c'ufica a 33 333 3513, W a thrt 53 d1 calving the pauerad CL . It 365 fleeiEGd t3 use 8313» tiona 6:! 0.753 and 0.1W5% C2 :0 33 fead. 301331033 of thesa concemtr3tione have viscositiea or 35;rsxfimntoly 20 and 6 centiysise reageeEively. 330m th C”” ~03Eflcr 33:.3 3M ed to watar, a vErg gelatiaeua film immeflinto 3 formed around 013333 of th. nofzfier. vary :30 atly decreasing th rate or caluticno The prabicm was 3:1335 by 610313 3L51 C t: :e ccr3ectE m..nt 14 of €33 ta 80 pounds a! water while the salutiGnEW3s bcisg agitfitefi with a C~4 Lightnin' 3133?. F33t3-fivo minutcs sf mixing resulted in 3 ch3r uniform aelufiiant The calumn 333 brcught to cgcrftins egailibriam by allowing it to Operate unficr 3 $1333 33% of cemflitiens far at least 30 minutes. baring 3313 333133, £005 r330 333 3305303 rate were £1333. 3nd 311 the athar 0 33131328 3336 allcwcd ta 333333 themselves 33003313313. The distillate anfl Lotficm prciucta 3033 refi'clefl 333133 this yartion of tfle run. Equilibrium 093333135 cafifiitifins 3330 said to exist in the tower when in-cnming 33d out-53133 streams remained essentially 6&38t3nt in qu33it; 333 Quality 33E: 3 pcriod 3f tiac. The visible effects of equilihréum were inaicated by cvnst33t 331398 of 3333m preseure. feed tangerafiure, $363. reflur, and graduct meter 33331333. 333 3 33333333 3100301 ccmcentration in tie graduct 3333335. When the £333: 3030303 the csnaition where it 333 09333313; 33 equilibrium. the CED aelutian.wna metcroa into the toy plate. It 333313 be 3331331333 at this yoint that £333 tmat time farward 3 3131333 mmsunt ct ogcr3ting tim r633 med; 311 of the 8333133 h3fl to be -3hen befare the anyyly 3f CEO 333 fecfl mtock was $336, fir the r0861VLr tfinhs were Iillefi. As the SIB aalution.waa startad 1333 the top of tha 031333, the 33001333 £3333 3333 13013305 from the 333310 30 15 tAA.t the egguLA AA AA lAA5ar recircuiatiAA. AAA flaw A? 033 salution.was regulnted to the desired rate AAA held at A ASA At Vfilue. TAG W A ling ¥.'tA AA5AA LAAA tAA tawer A5A£n came to equilibrium tr A tAA Affect- of tie CNS, unurLll ALOut 20 AinutAAo SAAglefi sf £0 Al. AAAA AAAAA Off erA each tray inta seven inch tc-et t ibes La.w~ AA ccelefi Aamylin5 0311. {AA the last three AA As a aligAt vacuum was usvd to syecé the fir.uinr of samfilea. The Bagglea were taken in the orAer 321. A33. 333. 333. $33. T. B. and Fa Gauge, meter, and ccna c-AA ta resaizv 5'9 Were trken Ana the BAA AlAA staggca. TAG tewcr Ara left in operfitien far a aAart gerisd cf time be clcnr it somewhat of viAco A Pul”°i Ans. Befsze t:w t0? Jer cogld be Aacfl far anothvr run it had to be claw Ad of all tAAv iAcAAa mafiarial¢ MA was sac» canzilnficd b; QAAL iA* AAA V$39Wu3 buttvbg gACtht 51A mtAe receivers into the kAttle. Acre it WAS AAA tea with clAAcd steam AA thvt the Alcohal 3A1 Artcr A A boiled a: flLtcv A3 a Viaccua Aaficr sciatica. Ants WAS diacaréed and the achAAl AAA water reused. The snmyle concAAArAAiona flnfi viaccsities were den tcrn‘nba in t? A AAAAAA described an page 36 CI DAAielA. A: - beam and A11;1AAA. (3) DAAA far tAA Alcohol-water density. teA,AAA1AAoncA1centrutian Acteruin¢tiua v*A AtkLn frsm 439 A: the Chemical Eflgincerg‘ AAAAAAAA‘AJ “err". (6) 15 D“:- '3 The followqu scetian 18 ccmyceea 0f the latcratoyy data taken in the procesa of the exyeriucnt. Eh data may be rowthy diviaea into two pnrfifl. Cue consista of special observations $35 the other 19 n rnal tower o:crati:.al data. The first psrt at the an a 13 far the stanflardizaticn of the Catwala £539 Vificcaimctcr and the aquaticn far its use. and an investigation of the effect of CED camcen‘ration upon the liquid density and viscesity. The secand yart. or marmal tower operaticnal aafia, lists several things. -hese include: csncentrntion or GEE feed aciutiun. rate af 030 food into thc toner, tamer rota. meter retainga, and liquid and vagcr samgle grapertios. l7 Standariization cf Cstwnld scesinetcr u"*"" dis- unit-1%) tilled water at 35.0 fies. C. (Kimble Viscosimctcr size 0—290) 10 ea. Witt? atmpne time 9083 9.83 9.83 9.86 average tiue 9.05 800. The visconi*v 0: water at 25.0 deg. C. 18 .8927 centipciae. v5 The dcnaity 18 .9971. Eta equntlun for uae with the visccsimetgr was flea velopea as follows: ul g dig; g‘ g gt '5- gift 3 g 0‘ ii L "I. . ‘J‘ mm a ;.-: :3 u 3' 03??? 6t '1’" s " .. .dv 3.90) u 3 .09105_dt where n.18 viscosity in centipoiee d 15 the fieneity cf tha fluid t is the time 0f efflux in aeccnfle. 18 Investigati n of c£1cct of C13 ctnc at: tion neon,aensity ana viscoaity. 9/l5/49 Ecight Front. Density Ecmycrfiture Density Euro Enter at .13 £05. C. Cor1;toc 31 deg. C. 1 .60975 .9995 3305 1.0C0 .9933 2 .061873 :9983 81.3 .998’ 9983 3 .5003 7 9938 21.9 .9913 9993 ‘ QC( £3468 :J9L 7 20.9 09987 :JQBZ 5 .030w11 .9937 21.1 .9937 .9933 6 .OCCll? .9977 31.3 .9979 983 7 .060659 .3930 $1.3 c9951 09933 9/19/49 8 .C1G 1.0606 33. 1.0015 .9982 9 .CO.:--O .9‘ ' 85.3 .9993 .9993 .COESO .998 83.6 0.999 .9983 .COlCO .9931 33.0 9339 9933 .090530 .9930 33; :9983 .9983 f1u°r 9991 33. .9984 .9 8? :06800 :9983 2 .3 .9983 3932 19 All of the viscosities were determined at a bath temperature or 85 deg. c. The viscosities are in centipoiss and time in Viscosity 1.12 Viscosity .82 seconds. Sample 2: Samgle a Sample 123 time 93.0 timc 40.4 time 25.93 89.5 40.8 25.94 87.0 59.8 26.15 85.5 40.2 84.0 , value value value used 84.0 used 40.5 used 25.96 Viscosity 7.4 Viscosity 2.56 Viscosityz.28 89.23219 51 3519.210 3: 53121210 35; time 15.89 time 9.45 time 6.63 15.40 9.29 6.60 15.00 9.56 6.62 12.68 9.58 '"'m“ 12.7: 9c55 12.6 ' value value value used 12.70 used 9.55 used 6.62 Viscosity .58 Samgls 1 38.111210 8 Samgle 3 time 6980 time 74:2 time 55.2 6.84 74.0 52.6 6.85 7460 53.5 6083 L. 5305 6.80 '**"' value " '” value value used 6.82 used 74.0 used. 55.1 Iiscosity .60 Viscosity 6.53 K Viscosity 4.63 Sample 10 time 40. 5 40.7 40.3 value 13.566. 4005 Viscosity 3.57 Bangle 13 time 704:3 7.42 7.42 value used Viscosity .65 Sample 11 time 21.84 21.84 21.86 value used 21.85 Viscosity 1.93 Sump le 15.... time 60 02 5.97 6.06 6.01 value used 6.01 Viscosity .53 Sample 12 time 9.12 9.00 9.13 9.18 9.18 value used 9.12 Viscosity .80 Run Bumber l 0.75% 0E0 solution Rate of CEO feed 81 8/1/49 Steam condensate 242% at 7312 12331.? 815 6318w “time ”fall use in 54 min. 6332 0" 6:48 6%” Rotsmetcr readings Diameter of CEO iced Feca 11.3 Reflux 3.8 tank is 12%". Product 2.? Scmgle‘gyoperticg Sample Density Temperature 8t. Frost. Eel. Erect. H01.Frgct. . deg. C. WW,A16’ Ale. ‘ Co « 321 .9648 26.5 .205 .092 x32 .9664 26.5 .195 .087 y22 09393 25.5 0356 01775 '0417 223 .9584 26.5 0243 0114 yzz 09029 26.5 6525 0302 .460 T .8890 26.5 .587 .358 B .9971 26.5 .000 .000 Viscosity Determinations 303. deg. Co 3650 Beth temp. 85.0 Time or efflux seconds 15:25 15.15 15.51 15.25 15.28 15.21 Value used 15.24 V180081tf 1030 centipo as 84.5 83.5 10.08 10.12 10.05 10.04 10.07 0.85 A“ 4... Run.fiumber 2 0.75% CEO solution steam to column at 77 psig. Feed liquid to column at 78 deg. C. Rate of CEO feed 258% an. '1. 22 8/8/49 n X Steam condensate at 6:14 101% at 5:12 bra. time fell Rotsmeter readings 5.43 0" Feed 11.4 6:05 7.5“ Reflux 4.3 . PTOdUCt 2.85 Diameter of CEO feed tank 18 13.5" Ssmgle Epoperties Sample Density Temperature Wt. Erect. M51. Erect. Mol.Frect. w flag. 0. , 8100 A10. AlCd* ’21 .9574 33.0 V .231 .105 -122 .9840 23.0 .061 6025 yea .9520 33.0 .264 .123 .213 £23 .9768 33.0 .106 .043 y25 09848 53.0 0402 6208 .302 .9196 33.0 .421 .221 .9945 33.0 .003 .002 F .9835 33-0 .053 3026 Viscosity Determinations Sample B B.P. deg. C. 93.0 89.5 100.0 Bath temp. 92.0 88.5 98.0 Time of efflux seconds 101.86 21‘08 25097 101.48 20.95 25.70 20.84 25.38 25.33 25.18 25.15 Value used 101.67 20.96 25.16 Viscosity centipoiee 8.82 1.81 2.19 Run.Number 3 0.75% 080 solution steam to column at 55 psig. Feed liquid to column at 80 deg. 0. Rate of CMC feed 23 8/11/49 Steam condensate 224# st 5:08.5 93% at 4302.5 1325 in 1:06 hrs. time fell Rotemeter readings 4330 FBBd 9.5 5304 Reflux 3.5 Product 2.6 Diameter of CEO feed tank is 12.5” Somgle_ggogertie§ Sample Density Temperature 8t. Front. 201. Erect. 301.Frsc1 4 deg. Q__ Ale. Ale. “f ‘ Alc. 321 .9713 27.5 .157 .068 x22 .9888 27.5 .042 .017 yea .9663 27 .192 .094 .150 :23 .9694 27.5 .170 .074 yzz 09575 2705 9250 .116 0393 .9298 27.5 .398 .206 .9973 27.5 .000 .000 .9897 27.5 .097 .0145 Viscosity Determinations Sample :22 x23 B 30?. deg. c. 95.0 8700 100.0 Bath temp. 94.0 8600 9900 Time of efflux in seconds 82.58 23.22 28.00 77.02 23.24 27.92 74.82 23.05 27.63 74.38 22.82 27.57 25.20 27012 26.90 Value used 74.61 23.11 26.90 Viscosity centipoise 6.47 1.95 2.35 Run.Humber 4 0.75% 020 solution 0 Feed liquid to column et 81 C. Rate of CEO Feed time 1211 4:14 0" 4:52.5 8.5” Diameter of OMB feed tank is 12.5" 24 8/17/49 Steam condensate 241# at 4051 :94# at 5358 147# in 1:15 hrs. Rotemeter readings Feed Reflux Product Sample Properties 9.9 3.3 2.5 Sample Density Temperature Wt. Erect. Kol.Freet. Ebl.Frogt. f deg. 0;» _Alc. K Ale. ‘A423 yzl .9687 26.0 .181 .079 322 .9692 26.0 .176 .077 322 .9682 26.0 .184 .0815 x23 .9869 26.0 .057 .023 ya:5 .9559 26.0 .266 .126 T4 .9343 26.0 .382 .194 F .9904 26.0 .055 .014 B .9980 26.5 .000 .000 Remark: Sample 325 taken before 3:23 Viscosity Determinations Sample X28 B. P. deg. C: 8505 Bath temp. 85.5 Time of efflux in seconds 12.62 12.74 12.72 12.65 Value used 12.68 Viscosity oentipoise 1.09 x25 95.5 92.5 74.30 70.00 71.80 69.04 68.45 68.45 5.70 100 98.5 33090 33.54 33.02 32.88 52.73 53045 33.46 2.84 Run Number 5 0.75% 020 solution Steam to column at 79 p Feed to column at 80 0 Rate of 020 feed 8/19/49 25 Steam condensate 1908 at 5:20 112; at 4:41 78% in 39 min. time fell ‘ ' Rotemctcr readings 4:36 0". 5:17 8%" Feed 10.3 Reflux 3.2 Diameter of 020 feed tank Product 2.9 is 12.5" Sample Properties Sample Density Temperature Wt.Frect. Ebl.Fract. Mbl.Fr§ot. w, deg. Co A109 Ale. A130 7 y21 .9702 23.0 .169 .074 ‘ X22 09897 26.0 0039 0015 y22 .9644 23.0 .220 .099 .142 $25 .9613 2605 0229 0104 I ‘ .9882 26.5 .361 .181 .9976 26.0 .000 .000 .9885 23.5 .051 .205 Viscosity Determinations Sample :2. x23 B B. P. deg. C. 95.5 85.0 100 Both temp. 9405 8400 98 Time of efflux in seconds 43.22 9.81 15.57 41.73 9.65 15.22 41.14 9.68 15.00 40.56 9.63 14.70 40.26 14.71 40.02 14.65 Value used 40.02 9.65 14.69 Viscosity in centipoise 3.48 0.82 1.28 Run.Humber 6 0.75% 080 solution Steam to column at 70 psig. Feed liquid to column at 79° 0. Rate of 020 feed time fall 3:48 0‘ 4:04 7“ Diameter of 020 feed tank is 12.5" 26 8/23/49 Steam Condensate 156# at 4:11 109% at 3:47 47% in 324 Rotametor readings Feed 10.4 RBflux 305 Product 3.9 Sample Properties Sample Density Temperature Wt.Fract. Mol.Fract. Mol.Fract. A _Mdeg. C. Ale. Alc:_ Ale. ygl .9393 24.5 yzg .9429 25.0 r .9237 25.0 .436 .232 B .9986 25.0 .000 .000 8 .9878 25.0 .052 .021 Remarks: Bun only partially completed. .1 .1. Viscosity Determinations Sample B 3.?- deg. C. 100.0 Bath temp. 9800 Time of efflux in seconds 14.80 14.80 14.57 14050 Value used 14.50 Viscosity in centi- poise 1.266 Ran out of CEO at 4:04. Run Number 7 27 8/25/09 0.375% 020 solution. Steam condensate Steam to column at 70 psig. Feed liquid to column at 72° C. 2425 at 1:15 7 130% at 12:17 Riggeof 020 ggig 1128 in :58 min. 12:14 0" Rotameter Readings 1312 9962" FEQd 10-1 Diameter of CEO feed tank is 12.5” Reflux 3.8 Product 0.1 Somolg Preperties Sample Density Temperature 9t.Fract. Mbl.Fract. 201.Fr§ctfi deg. C. A10. A100 #4 ‘10:: y21 09194 2805 .445 0338 X22 .9603 30.0 c224 .102 yz2 .9069 28.5 .500 .282 .443 X23 .9445 2905 .317 0153 £23 .8764 2805 C635 .403 0408 .9033 29.0 .514 .293 B .9966 50.0 .000 .000 .9855 30.0 .057 .023 Viscosity Determinations Sample :22 :23 B BOP. deg. C. 85.0 83.0 10000 Bath temp. 84.0 82.0 98.5 Sims of efflux in seconds 34.42 33.73 15.94 34.33 33.60 15.75 34.05 33.68 15.33 34.04 14.10 14.06 14.10 14.10 Value used 34.04 33.63 14.10 Viscosity in centipoisc 2.89 2.81 1.26 Run Number 8 0.375% 030 solution steam to column at 80 psig. Feed liquid to column at 77° 0. Rate of 020 feed 28 8/26/49 Steam condensate 185% at 5:28 1092 at 4:52 3 3 . time fall 76. in z 6 min Rotemeter readings 4:49 0" 5:17 10" Feed 10.4 RBflux 3.6 Diameter of CEO feed tank is 12.5" Product 2.3 Ssmole Eroyerties Sample Density Temperature wt.Freot. H01.Froot. E01.Fre3t{ M deg. C. Ale. Ale. Ale. 1 x22 .9812 25.0 .095 .042 yzz 09433 24.0 .333 0164 .297 123 .9748 25.2 0139 .059 yzz 59250 24.0 0454 0231 '355 .8939 23.8 .575 .347 .9982 25.0 .000 .000 .9907 24.6 .036 .0145 Viscosity Determinations smpla $22 X23 B BOP. deg. C. 9100 88.5 100.0 Bath temp. 9000 87.5 9800 Time of efflux in seconds 43.20 41.33 18.32 43.32 41.28 18.38 43.22 01.22 18.28 43.10 41.36 18.38 41.20 18.28 Value used 43.21 41.28 18.33 Viscosity in 08Ht1p0183 3975 3055 1060 Run Rumber 9 0.375% 030 solution steam to column at 90 psig.O Feed liquid to column at 78 0. 8/30/49 Steam condensate 199% at 531205 29 95% at 4:20;: 34863190: cm fifi 104.4é in :52.5 min. 4220.5 0" Rotemeter readings 5:11 7" Feed 10.0 Diameter of 020 food tonk is 12.5" Reflux 3.7 Product 2.8 Somglc Progerties Sample Density Temperature Wt. Frost. 301.22eet. moi. Fr etfi - ‘9 deg} 06 A100 Alec filfilOOE 3 yZl .9658 19.0 .222 .100 $22 .9604 21.5 .253 0133 ygg .9620 20.0 .248 .114 .470 :23 .9850 21.4 .077 .031 ygs 09515 20.0 5313 0153 .248 .9097 20.6 .517 .295 .9988 21.3 .000 .000 .9895 21.5 .047 .019 Viscosity Determinations Sample :22 x25 B 30?: deg. C: 3405 92.5 100.0 Beth temp. 83.5 91.5 98.5 Time of efflux in seconds 7.90 23.76 13.77 7.96 23.10 13.68 8.00 22.97 13.47 8.08 22.80 13.37 7.91 22.96 13.39 7.91 22.98 13.34 8.00 13.37 Value used 7.97 22.93 13.37 Viscosity in centipoiss .676 1.98 1.17 ....... ...... 30 Run.Bumber 10 0.00% CEO solution Steam to column at 85 psig. Feed to column at 80 deg. C. 9/2/49 Steam condensate 194% at 5:07 115% at 4‘29 Rate of CEO feed 79% in :38 min. time fell Rotometor reafiings 4:28 0" 5:04 7.5" Feed 10.65 Reflux 3.20 Diameter of CEO feed tank is 12.5" Product 3.35 Ssmole Properties Sample Density Temperature Wt.Fract. MOl.Froct. Mbl.Frant. A“ deg. 0. Ala. 3119. 1.13.7 g ’21 $9475 2108 .529 0161 222 .9374 24.0 .374 0189 yzz .9380 22.2 0378 0‘925 0521 3523 09549 2405 .277 0130 yzs .9274 22.1 .430 0288 9542 .9276 22.1 .429 .228 .9979 24.1 .000 .000 .9880 24.3 .046 .018 Viscosity Determinations Sample X33 223 B BoPd deg. c. 82.5 34.0 10000 Beth temp. 81.5 83.0 9888 Time of efflux in seconds 8.22 8.38 8.82 8.08 8.40 4.77 8.02 8.50 5.90 8.00 8.38 3.82 8.04 8.45 8.83 Value used 8.04 8.42 8.83 Viscosity in centipoise .666 .711 .770 Run Humber 11 No 080 solution used Steam to column at 80 psig. 9/5/49 Rotnmetcr readings Feed liquid to column at 78° C. Feed 10.7 Reflux 3.55 Product 2.80 Samgle Properties Sample Density Temperature Wt.Frect. Ebl.Frsct. HOl.Fre2t. # deg. Co .Alc.‘*_ A100 Ale. 5 321 08950 2105 0587 .357 x23 .8958 21.8 .572 .343 yzg .9103 21.0 .513 .293 '..510 323 .9333 22.0 .401 .207 323 09020 2102 I548 0322 .531 T .9017 21.5 .549 .323 .9973 22.1 .004 .001 .9894 22.4 .047 .019 Viscosity Determinations Sample x22 x23 B B. PO deg. C. 8006 8200 9900 Beth temp. 79.5 81.0 98.0 -Time of efflux in seconds 8.60 8.28 7.01 8.71 8.13 7.10 8.55 0.16 6.96 8.55 8.10 7.05 Value used 8.55 8.13 7.02 Viscositi in centipc so .677 .671 .613 Run.fiumber 12 0.75% CEO solution Steam to column at 100 psig Feed liquid to column at 80 Rate of 025 feed 5c]. ()3 CU 9/9/49 Steam condensate 222% at 5:53 88% at 4:50 x f n. 8 time fell Rotsmeter readings 5326.5 0" 5:51 6587" FGBd 1006 . Reflux 3.6 Diameter of CEO feed tank is 12.5" Product 2.75 Sample Properties Sample Density Temperature Wt.Frect. lbl.Froct. 851.3ract; v_ a w p deg. 0. Ala. Ale. fidlc.‘ j 321 .9590 25.0 I188 .085 332 09870 2500 1060 0024 $22 .9538 2500 9224 0102 5205 X23 .9859 25.2 .064 0026 0218 yaz 09543, 23.0 .287 .13. $9073 2306 1511 0290 .9976 24-3 COCO .000 .9892 24.0 .046 .018 Viscosity Determinations Sample x22 x2 Ba Po deg. Ct 93.5 93.5 100 Bath temp. 92.5 92.5 98.0 Time of efflux' in seconds 12.12 80.4 9.03 12.12 79.1 9.06 12.16 76.7 9.00 12.03 72.6 9.02 70.8 71.4 Value used 12.11 71.6 9.03 Viscosity in centipoise 1.05 6.2 .789 f '1- (,3 9/13/49 Steam Coneenoete 195? at 334% ' . It llfif at figug 7;: in we min. Retemetor food Ram 00:11:01? 1:; 0.3?5fi CED solution Steam to col’fin at 80 03169_ . Feed liouid to colleen at 73° c. Rete of 030 food tfire fell 2:50 0” 3326 11.5" roeéinca 10.7 Reilux 3.1 Diameter of 030 food tank 13 12.5" lroouot 0.1 EFfiQle Eregertieg Beagle Density Temperature Lt.Froet. Hol.Feoot. Eo1.Fréo§. A D l _ fiegp C.* 116.;y w ‘_Alo. Alo.rv :31 .ovoe 31.7 .650 .422 ”Le .eveo ea. .ce- .437 333 0&533 31.3 .690 .éefi .61& £33 .oee a... .657 .453 323 08631 3107 c7175 c4985 063' T .ovee .7.5 .625 .403 e .3071‘ 2o.o .000 .03 F .9911 2o.0 .038 .012 Remarkc: Viecoeity Determinations v.— f Steam euyply dragged to £5 poig. flaringrun. Samole :33 x33 B B. P. 56$: C; 89:4 00.0 100 fiflth tfififlo Time of efflux in fifieflnfifi anue need Viecoeity'in centipoiee V9.0 8051 3‘73 8.73 3.73 8.73 $674 79.0 8.78 o.vo 3.75 8.72 3.72 .669 93.0 15.67 15.65 15.69 15.64 15.66 1037 Run.fiumbcr 14 .0?5w 03:0 eclution steam to column at 100 pa 3. Food liCuil to co luau at 80° 0. I :nte of 0:0 feed ”é {a 9/36/49 Seern 60W1MB t0 hail n4.- 4' 0&1?“ ‘6 “233”“? :?IU 17.5" at 4:05 time fell 37:: b“ Dior wetcr of co ndeaeetc tank 3:06 1” 12 18.75" 8:07 2" 3:10 3“ Dieeetor of CEO fend took 18 3:32 4" 13.5" 3:30 5" 3:34 6” Rotumotcr renalnga 2:38 '7" 3151 8" Fe 10.4 Eefl‘fi 3.8 Broéuet .05 .gggglg Profortiee Semgle Density Tomyoreture fit. ~ect. Hol.Froet. Lol.ET*gt. “WV GQEc Cc £180 £10. AA 110. w 331 .9001 3 .0 5&3 .317 3,-2 0.1375 2602 .965 .133 322 .3701 34.8 1673 cééé .518 :LL .9313 ' :3 .o .376 .191. W 325 .8620 25-1 .?Cl .4775 .521 T .9019 36.9 .53 305 B .9979 37.6 .030 .00 F .986? 2?.2 .055 .GLL Viscoeity Determinations BQPc deg. C. 83.5 8205 100-0 39 th tCEHQ 01.5 01.5 9300 Time of of"1ux la seconds loo. 168 "0.:1 140.5 177 E e :7 17395 $3.?3 39.18 I) V") 1:90; 0 L3.13 370'3 37‘90 37072 Value need 144 173 27.01 Vleceoity in ' 06flfi130186 11093 léclfi 39%3 Run Number 15 0.75% 0E0 solution Steam to column at 90 p815. Feed liquid to column.ut 82° 0. Rate of OMB feed 35 Steam condensate 3.9” at 11:09 19.5" at 12:08 time fall ‘IITUZ 0 Diameter of condensate 11:11 1.0 tank is 18.75" 11:14 2.1 Diameter of CEO feed tank 11:25 8.0 13 12.5" ' 11:27.5 4:00 11:53 5.3 Rotumeter readings 11:38 6.4 Feed 9.7 1133905 700 Reflux 3.1 11:40 8.1 Product 2.85 11:43.5 9.0 11348 1000 Sum31§_Propertiea Sample Density Temperature Wt.Fract. Ebl.Fract. 801.3ract. deg. C. WAlOa A10. A193? ’21 .9792 22.3 .114 .047 122 09875 23.0 .058 1023 yea .9554 2208 .213 .096 0205 :23 .9764 22.9 .152 .056 323 . .9585 23.0 .260 .121 .345 T .9482 28.0 .321 .156 B .9I92 22.9 .000 .000 F .9846 23.0 .076 .081 Viscosity Determinations Sample x22 x23 B B! P. deg. C. 9305 8805 100.0 Bath temp. 92.5 87.5 98.5 Time of effluz in seconds 24.92 27.22 23.85 24.68 27.80 25.94 24.64 27.40 28.93 24.78 27.40 83.80 Value used 24.70 27.40 23.88 Viscosity in f can'tiPOiae 2014 2036 2.09 Run Numb er 16 0.75% CEO solution steam to column at 85 p818. 36 9/29/49 Rotumeter readings Feed liquid to column at 88 deg. 0. Feed 10.5 Rate of CHO feed Reflux 3.3 time fall Product 8.7 $313.5 ob 8:14.5 1.0 Diameter of CEO feed 8:16 2.0 tank is 12.5" 5317.5 3.0 5320.5 400 3827 500 3:33 500 3333 7.5 Sumgle Progerties Sample Density Temperétufe Wt.Fract. Mbl.Fract. HOl.FractX __ A deg. 0. Ala. Ale. Alc.* . yzl 09779 24.0 9120 .050 122 .9844 29.1 0056 0027 322 .9758 26.8 .127 .053 .22 :23 .9702 29.1 .160 .069 y23 .9698 26.5 .171 .074 .580 T .9502 27.2 .295 .1505 .9979 27.8 .058 .015 .9896 27.1 .058 .015 Viscosity Determinations Sample x22 :23 B By P. deg. C. 9300 8705 10090 Bath temp. 92.0 86.5 98.5 Time or efflux in seconds 31-20 18.73 28.04 81.13 18.47 27.98 51.80 18.89 27.95 18.48 27.75 18.44 27.81 Value used. 31.21 18.45 27.84 Viscomtg 2-65 1'55 p.42 37 TABLE I SUEEARY 0F DAEA .L -22nd trgg 23rd tray .- Over-all Bottoms ; Run Efficiency Viscosity Efficiency Viscosity Efficiency Viscositdf ____'_‘ w @QQGGPNNP F' Pd 5* F! .4 5- +4 at tn 9- c: to F’ c: 0.26 0.17 0.20 0.01 0.27 0.22 0.19 0.04 0.09 «0.28 0.16 0.23 0.68 0.86 0.017 1.30 8.82 6.47 1.09 5.48 2.89 2.73 0.68 0.67 0.68 1.05 0.67 11.98 2.14 2.65 0.44 0.47 0.10 0.58 0.10 0.56 0.85 0.29 0.10 0.22 0.29 0.20 0.44 0.10 0.076 0.85 1.81 1.95 5.70 0.82 2.81 5.55 1.99 0.71 0.67 6.20 0.67 14.16 2.86 1.58 0.292 0.208 0.250 0.208 0.208 0.292 0.292 0.375 0.208 0.208 0.208 0.208 0.624 0.292 0.292 0.208 F A-vv-v v~ . '7‘... F--.“ ....7...J_—...._._. “—7, .44 -————.— ._ -.. , .—.7 ..7. -7.- _ 7 -7.. ”h u. , --7-L—. .-,,... i.“ .—7 _____‘7- I17 7777. | 7 7 III. 7 7.777. I. .7. . 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III 7II|777 v 67!. ..... lrI7 7I‘I’7I777 . .1 77,7777 76'. 117171.777 7.1.77 I .7 & III III I #1.! o. I. :4 IIII. III. 7 7-77 47717II‘7II7 7 l LY! .. o .O' .7 lit II 1% V _ . . ,7 . 7 7 . . . . . 7 J... u . . v 7 . _ .. 4 _. fi . 1 _ .u. . so.“ . V ~ ’ _ . U . u 1 .1 l.k fl _ a ’71.». . .. ,7 . , v . ) . . . 7 . 7 . _ . . o . . 7 . p h. 7 7 o v 7 . 7 V In w H * . .A . . . v 7 . .v n v II. I If . _ . .. 7 _ M . _ . 7. . w . . ., 1 _ J .. . _ J . . . . . . . ., . V. v . u . . . . . 7 . . _ . . . . . . p thm . [w . H . I .0977 7 7 7 . 7 -7 77 7 7 7 7t 7. .777 77. . 7117777 71 .7 777 . 7 77 I .7 . 7,..- 7 I 7 7 7. 7.7.7717. . 0. £7 7 7. 7 7 7.9777777? 77 7477.7. I. I. . .7777... . . 7 , . . _ 7 . a! . . 1 V, 1 . . . . . . , . . 1 o a w _ . . . _ . ~ . . V V .. 7 J 7 . . . . 7 . 7 . 7. V . 7 . . . r 7 7 . I . . . . 11.7 . I. . 7 7 7.. V . . — . . . u . .. 7 . JJ . . _ 7 _ . _ . m ”7. .. 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L7. .7|9777. 777.77I777. 7 .v IVATII7I7I7VI7377I. 7 I71 A . 771‘ 7 . _ F . .7 I ,. H . . V , 1 . . . . _ 717']! l .7 77 _ . . 7 _ . . 7 o . . 7 . _ .v. 7 7 I 77 . Q a v 7 t. I 7 I .I . . o 7 c l af‘ 7 7 . 7 *7 . . 7 I 7 II 9.; . In: . , . . . . . {'11: . . 1’J . . . . .. 7 H . . . . . . I}? o . . V c . _ . . . . . . t. I . . . . 7'a‘l’7'flli . 1 I VII ‘74 I 77. . V _ . . . 1 47... 7774777747777 “L7. 4 , H -...J7|.74777....7777.7«777.~-§fi717.17717747i4..777 7“ fl «7 2 .7 a 17 M V 2 7 A 2 _ 4| 4 r u 7 , . . H . V. — . «I .V . 7 z , . §o . 7 (- . 7 .1 . 7 W .V . . .77777I,.-7 . . 7 . . I..." '1 ' _ 1117' I . .0 .77 III! . alul .Y.I.|I.I7II7I I75- II'OI.’ IIIIII {I‘ -l.-.‘ I'll-"I 11.1" '1" 1 I .1 I." I 'I-I'I'II‘I' Ii1fi‘ii‘ ' I‘a'l. o '——. fill; I'I4101II'1I.‘ OI. 1-7-1.1.111111 1‘17 . . . 1 . o 7.1 . . . . . - m .. . 1 . o . . . m . . o * o _ . 7 . .7. 7 . uI I 77 I I I ..I . u . a 7 . . . . . q 1 n .. .... .7+ - 7 .1- 1. 7. - -7 . . . - -. 1 . . — . . . 0 . H . g o . 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V 7...: \‘pl‘. ‘ O . 4 f I. . \- ch*« ‘ 7 — f \.IH7 b‘lr... v. 41 DISCUSSION It is important to note that the efficiency of this tower is unusually low, while it is often possible to easily reach 95% efficiency with connercial towers of this and other systems. With this tower the average over-ell of» ficiency was aphroximotely 25%. Similar results have been shown by other hereons using the tower in the past. Naturally one can only postulate upon the reasons for these low efficiencies, for there may be many. The seemingly most obvious reason is the small amount of vapor specs between plates. The individual trays in the column are spaced on six inch centers. Such a distance is recosnized as being very near the minimum. it such a distance a Very significant amount of entrainment may result at the higher vapor velocities, reaucing the overoell efficiency. The high ratio of toner wall surface area to the tray ores and vapor space may also add some explanation to the ef- ficiency figures. A column of small diameter such as this one may have the coefficient of heat transfer between liquid and vapor reduces because of the liquid collection upon the cello It is understood that the transfer occurs, not only between vapor bubbles and liquid on the trey, but also boo tween the vapor and liquid droplets in the vapor space. A lengthy discussion might result over which is controlling. If a portion of the liquid droPlets collect upon the tower 42 wall in the form of a film. the transfer surface area is re- duced, resulting in a decrease in the transfer coefficient and over-all efficiency. Other conditions, such as the small number of bubble- caps per tray, may also contribute to the trend of efficiency figures. It must be understood, therefore, that any conclusions drawn from this experimental data of this problem should be taken in a relative sense with regard to other towers and systems, rather than in the absolute. Figure 4 is a drawing of one of the bubble-trays cepied from the company prints. It illustrates the lay-out ot’the bubble-caps. weirs, down spout, and sampling ports. It is difficult to explain the variation in individual tray cf. fieiencies except perhaps by the close location of the camp- ling ports to the bubble-caps. It might conceivably cause a local concentration change if the liquid is depleted near one side of a cap. i change in concentration of the sample con cause an error in the calculation of the theoretical one richment and the resulting plate efficiency. The results of the problem are shown in Table I. Figure 12 illustrates in graphic form the ovor-all tray ef- ficiency versus liquid viscosity. Over the range of viscosity studied here. there is no apparent correlation between liquid viscosity and bubble tray efficiency. 43 The data observed here is plotted over the curve of Drickamer and Bradford in figure 13. The two do not agree. Drickamer and Bradford include in their original data only one point at a viscosity of greater than 0.5 centipoise. It is logical to have some doubt of the validity of the cor— relation in the region from 0.5 to 1.5 centipoise. Their correlation would indicate an efficiency of near 30% for towers with a liquid viscosity near that of water. and correspond- ingly lower for higher viscosities. While not true for this particular tower, it is known that many commercial al~ cohol-water towers Operate at much higher efficiencies. and the results of the present work indicate that the efficiency does not necessarily decrease with increasing viscosity over the range observed. Figures 15 and 16 illustrate the effect of CEB conn centration upon the solution density and viscosity. It was discovered after extensive duplicate calculations that cor- recting the solution concentrations for any change in density due to the slight amounts of GTE had a negligible effect upon the resulting efficiency figures. It was necessary to determine the liquid viscosity at a temperature slightly below the actual boiling point. If any boiling had actually occurred during the determination it would have caused considerable error. For simplicity, the boiling point was determined from the concentration, and -‘__ C . . l l . l ——. - m , . n . I 1 I. ... . . I; ..II t-II. .I .III A . I - . . . v .IIt .’.I.Il.. '''''' III- .IIIIII.I.1I¢Iv.-I I . .. . r... ... 5 . \\ . \ a 4 fl 0!. ~ . . IJ . \ . \I I... 11 . N . I. .I. . II s .Ij . x I .- ‘ . r 9 K ...1, - vi . . I nr/ . . . ...} u . u .... a . . . i , . ,. IN.\\.—.\.IA ‘k‘. . _ . H ..a a .., . .l.’ 1fl.‘. \.. f\ ..h. ~ . .... c . . .7 . \ . 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In“ (5) am " ‘ W Y : 011111 I- Iv}? 5 In 52%;... 7:. t ) faking a heat balance around the toy plate Equation (1) may be written for the top of the column and for the top plate vt4~1.=ot(D-o _ (8) Also for the top glete Vt-l Vt.1 Another important equation around the complete tower 1:. w a F I C - D (10) and around the condenser vtzorxn (11) It was necessary to modify equation (5) for use on the f~1 trey'when the actual feed comyoeition differed from the theoretical. 3m 1: 553. 015112 I If? - W (13) Va VIE“ #3? I I 44444 III' E I I I IIIIIIII‘IIUIIIII II I. II ‘I. r 1 I. I III I I II O III II II II!!! I I III III, II II I1 I: I, I III IIIII1 Il’Il lI I II I I III II' If [I I 1 III II VIII It. I 11 I.‘IIII' I “ I . g u . _ .V N U I y . Ie o I r. I v I I. I I I I‘ I I a. I I., . I . ‘ I, . . , . m I I. .. , . I“ u 4 1 u I .11“ , . . . . ' L h 4 ‘ u I F V ’ L- ) ‘I L I A . . II . g . q I I r . . . _ I _ 5 . , . . I , 1— ~ I. II I . I. I v . I . . r I II I .I. I . I I.. '1 I I . 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I .IL 52 COfiCLUSIOflS 0n the basic of the experimental and theoretical work done, the author believes the following conclusions may be drawn: 1. 3. 4. There is no definite correlation between the efficiency and liquid viscosity of a bubblegtroy tower in the viscosity range from 0.6 to 3.0 centipoieeI The correlation of Driekemer and Bradford is in error I in their higher viscosity range if it is to be used as a general correlation covering ell types of systems. There are many things which have a for greater effect upon the tray efficiency than the liquid viscosity. Some of these ere, elot area, bubble-cop design, Icir design. downspout design, trey diameter, and vapor and liquid rates. There are several improvements which would lessen the difficulty and increase the accuracy of future work with this tower. Some of these improvements include: thermometers in the feed, reflux, and product rote- metcre, and condensers. a large diameter vapor connec« tion between the kettle and column, and rotemeter celi- brotion in the lower flow ranges. 53 CALCULATIOHS Sample calculation of run number 3. Basis . 1 minute Hurphree Efficiencies ~ E22 3 5' 2 "" y21 8 0084 “‘ .0675 y - ygl .150 , .0575 L116 "' 0084“ g 0.104 .393 a 0084 8 O. 200 E25 *fifaz “<¥g§_ g V25 - fee The following calculations, along with all the others. were 00mgleted in tabular form. Since the actual calcula- tions are very lengthy. the complete calculations from only Run H05 3 will be given.- A.condensat10n of the Kore important. figures 0: the rest of the runs will be given at the end of r“ the calculations. Run H0. 8 E01 tract. EtOH in feed 0.0145 M01 fractn EtOH in distillate 0.206 Reflux-u 0r (Corrected) (See ref. 8) 0.281 351. Product - D " " 0.073 gal. Feed a F " " 0.49 gal. Spec. Gravity of 0B 0.905 " u “ F 0.990 " W n n .950. Weight of OR .11 # Weight Of F 4004 f Weight of D . 0.555% wt. tract. EtCH in OR . 0.398 Wt. EtOH inOR 0.8405 Wt. water in OR K018 EtOH in OR Mole water in OR Total mole of OR Wt. front. 131501! in F Wt; E1303 in F Wt. water in F Hole EtOH in F H013 water in F Total mole of F Wt. EtOH in D Wt. water in D Mole EtOH in D E013 water in D Total mole of D Wt. water in 0 E015 water in C F plus C W a F J G a D Vt 8 OR ‘ D Total heat of vapor . H Total heat or liquid - h Het heat of vapor wlfln 1.27 # 0.182 mole 0.0705 mole 0.088? mole °:_QR 0.037 0.149 # 3.89 # 0.00525 mole 00216 3018 0.2193 moleflorgl 0.225 # 0.340 # 0.00489 mol! 0.01888 mole 0.02577 mole of D 0.641 # 9.0362flpole of 0 0.2555 mola 0.231? mole of W 9.1125_mols or 7% 20815 Btu 5000 Btu 17776 Btu in BE 2000 Btu 1n_gt 3 0.0248 0.0145 For purposes of 55 Tabular form of Sorel calculations calculation Ifi was arbitrarily taken as 0.001 Estimates H b. ”H at vn or 715 let est. yt-l 3 .10 20758 2965 17795 2000 0.1123 2nd est. yt-l : .071 20758 2986 17752 2000 0.1127 let est. yt-z : .05 20715 5028 17690 2000 0.1151 [R h HH' Ht 75 let est. yf-1 a .035 20705 5072 17655 2000 0.1154 H h HE: Ht 7m lfit GBtc y:_5 3 0007 20674 3201 17473 2000 0.1145 let est. yf,4 a .005 20670 5210 17460 2000 0.1146 3 a x. " onll “ E [5" " K a (19) (D) M ' x511 * °m¢2 7h 2 e 3511 ‘ omll m vn u f: ( Q ( )mF) S I (Kw) (W) m 56 1. 0521 = , C Vhfc D Vth-D J K ya x; 0.0502 0.1458 0.0255 0.1247 0.0275 0.0455 0.0711 0.0002 0.0362 0.1489 0.0338 0.1251 0.0275 0.0436 0.0711 0.0083 0.0562 0.1495 0.0255 0.1255 0.0092 0.0254 0.0526 0.0002 omll' . w W vmxc' 3” Q 3 5’n ;n* 0.2517 0.3541 0.0071 0.0380 0.0020 0.033 0.0041 W Omll Z 3 3n I; 0.2317 0.3457 0.0245 0.00203 0.0233 0.0030 0.2317 0.3462 0.0110 0.00202 0.0090 0.0014 0.2317 .3465 0.00423 0.00202 0.0030 0.0003 less than 0.001 A Therefore, in the third run. the Sorel method requires seven theoretical f“1. 1’2 8.110. f4. theoretical trey. culctione. calculations is six. trays. Since the retailer or the tower acts as one These trays are t, t-l, t~2 a 1. tray 1.4 ie not counted in the efficiency cola The theoretical number of trays used in the efficiency Eaver‘all 0 6/24 C 0'250 Viscosity of bottoms . 2.55 centinoiee 15-5 11 0.0105 0.4 0.q 0.6 0.q 0.. 0.0120 0.d 0.0005 0.0 0.0120 0.c 0.: 0.c 0.6 0.c 0.0043 0.c 0.0004 0.( 0.0070 0.: O.( 58 coup-ow 58 NOEEHCLATURE bottoms procuct mole of CHE solution liquid density. gmz’cc mole of distillate efficiency murphree point vapor efficiency feed tray mole of feed molal heat content of liquid effective liquid depth. inches molel heat content of vapor Henry's low coolticient, #mola/ft.3 atm. net heat of vapor above liquid cf its boiling point mole of overflow from the nth tray total Pressure, atmospheres time of efflux through the viscosimeter, seconds distillate sample viscosity, centipoise mole of vapor bubble-cop slot width. inches mole of bottoms Product composition of liquid from the nth trc‘, moi fraction composition of vapor from the nth trey, moi fraction theoretical composition of vogor in equilibrium with the liquid on the nth trey, moi fraction . v... uni. a c .r.. . r r .Mv. FD (1) (2) (4) (5) (6) (7) (8) (9) (10) 60 BIBLIOGRAPHY Corey, J. 3. and Lewis. W. K., Studies in Distillation, Industrial and Begineering hemigiiy, V01. 24. 882-883 (1932) Cellulose Products Department. Hercules CHC Cellulose Gum, Form 500-87 Fm lu49, ficrcEIes Powier Com- pany, Wilmington, Delaware. ‘ Daniels, Esthews and Williams. Exyerimentol Ph sicol Chemistr McGrsw~Eill Book Companyifiré.‘eu1tion, flew YorE 1941). Dricksmer, H. G. and Bradford. J. R., Overall Plate Efficienc* of Commercial Itdrocorfion Cqumns‘gg a T E'