“A STUEN 0F CONTENUGUS FOAM FRACTIONATSON Thesis 'for the Degree of Ph. D. MICMGAN STARE UNIVERSITY KENNETH EDWARD HASTINGS 1.9167 ' iIll'iilTn’l'lTlfilII?l’lflflfiflfiil’fili‘fll’l’lfiINTI?WIS!I ., ,3 R A a , ES“ 3 1293 10814 8267_ Michigan 308 U . .1” This is to certify that the thesis entitled A STUDY OF CONTINUOUS FOAM FRACTIONATION presented by Kenneth Edward Hastings has been accepted towards fulfillment of the requirements for Ph.D. degree in Chemical Engineering Major professor Date August 3, 1967 0-169 "g .1, y . - N k; a U W AllSlRAC'l' A S'l'l'lfi' OF (IUN’l' l NlTOl'S FOAM FRM‘. l‘ I ONA'l' 1 ON lijf Kcnnctll Eda-lard Has: iong In order to develop a method for prtllL'LliiLL tit scparatioas acnicx'cti it‘ a foam t'rac-io;t-a_io;t column, the conccpt of tin: lti‘igltt of a transtcr unit was applicd to thc continuous foam fractioratio‘ of aqucous sodiw 1.;ur i Stilla‘cc solthLtiz‘. it‘. a column. wi‘u enricuint: anti sirippijigt Hcctit'ts. 'l'itc column was first operatcd as a onc-s;a c ScparaLor wii'n no strippin; or t‘xtcrnal rct-luxittzg so that L’Qllillhfill'n dill” could inc ooiaiAt-gi. 1.1 this mic-Siam) scparator. liquid in tl'tt- 'notto'n ol- illt' colunn was gassvti to produce a risinu foam 'ncd and bottom prociuct liquid. ’l‘nc- I’lSlttfl loam was L‘oalcscc‘d ovc-rlicad and pumped to a tank wcrc it was mixed wi'n no,— tozn product. l'Vccd, withdrawn from this tank, cntercd tuc t't.‘ll"t‘.tt ocloxc the foam-liquid intcrtacc. At Stcadv state). samples old coalesced foam. and ho.to'n product were withdrat-Jn and ll‘t‘ conccntratiotis twrc "icasurt-o. The effects of foam drainage, intcrnal rcfiur-L. and count(arcurrcn: mass transfer worc St‘partllt‘d i)\' showim: tltat toa'n drainant- and intcr'ia‘ rcflux Wc‘ft’ ntmtligihle, and hence all incremental separations above onc- staue scparations ocre caused by countcrcurront mass transfer. Fnricni»; and stripping: scctions of various heights wcrc E’Xé]".:.ttt”t’l to find out what: variables at‘t‘cct the height of a transt‘cr unit. 'I'ltc ltcigltt of a transtt-r unit for either an enriching or a stripping St'c‘l‘itm was found to correlatc o'npi r i cal 13." with t he flow nu'u'ncr . ill. , "I ' \i‘lz‘ aru VaS' l. Ll) 1? low .\'umoer = .2 l- I'L‘ " "1.) + LI' ldhercw - . . - , '5 . LD = lhwwitlow lltpitd tlcnv rate (CTN /WLH-) L = Upflow liquid flow rate (cmj/uin.) U ‘ t _ .r 7 A ,\ 3 . b — has flow rate ttm /m1n.) litis lieigdit t~f a) trarusfer tuiit (W‘rft’laiitni wens uscml tt) PrtKllCl top lvott oat prtvluct_ ctinctuitrzitituis for tsxrngrinuuital rtuis iti a twilunui dd 32.4“ cnricuin: section and a 31.5" stripping section. The calcul t \ - . . . +c. . bottom product mole fractions agreed to within -0/ and toe calcula - . .. . +_ -J . , . prodtu t midté lfaCIIAHiS agretml to wiulrui -/.7’.tit tne (HKPCrlThWWlal for this cold Til ll . and th a a I. 0 d t ed top values A STUDY CF CONTINUOUS FOAM FRACTIONATION By Kenneth Edward Hastir s A THESIS Stdunittcd 1A) Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY De urtment of Cucmical Enqinoering I \k i917 /‘/4 [MT .l.....\) J. - -'_ J.- A Clie (Qtzfifl’ 0'3 EJEIUOI 0.000090000000000000000 2. Enriching or Stripping Uoctio:.............. 3. Upper Section of an inriohirg Colurm........ A. Lower oncolo“ of a Striprirg ”o u” ........ 50 Ip’.iffiiL€ly 17.11 Enri‘Chiu, L)?\/LI.LO: 00000000000 ()0 A Stripti‘i? C‘CtiOF OJ. EilniJu‘? ll'fi‘li-l.toooooooo To LO’DF U3Ctiop Of a Strillifig CClu.aooooooooo 8. Enriching Section in a Vnmhiucd Coiuuu ..... é'o “gal P‘Oillt .1." EL Ct'i'ltlilttt‘tl (:01l1'71l70099000nooooo to 0“ Calibration Curve tor th; Conductivity Coils an... .J.c 08.171 ‘I‘EC‘biOLZic‘oiCl. :17 1’ 31'3“. ‘5. 5 v-\ o f: 1 1 i r) TV! '17" C 3 4- , , , “(4* L, as; - .1 -' C.‘ ¢ ‘71 a .,‘ _' - ‘3 (”V ‘1 0 ‘ v‘ i2. ouria c3 -=L~ioi on or ooaium 3 3 a L3ur;l du lat; CO. .3 {D (t- +— O *4. .......OOOOCOOOOOO ’N' 5 5 7* ‘v- -~ T‘ ‘fi‘wq r. ‘. r\ v-\ fl r‘ 1‘ ‘v' ' ‘3 ‘ 1). area Ate‘aiei LULLi? “iamrtsr a— a functior ”- 4.4.. .. -. _; " . Ci liOobOLl I‘Oauct A'AOle F1 (ft/10.00.000.000... it. 3u1;ace Excess as a L r:ar I“1.1nci'.;'to:: Cl l‘Otl.O.’.’; PrOtLUCt C073C3YV-WL’:LO 4000000000000 15. :est 0 on a One 3 U] f the inilitl ii. Pilationship _L \ b"g‘; t-)'917‘ar3t0rooooooococo-000.0000 16. Tie Fffoot of Puttle Rosiieace Fine 0; th: Fraction of Lituii it the roar for Fiff3r3nt Column Heights with 3 W40 ton Iioiue'Cohceh- tratior of L.6 x 10—0 gm mo: es/czzt3 SOL :...... {:4 O H 3 D O Y Ci H—’ ._.) ta 1?. The Effect of iubtls Resi: Fraction of Liquidi n h3 :oam ior Li‘ ColeiHoighustdthzzi tration of 2.7 x 10-6 gm poles/ on3 3 +‘\ to J?“ \ -37 18. The Ei fie ct of the height of th3 Column of 0am on the Fraction of Iiluii in he FoaL1 at Different Foam 3 Les Li.h Egttom Proiuct ConC3ntration of 1.6 x 0' gm moles/cm soln........................................ A6 7-1 D‘ 1. 34m ch 19. The Effect of the Height of the Column of Foam on the Fraction of LiQuii in the Foam at Different Foam Rates With a Bottom Product Concentration of 2.7 x lO-U gm mOlBS/Cm 50130000000000.0000.000000000000000000000000 A? 20. W0 tarison of 3:-:r3 rimew a1 -‘ata With the W31 for an lili.it31" iall E lichin; QQCtiOnoooooooooooooooooooooooooooocoo-0.00.00.00.000000000000 £8 21. Che Height of a Transfer Unit in an Enriching Section Versus the Downflcw ’toLIIJflO1-J1%).atiCOOOOOOOOOOO.00....0.00.00...OIOOOOIOOOOOOOOOOOO DC‘ 22. Comparison 01 -xnerimentai Data with a IO;131 11:3, t‘ipllll, L)'3CUionOOOOOOOO0.00...OOOOOOOOOOOOOOOOOOO 51. 23. H3ijht of a ir1.3"3r Unit in a Stripying Section Corre1ated with the Upflow to [O DOWflOw iiatiOOOCOOOOCOOOCOOOOOOOOOOOOOODOOOIOOOOOOOOOOOOOOOOO5 i; 240 Egight Cf & Iranm Cr Lm lb Ccr11CJ&t LOnOOOOOOOOOOOOOOOOOOOOO0.00 \\-FW KC») 25. A Correlation Eetw een th3 Amourt of Liqui. in the Foam and the Gas Flow Rate for a 71" CUB-Qtage Separator...oooooooooo00000000000000.coo-cocoon...90 )3 26. A Correlation Cor Wh LV3rhea i LiQUii Flow Rate in a MUlti‘Stc ged S ?paratcroo00000000000000.0000.no...o~~ 56 270 Graphical 301uti0fi Of Run ghgooooooooooooooooooooo0.000.000... /7 28. Eject Of t}13 (:“Xni)il]()gi (:()1{ln[1 blq‘rlfl1..OCOOOOOOOOOOOOOOIOOOOOOO.0. 6C IFTRCDUCTICN 0 Although maly technigues are available for separating homogeneous solutions, only a few of them are economical at low concentratioes. One of the most recent techniQues is foam fractionation which concentrates surface active agents by foaming them. Foam fractionation utilizes a guan— tity of feed solution which is gassed to produce a rising foam bed and re- sidual solution. This foam is collected overhead and coalesced to form a solution of higher surfactant concentration than the original feed solution. This fractionation process can be made more efficient by countercurrent mass transfer in the column of foam which produces a multi—staged effect. Foam is essentially a honeycombed arrangement of gas bubbles separated by liquid lamellae. Some types of foams, for example the head on beer, are uniform and stable; while others, such as sea foam produced in the surf, are composed of a wide range of bubble sizes and are QUite unstable. Some foams are rigid and contain very little liQuid, while others are fluids with thick liQuid walls. The most stable configuration of anm.has been theor— ized (45) and found to be one where all liQuid lamellae intersect at angles of 1200. These points of intersection form "Plateau's borders" where liQuid films are the thickest. Most of the liQuid drains down through the foam by way of Plateau's borders, because of a pressure differential (6) between liQuid lamellae and Plateau's borders. This pressure differential is caused by the amount of surface curvature existing at different points along a polyhedron shaped bubble. Pressures in liQuid films are the lowest at Plateau's borders where the air—water interface is the most concave 2 towards the air phase. This effect of cur'ature causes smaller bubbles to have a higher gas pressure than larger bubbles; therefore foam will always coalesce into larger bubbles. Gas bubbles are found in many different shapes and sizes. Spheri— cally shaped bubbles (k = 6.0) are formed if large amounts of liQuid are entrained in the anm (wet foam). But as liQuid lamellae become extremely thin and accordingly the fraction of liQuid in the foam decreases, the gas bubbles are distorted to polyhedral shapes (dry foam). Dry foams have been found to consist mainly of dodecahedron shaped bubbles (13) with k = 6.59. Where k is equal to the area constants divided by the volune con— stants (area constants = area of bubble/Di, volume constants = volume of bubble/D3), Area of Bubbles n 'h a 1 : k Volume 01 bubbles (l) C? U 44PM Wh e r (U 0. DA Area averaged bubble diameter ll DV Volume averaged bubble diameter A study of surface chemistry explains why foam fractionation is economi— cal at low concentrations. Interaction forces between molecules are great- er for a liQuid than for a gas. Molecules in the liQuid which are within a few molecular diameters of the gas-liQuid interface are subject to dif—— ferent environmental forces than molecules well within the bulk of the liQUid. These environmental surface forces decrease with the addition of a positively adsorbed surface active agent, which concentrates at the inter— face. Surface active agents (surfactants) may either be positively or negatively adsorbed at the surface. f they are adsorbed at the inter— ace, then a partial separation can be achieved by removing the surface F‘J from the bulk liQuid by some meazs. For instance, a knife edge could be used as a mechanical means for skimming off the surface of a liQuid, but this is not practical. The simple process of generating a foam is an ex— cellent way of producing a larre amount of surface area and removing this generated surface from the bulk of the liQuid in the same operation. Foam fractionation is different from froth flotation although both involve the gassing of a liQuid. Froth flotation is an established pro— cedure in mineral dressing where the surface characteristics of one solid are modified so that the particles will readily attach themselves to air bubbles. Froth flotation involves the gassing of a liQuid which contains suspended solids, while foam fractionation involves the gassing of a homo- geneous liQuid which has surfactant dissolved in it. A one stage foam fractionation column can be transformed into a multi— staged column by the application of any or all of the following factors; external reflux, internal reflux, central feed, and drainage. External re— flux is caused by coalesced overhead foam being added back to the tOp of the column. This results in the upper part of the column acting as an en- riching section. Internal reflux is caused by poor foanlstability with bubbles coalescing in the column, and this effect reduces the amount of surface area and forces some of the surface active agent back into the bulk of the liquid. The feed stream entering into the middle of a foam bed causes the lower section of the column to act as a stripping section. Down— flow in a stripping section is usually composed of either the feed stream A or a mixture of the feed and external reflux. Drainage results from ex—— cess liQuid being entrained in the foam and draining down through Plateau's borders as the liQuid lamellae become thinner. The external reflux and feed flow rates are quite easy to measure experimentally, but the other two factors are rather difficult to take into account. Stable foams are produced by a combination of uniform bubble diameters and a high elasticity. Uniform bubble diameter: decrease the chance of bub- ble coalescence due to a gas pressure driving force. Elasticity, as defined by Gibbs (l7), is important because it determines how well foam will resist coalescence. d . s=2A$ (2) Where: E = Gibbs? elasticity A 4) Foam persists only as long as liQuid lamellae exist. A surfactant that is Area of the liQuid film Surface tension (D positively adsorbed at th interface causes the surface tension to be smaller at the interface than in the bulk of the solution. If the surface layer is damaged and the nderlying liQuid is exposed, then the greater surface ten— sion of tie underlying layer pulls the edges of the wound together and thus causes complete healing of the surface. A stable foam should therefore have a large positive elasticity. Foam stability may also be affected by the application of other less common conditions. High viscosity liQUid lamellae resist drainage and hence enhance foam persistence. Liquid films with a large surface area are less stable than those with a small surface area. llS causes small bubbles to 5 have a longer life than large bubbles. Foam stability usually decreases with increasing emperature and this is primarily due to decreased liQuid viscosity and increased gas pressure within the bubbles. The pH of a surfactant solution does not affect the stability of foams, except for those produced by colloidal agents. Neither pure liQuids nor saturated solutions usually have appreciable foam persistence. Detergents are the exception to this rule and have considerable foam stability at saturation. r t DJ FT The present interest in foam fractionation has increase ov (D ‘ e 'i 9 last ten years because of the increased usage of synthetic detergents. Eioiegradable as well as non—biodegradable detergents are widely used in large quantities in industry and in the home, and these detergents pollute the country's streams, river, and lakes. In some cases, the nation's water supplies are polluted faster than bacterial action can break down biodegradable detergents. Foam fractionation might serve as an excellent means for removing these surface active contaminates. Foam fractionation is presently used in the sugar industry to remove color contaminates which are surface active. Another possible use for foam fractionation is in the separation of non—surface active ions (4t, 46). A detergent sometimes has an affinity for a particular ion and forms a surface active complex with the ,non——surface active ion.~ This complex can then be separated from other ions in the bulk solution by foam fractionation. BACKGRCUND WORK There have been many papers published in the field of foam fractionation, but only a few have contributed significantly to the state of the art. Most researchers have taken an empirical approach in solving foam fractionation problems. This leaves a researcher at a loss when trying to scale-up the already studied system or in looking at a new one. The following review of past work has supplied this author with the necessary basis upon which to build a more theoretical approach. Lemlich and Lavi (Bl) studied foam fractionation of dilute aQueous solutions of Aresket-BOO (monobutyl diphenyl sodium mono- sulfonate) in an enriching column. They gathered data on the separations achieved as the external reflux ratio was varied from zero to infinity. Their results have shown that at various gas flow rates and bottom product compositions, increasing the exter— nal reflux ratio improves the separation. While they apparently have shown the above, they have not separated the effects of inter— nal reflux and drainage from the effect of external reflux. Lemlich and Erunner (8) develOped a mathematical model for the foam fractionation of aqueous Aresket-BOO in an enriching col- umn. Data were gathered on a one theoretical stage foam column and an eQuilibrium eQuation was presented _ 4,5ch _ CT—CE Lo () Where CT = TOp product concentration of Aresket-BOO (mg. moles/ml.) C = Bottom product concentration of Aresket-BOO (mg. moles/ml.) S = Bubble surface area per volume of gas (cm2/ml.) c = Gas flow rate (ml./min.) T = Surface excess of Aresket-BOO based on CB mg. moles/cm2) L = Overhead liQuid flow rate (ml./min.) mheir experimental results indicated that surface excess is constant over part of the concentration region. They chose this concentra- tion region for a study of a multi—staged enricher. This enriching column model assumes drainage to occur but neglects internal reflux. Cn r: cT (33x+1) G 8 TB GDB (aEX + l)LU(l — 3%5) 6;: I003 +08 + I0 (2) Where REX = External reflux ratio ODE = Concentration of downflow stream draining into the liQuid pool at the bottom of the column (mg. moles/ml.) LU Upflow liquid flow rate from the bottom pool (ml./min.) For an infinitely tall enricher with low reflux ratios, CDE .is as- sumed to be equal to CF which is another way of saying that the driving force at the bottom of the enriching section is zero. CT‘ (REX + l) G S T ("‘0max. = I B + (3) CE LO CB Their experimental results have shown that Equation 3 overestimates the separation achieved for Rsx>'l, and becomes more accurate as Rh L X approaches zero. 8 ”allir.g (i9) has develOped a method for studyins the effect of column height on foam ‘ensltv for a one— st age separator. From his foam density profiles, it is pos sibl eto dualitatlvel pre~ict how much foam drainage is taking place. walling measured overheg d foam densities for aqueous sodium lauryl sulfate as well as four other systems, four different column heights, and various drainage times. The drair age time can be approximated by dividing the vol— ume of the column of foam by the overhead foam le3 , and this is exact for the case of negligible drainage. These experimental data were then cross-plotted for different corstant foam flow rates to vield a plot of foam density versus column height. Wailing found (4 Ft) that so iiur laury l sulfate exlmibi ed a foam low rate TBflOD where foam density did not vary with column hei ght, and hence foam drain— age was negligible. Not all of tie systems that he studied had such a Teflon. C) Lemlich and Leonard (32) have develOped an equation for predict— ing the overhead liquid flow rate for a stripping column with neg— ligible foam coalescence. Their model is the solution of a differ- ential momentum balance for interstitial flow in Fla te au uis borders which are of noncircular cross section. This solution assumes lami~ new flow and Newtonian surface viscosity, and the velocity orofiles M had to be integrated numerically. Their model prelicts foam.density to be constant throughout a column section and this is contrary to a great deal of literature data. Leonard's column was not constructe 1% .prOperly to handle moving foam beds and so station r* foam beds were A 9 stud'ed in order to verify this equation. A great deal more work needs to be done in this area before reliable overhead liquid flow rates can be calculated. Haas and Johnson (23) calculated heights of a transfer unit, based on the downflow stream, for a stripping section which concen— trated the Sr—89 (sodium dodecylbenzenesulfonate)2 conplex. Their column had a drainage section directly over the stripping section and a drainaee model was develOped to predict the amount of liquid drainage entering the tOp of the stripping section. Many different liquid feed distributors were examined and the sirple process of adding liquid through one tube at the column axis was found to be adequate for column diameters equal to or less than two inches. They gathered data on.eight different liquid distributors for a six inch column and two different distributors for a 2A inch column. r1ese studies indicated that downflow liquid channeling was the biggest problem in scaling-up column diameters above two inches. Six differ—~ ent types of gas sparvers were tested and the importance of producing a uniform foam with small bubble diameters was observed. For the same set of conditions, stripping sections from 10 to 28 cm gave approxi— mately the same height of a transfer unit, but stripping sections from 50 to 85 cm did not even yield the same order of magnitude height of a transfer unit as the shorter columnS- These discrepancies were blamed on inaccuracies in measuring more than 8 to 10 transfer units, liquid channeling in columns greater than two inches in diameter, and inaccuracies in estimating the amount of drainage. This paper was the first step in trying to calculate heights of a transfer unit, 3 but the results were too inconsistent to develOp a correlation. TEECRX This section presents the mathematical solutions of prOposed {D O B ,3 p 4:) h d F O Q) l models for estimating the separations achieved in tion column which is composed of enriching and stri pin; :ectior s. r a Ur ess otherwise referred to, these same mod ml W11 untions were ['4- U derived by the author of his thesis by using the standard defini— tions of surface excess, a one stage separator, n mbero Wtr sfer Tht of a transfer ur.it. units, and the hei 1g Foam is made up of a lar?e amount of sarfac ce area and a small volume of liyuid. The concentration of surfactant in the liquid is constant up to a couple of molecular diameters from the air-water interface where it increases to a hig1er value due to surface excess. "D P) amount 01 surlactant at the solution surface 0) (.4?— I; (D s i U) :3 b5 i. Q: o (D (D o (I) m in excess of what woul: be oresent if the bulk concentration were extended to the surfa e, and is expressed as excess surfactant per unit area of surface. This eguilibrium surface excess is described by the Gibbs (l7) equation which is given below for a dissociating surfactant. c a __1_ if — .— T _.- prt JG “ “ prt der (l) (D The a‘o v equation was derived from thermodynamic considerations of .1 a solution in static eguilibrium and should or; " be applied to highly pure surfactant solutions well below the critical micelkeconcentration. ll In this region, the surfactant molecules exist as independent entities. They only feel the effects of environmental water molecules and are not influenced by other surfactant molecules. Adamson (1) has reviewed research which was performed by Brady on the sodium lauryl sulfate and water system. Brady was able to show that trace amounts of lauryl alcohol will greatly affect the surface tension data for this system. The Gibbs surface excess equa— tion may not be used to predict surface excess in this thesis because the surface tension data taken by this author were similar to those taken by Brady for sodium lauryl sulfate solution contaminated with a trace of lauryl alcohol. A. EGuilibrium‘Eguation An eguilibrium expression relating the concentration of coalesced foam to the concentration in the bulk of the liQuid may be derived by studye A b_' C) ing the mathematics of a one-stage sep— C , L arator. The surfactant which is car— T Y’ O ried up into the foam column will be C . B treated mathematically as two separate . G contributions. The first contribution Figure l A One—Stage is the surfactant which would have been Separator carried up in the bulk solution if no surface excess were present and the second is surface excess. A material balance may now be written around the column of foam in Figure 1. Input — Output = Accumulation 1'14— U A steady state conditions, the accumulation term is zero. l2 _. F’ ._ Surfactant entering [Surfactant entering Surfactant due to liquid en— + due to surface ex— - leaving in = trained in the ris— cess at the gas—liquid the tOp ing foam I [interface of the foam—JI product '_JO The first term, LCCB’ takes into account surfactant which is carried along in the bulk solution around the bubbles. The second term ac- counts for surface excess surfactant which exists as a monomolecular layer at the interface, and is calculated by taking the product of D 13%? flow rate G, and the surface excess TR. The third term, LCCT’ repre— the area to volume ratio of dodecahedron shaped bubbles k , the gas sents the rate of surfactant leaving the overhead foam breaker. 2 k D G T __A__§ _ , LOCB + a; LOCT o \2) Equation (2) may be rearranged into the following form TB (3) 17’ Similarly for l T’ the above equation is divided by CSol . which is the total gm moles of solute and water per cm3 of solution. c c k QE.G TB . T = __£L___-+ C *- D (a) CSoln. CSoln. Soln. 6 10 Therefore, 2 k Du G Ta YT = KB I: .4 (5) CSoin.Dé LC 13 Let us assume that the surface excess Tp can be expressed as a linear function of the bulk liquid mole fraction. TB = aAB + b (6) By substituting Equation (6) into (5) 2 2 a k DA G b k DA G ( > Ym=xfi+ L3 Ker-""37;— 7 l D CSoln. 0 g B Soln. C 9 The assumptions used in deriving Equation (7) are the following: 1) The liquid below the foam-liquid interface is thoroughly mixed and of concentration XE‘ 2) If internal drainage does exist, then the bulk liquid that drains down from the column of foam has the same concentra- tion as bottom product X This assumption implies: B. a) Liquid entrained in the foam has the same concen- tration as bottom product XB. b) Bubbles do not coalesce to form internal reflux as they rise through the column, since this would decrease the surface area and increase the con— centration of bulk liquid in the foam. 3) Eubbles are dodecahedrally shaped with k = 6.59. A) The gas-liquid interface of a bubble comes to equilibrium with the bulk liquid around it before the bubble leaves the pool of liquid and enters the column of foam. E. Definition of a Transfer Unit A foam fractionation column is analogous to a packed distilla- tion or gas absorption column. They all are continuous countercurrent I lg mass tranSLer Operations and the bubbles in a column of foam serve ' 3::oe rie nce in distillation and as abso ption J. as risine packing. theory (48) has shown that the concept of the height of a theoreti— cal pl Mb should only be applied to step—wise Operations such as a p late column, an dthe concep of the height of a transfer unit should onlyt e applied to continuo cont; ct ole rations such as a packed LOWETo A foam fractionation column of cross—sectional area A and hcijr'nt Z is shown in Fia- Too (T )m . (L) " L LID .L A U m Plane ' i ,3 I) '4‘ ‘ . - j 3 3 _. .- ‘1' ‘1 '; wr l.ll"( a. Lht ditttrtntlal ”Div 1UT material balance for the 1 t X? YU volume clement Adz equates ‘ T L the rate of mass transfer to I --, —~——e~— —-—~-. - ._ dz. ._~l_iul_“i- .i_l_lwmn.ll_-.ia_l_ the product of the over-all ‘ mass transfer t'ncfficicnt, concentration driving force, ‘_’“‘4_~T‘*‘““—‘7§‘Jmm Bottom (Ln)? = l5(LU.)E L.’ ‘J ' and the area for mass Plane . ‘ iY . I V. .‘LDE ' U‘) V 1 transfer Figure 2 snrlchirt or Strippir SQCthE -:: 7 = t. _ gig-"7 caviUcSOlm) zmuU Yu) 0 0251011. a. (8) The upflow rate 1U is approxir.tely constant be ecause the mole fraction of surfactant YU is very small and internal foam d‘ain- age is assumed to be negligible. Therefore, . U l" = e ‘5'): - \ 'dZ Cf CSolr.*tVltI 1hn“m(‘U' {J/ 9J073.“' (’) l5 Rearranging terms and integrating lama = (Yfi - YU/' (10) Let us define certain groups of variables in the customary way: UT dYU Number of transfer units = N = 3 (1U - YU) YUB LU HGiéht Of a transfer unit = H = kmamA Therefore, C. fiumber of Transfer Units In An Enriching Section The enriching section shown below is assumed to have constant .\ upflow and down— ‘5: “'i;' ‘‘‘‘‘‘ —~ \W\’\\~\c LO \... flow liquid flow LT f I L YUT f : R YUT rates. The num— ' a i _ ber of transfer f i :1 units is given by v/ f 1 k _-/ #‘w—‘ h- I "- \ , “will at Figure 3 Upper Section of an Enriching Column 16 . Lo LD Experimentally measured tOp product concentration = X? A? a? a k DE G X + b k D? G “"“"*" B u a CSoln.LU39 CSoln.LU ”3 \I 2 f‘ w k D u b DE G YU = XI) + a A X. + k '____-——__- D CSoln.LUDa Osgln,LUDé (l3) YUB = xB + Material balances are given below for any arbitrary section of foam column at steady state. Input — Output = Accumulation = O The material balance for the total amount of material is LUCSoln. - LDCSoln. — LTcSoln. = O or and for surfactant LUlUCSOln. - LDXDCSOln. — LTYUT CSoln. - or r = x + LT r a S (15) U 3 E6 U1 The above linear equilibrium eguation, 13, and linear Operating line equation, 15, indicate (AB), as derived below, that the logarithmic mean driving force is the correct average driving force to be used 17 in calculating the number of transfer units. Rearranging Equation 15 LU 7 L1 U UT’ D LD L3 and then ’ 2 b k DE G (LU LT )(a—éra k D G > ——-Y - —-'Y 1 + l. + ““““"‘ LD U LD UT Soln. D? CSoln. LUD; (16) Substituting into Equ uation. 12 .4 H: C >1: ll rT EIU LT >( a kd D[‘21 G ) b k D2 G —— (IT--é55§ + LU - LDYUT SOlH +1 CSoln.LUD§ C1 U3 (17) and integrating by Observing that YU is the only variable‘ V _ " YUL - YUB 1n (LDTl-L¥H$)E ”L (LU' ‘ LUTLE ‘”(LJB ‘ LUBLE (LUB LugLs . (182 OF LUT ‘ LUB N; = a ’- (19) L UU'“flfiU4 D. Hei ht of r nsfer Unit in an Enrichin” Section The height of a transfer unit in an enriching section is calcu— lated from.experimental data by using the following expression: r _ E hE — (20) E. Number of Transfer Units in a Stripping_Section The general expression for the number of transfer units in a strippi ing section with constant upflow and downflow liquid flOJ 18 o o . LP rates 18 Similar to that J of an enriching section, XD ‘, /”/"L , N L ”"\\ Equation 12. L L\ /( } -—~L—L-LL-—- LEL L LU — YU) (21) KB L ,5 Figure 4 Lower Section of a Stripping Column Where: LUF = LUT L3 —LF YUF = Experimentally measured tOp product concentration 2 - L D G b k D G Y = X + a K A X .+ UB B _'_"I'Tr)‘ 9 5-47 CQOln' 0'9 Soln.LUD 11‘ 2 f“ ' V, 2 YU : XD + a k DIX—v33 XE) + b JR DE G ( ‘ L”SOUL-LUDV ”Soln.LUDV ‘22” LUB\-<.t the tan» 0. his: enzichigtg sectaxri.1s gitrni L, :1, p" o" Tmfi': a! .1 - 4- . 4 r —1 r; H-A 4-1- Equation 3'. squatiOn 2 L3 2 a Le Gael to GalCLlate on: Belting D r; . "_ I J I" _;_". -_ n 1 _o _‘ . a : .31 -.- mt: . A] 1%.? iorce at tne ectto 01 the enriching section in a COmLiflv column a , . ,r , a L. 1-, 1 a "I -- a p ,1 ,1 1 : m i. 3, ., 4. 1.? of.uia.tec-use'hrfi s the corcmiaufiion oi lot rugaiq into this “ ‘ L /“ —- \ _ “ " "’ ' \""““\\ e3 4"? 'ww-Lon’ < ‘1 ‘\ uJ/CU‘OI-‘A chJlJL/(Lfi. T It 1] \ um 1 - L .L 71‘ i .. "‘41? C Li ‘ V' 1, Of v o i ' ~ 35 UT £ i Firure 8 1 ~ 1‘ j \' '. ”-3 .- + a 1 l - dlsnla s the new \ / 1 ° - T A A \ . L): ‘J \\ - A T \ _ C > s; pol" necessarJ s \W\ 36 I ’ F \ ‘L '7‘ UT: in Ori‘ler to drerine 1r ' "1‘ .‘NW 1 | r t7 ' I O C N ‘n 1 ’3 115 craving iozt ct. V P The material bal- ance for wate and surfactant arouni the ent L C Lan C O V l I" 3 *3 22123. C11 v-‘I Lafi ”f11)1{§ 8 a .A..\-_-.)%. ‘4 . :‘l‘l‘lCfllIig 830133.011 LL11 a Combined Column I —‘ ww- 4.1.c. L4 ’7ve: by' , .‘_h L C C Soln. a Soln. T Soln. or LC = In + Lm (57) -‘ '1. .0 n L. J are oniy ior suriactana l V C“ L X “C” Ttl- C = O CiUF Soln. EJIM boln. ‘HJUT 301p. or T v = T Y“ ‘_ ‘r 11- _ \ “30}? ‘C U: ‘41" U: (’ 8) Eliminating L0 f'Or Equatior 58 uith the jelp of Equation 57 Lw la -. _ l \ - ‘il in? _ ('3— + l/iU‘fi ly?.'1(- ) fit Ln 1 G1 in J LJ Since L3 = L; in an enriching section LT Lm *3? (LR ) LF ULQEE ( The expression for the driving force at the bottom of an enrich— ing section in a combined column may be written by observing that Y is in equilitrium with XDF' UP (21"; _ 222:» = an + k DE U in -- Y, , (20> ”1 of 1.: ”F C L -) ml d} Sdh.dv unere YU“ = Experimentally unknown foam concentration at the feed r point TDF z axes + b Substituting Equation 59 into Equaticn 60 to eliminate XDF and T,? T k D2 G 7: ‘Jm a. I“ (Y ~1>1=(——£)<22-1’Um)+ UF UF E LR Ur 2 CSOanLCU LT LT *- b k D? G (-- + Dim - (—)1' m '1 L 3 (61) LR Ur LR U‘" JSOllfl.o G g In the stripping section, Equation 26 may be used to calculate the number of transfer units and Equation 54 describes the driving force at the bottom of the stripping section with LD = LR + LP’ 1) Equation 50 may not be used to calculate the driving force at the tOp of this section because the downflow liquid stream enters the tOp of the stripping section at concentration Y we instead of con— 1..., centration Xi or X a. r 3b The mate‘ial balance for water and surfactant in the downflow ..\/ . I‘Tr .JJ - C(“ + L1A\C’.‘ *9. 00111. : Soln. OT _{ ;5 5-4 C1 or The expression for the driving force at the tOp .L Comb i nod Column .2 ,1 = O u 3F; solh. (63) (64.) of t he stripping section in a combined column is written by noticing that Y“: is in eeuilitrium with XDfii. r: .x. r- 1);. , 1r - _ 2. .z *' [f (2 2m . —— Ante“ + T 22 2m (6») UF «5 JEL . : ltfi CL) Ol.’ o ‘40 L A hmere Y = 7239s "imentallj unknovm foam concentration at the 1‘s ed poirm Tara = aXDFB + b Combining Equations 64 and 65 in order to eliminate X“FD and TDFD 1T1 akDZG bka (17"):‘_ UPS) :( LRKDE: I?) + _._—_L—_) + {'1 _ V- UF C L D: L 3” ‘UF L+R LF 30122. G v 301: -. 1? (66) L. Summarv The equations given above, unless otherwise referred to,,.ere ) 'ved by the author in an effort to pres ent a mather atical model for a continuous foam fractionator. Some of the above equations were used to calculate driving forces for mass transfer in a column of foam. The logarfl miriic mean driving force w as calculated from these driving forces and it was divided into the foam column separation in order to calculate the number of transfer units. The height of a transfer unit was found by dividing the number of transfer units into the height of an enriching or a stripping section. This height of a transfer unit is a measure of how efficient a countercurrent .. ass transfer section is in utilizing the available drivi% force under a given set of conditions. A correlation for these experimen- tal heights of a transfer unit versus some group variables would give a means of predicting separations. The following sections of thi8\theSiS are presented in order to show the experimental justifi- cation of this model. EXPEFE ‘EITAL KITUCDS Standard solutions of sodium laurg, l sulfate or potassium chloride were prepared b" weighing out the salt on a Sartorius Selecm balance and adding it to a measured volume of distilled water. nterface were determined at U) :1 "S H: 951 O ( D c.1— 93 H g tn 0 .5 :3‘ CD a: f m d. (D "S H 0 various concentrations of sodium laurvl sulfate by the use of a 'TT' Ceno-Dufiouy Tensiometer with a four centimeter platinum ring. 1ne 1 experimental surf ace tension of water distilled in metal was found to be 70.7 dynes/cm and this co:::pare u favorably to the literature value for highly distilled water of 71.9 dynes/cm. A tmla inu: electrode cell in conjunction witn a conductivity bridge (Industrial Instrument Inc., model RC—lB) was used to mea— sure the bottom product, feed, and tOp product conductances. rigure 10 is the calibration curve of specific conductance as a function of sodium lauryl sulfate concentration. Specific conductance is de- fined as the product of conductance and the cell constant. a corre— la tion for specific conductance was necessary in ordw to calcula the concentrations of product streams from the foam fractionator. special care was taken in ”Le suring conductance readings The cell was alwa 5 filled vith distilled water when it was stored. The cell constant was deterr;1ned at regular intervals with a stand rd potassium chloride solution (0.0200 molar aqueous VCl, specifi 1c conductance = . — r.-_ ' 1‘ ‘ , ‘n 1 . 3' ' f‘f' , S T771 »‘ 7'" (3.002768 Oflhll- cm l)1n01der to correct fo1 s113ht change . 'bnmrorn vln-li.l’il 4" '1‘! oil ‘1‘ '1 1:11. ill. 5 I‘ll ‘ . i! u...“ .1. v Specific Conductance ((micromhos/cm) x 10—2) r 34 q»- L I dr— —4 «1h- 8 N b C\ «L- o "D "\ ° P 6 Concentratlon 01 oodlug Lauryl Sulfate((gm moles/cmjsoln.) x 10 ) ‘ ure lO Calibration Curve for the Conductivity Cells. I ill 1.1.. In ‘1}.[ ‘ 35 solutions were used to rinse the cell as many as six times before a reading was taken. This method vas repeated until successive readings remained constant. Gas flow rates were measured with a no: test meter and elec— tric timer. The wet test meter was checked by positive displace— ment and found to be accurate to within 2—3%. The relative humidity of the air used to generate form was assumed to be 100% because the relative humidity was 98% at one hundred times the normal gas flow rate. Li;uid flow rates were measured with a graduated cylinder a d timer, as well as with Brook's precision rotameters (R—Z—l5A and h—2—lSE). Feed and reflux solution were pumped into different parts of the column by diaphragm pumps and flow rates were adjusted with Hoke precision metering valves. Each liguid distributor was made up of a single glass tube discharging liquid along the vertical axis of the column. Li1uid levels were controlled by gravity and Hoke precision metering valves. Gas bubbles were produced by forcing air through four sintered glass spargers and the foam was coalesced by orce in a stainless steel screen basket. 1”“) centrifugal A Nikon F Reflex Camera was used to take pictures of a one square centimeter section of wall bubbles, and the negatives were enlarged to three and one-half by four and one-half inch pictures. These pictures were then enlarged on a Kodagraph RiorOprint Reader. The overall magnification of the process was 200 times. In order to determine the area averaged (DA) and volume averaged (3V) bubtle s. (diameters, the bubble diameters of a randomly selected zone of bub- lDles were measured. Ill I I'll Oll 36 The combined column experimental equipment and accessories were set up as sh wn in Figure ll. This foam fractionation column . was studied as a one stage separator, an enriching section, a strip— ping section, and a combined column. Prescribed amounts of sodium lauryl sulfate and distilled water were added to the feed tank. Air which was humilified with water was bubbled into the column for 2 to 14 hours while column variables were adjusted and time was allowed to reach steady state. He etitive samples were taken from each stream until successive readings remained constant. Then all of the other important variables such as gas flow rate, bubble dia- meters, and liquid flow rates were measured. .mzpmpmmm< :owmeOfipompm Emom esp mo Empmmwc fl 853a 37 not: name at: waspflam [I Kdfimom moxmopm Emom poseomm Q09 955* admwom xcma vmmm 9=Sm pooh mommmdpwm Lopez :Edfloo l /,4 , a_“/: I ’/ / \ \\\\\_ I'D flgnfi.- // ’/// \\\ |( upon“ DDDDD nounm . - DD“ ALL 1] hepfifim ha< hopmadmom enammomm wmthEoo 38 The develOpment of the equilibrium equation which was used to predict multi-staged separations in.this thesis can be traced by ex— amining the first four figures in this section. As previously explained in the Theory section, surface excess could not be predicted from the Gibbs equation and the surface ten— sion data for aqueous sodium lauryl sulfate solutions as shown in Figure 12, because the surface excess was never zero or negative in the model region as the Gibbs equation would indicate. Experimental data from a one—stage separator have shown that positive surface ex— cess do: exist up to a concentration of 10-5 gm moles NaC H ,SC,/cm3 12 29 4 solution. The diameters of bubbles formed at a sparger are a function of system geometry, bubble formation pressure, and the surface tension of surfactant solution. Since all three of these do not vary over the model region, the area and volume averaged bubble diameters are constant as shown in Figure 13. In this same model region, the surface excess for a one-stage . separatorvvas found to be a linear function of the bottom product InOle fraction. A least squares fit to the data is shown in Figure la. This surface excess equation was then substituted into the equili— brfiimiexpression and an equation which relates foam concentration to blllk liquid concentration was derived. Figure 15 is a comparison .QOdemenozoo m+emadm amazed 73mpom mo soapoQSL m we SOHmCmB comwmmm NH omzmflm X cow 5 on x no m a . AQOH A .p H oEo\ HOE E VV COHpmpcho:oo 0.0H 0.5 o.m o.m O.N O.H 5.0 m.o P IP F r F a q u d 4 - ' db clu- cu- \P 4 qt- J. .4 GUI- :owmmm Hopoz , OH ON om 3 Om (mo/seuflp) uotsuel eoegang \‘ > J 40.3,, .. 3x. . “.1 .QOflwommm maoz poseomm Eompo: mo coaponsm a me mmuasmfln camps: eerdacsx came ma mcwndm AJOH x mxv Cowpommm efioz podwomd Sowpom 40 H.H db no m.o tr 4 41+ who 1 0.0 D u 1“ m.o Q "eaaav eeaw r-«_ I.“ 4 C? L. ‘ ih‘r‘cj (Vida I I... demetq a‘ 8 OT x °mo) J (Z .moapdmpzoosoo peduoa; Soppo; mo coapocse amazed m .owz oodmmsw AJOH % mxv sowpommm oHoz woscomd anpom £4 madman r. c H.H 0.H 5.0 0.0 5.0 0.0 m.0 :.0 p ~ Li bl lb pl F a _ 1‘ l4 141 q A O -rm.o Cowmom Heeoz camp powwomo mmpwm mwu pflm mommSWm pmmoq ca pom: mpmflom memo 1.04 esmmmq w samba x 3..“ + 2.8 a fimd n me + Lr + 3 mW ..O.N m soegang \_- ) l sseox OI X Zmo SGTOH ms (OI .eOQsmdaow mmwpn o:0 a so QHLmCOdeHom :fifimnflafldwm ozp mo pone ma omsmas Orr OH Va .HiOAaX 1. ”H4 rHOPNfiH$Q>.U 33.6 «J \A 4 com) J) o : . to 0: p0 (so a toe coapawe an tcpaasoaao 0.o mo seepompm m.o mmo 0M0 mso sso mwo. N.o H.o L - u I d J l a At OOH. Afio.m new mmm lro.e zmb.mw “mul.o.aoa mmw zm.me mmwm o.ooa .T. fro.m coapomm wcfigoflucm co psmfium mpam was o 0:183 1 ‘f {E - L. ll) 93 on [equeutaec ‘ a 5 (fix - Ax>/<3x - 19THOI' r. c aeaedeg p UO'E A9 A correlation for the height of a transfer unit in an enriching section as a function of the downflow to upflow ratio is shown in Figure 2l. Consistent results were obtained at various gas flow rates and heights of an enriching section in comparison to those of Haas (2A) for a stripping section. The driving forces for mass transfer in a stripping section were found to be very finite at both ends of the column. The curve shown in Figure 22 was calculatec ssuming that the bulk liquid around the bubbles comes to equilibrium with the feed stream at the feed ‘. point, and surface excess, TB’ remains unchanged from its value when it entered the bottom of the column of foam. All other concentrations and driving forces are treated similarly to those derived in the sec— tion on theory. The height of a transfer unit in a stripping section did not correlate with the upflow to downflow ratio as it did for data from a rectifying column. However, the height of a transfer unit divided by the feed liquid flow rate does correlate with the upflow to down— flow ratio for short stripping column$)as shown in Figure 23. For taller column53the data did not correlate very well and this is in agreement with Haas (24), who found data for taller stripping sections to be more inconsistent than for shorter sections. Figure 2A is an attempt to correlate height of a transfer unit data for both enriching and stripping columns on one figure. The flow number was discovered by a trial and error process, and the in— termingling of data points on the V shaped curve is a good indication that there may be some theoretical significance to this plot. I Height of a Transfer Unit HE (inches) 50 lOOd 70+ 0) O Ifi—V— I?! 9—.» a Gas Rate Height of Enriching Section 5‘t . (cm/min.) (inches) 3-~ EB 188.0 . 42.5 2% fl 1A8.5 42.5 I W 0.25 0.35 0.45 0.55 0.65 0.75 Fraction of Overhead LiQuid Returned as Reflux (LR/LC) igure 21 The Height of a Transfer Unit in an Enriching ection Versus the Downflow to Upflcw Ratio. F C U -‘lIIII I I'll 51 .QOHpomm meammflspw w Cfl Hmpoz w zpflz meme HmpCQEfipegmm mo QOmflpddfioo NN mpsmflm AmA\Ouv pflswflq Unexpe>o mmEooem Loan: poem mo coapompm mm. mam mp. asses I/l/IJV mm. b d 3. . mm. D d =m.me a.qa “6N =m.ma n.¢m mmw =m.ma o.oH mmw =m.ma .sas\nso m.aa .+. mm mo pnmamm . spam ewes ma. g pedefnoIeg oq Teduemtaeng 30 01193 52 .Ofipmm BOHHQEOQ op SOHMQD esp Lpflz webmaephoo QOflpomm mcflmmflppm w cfl was: hegmcmpe m mo pzmflm: mm opSmHm AaQ\oav capam soaepzoo cp.3oamga 3.. as. 3.. 3.. mm. mm. 2. .l t. t. 4 . J . m. game in 6 zm.NH mtqm E 4d. 5 .ma 0.3 mm 2m.NH .GHE\MEO m.dH LI L.m. .oom .gawpm 0gp mo pawns: spam emma .fis. Lt F. t. is. ..o.H .ao N 6 Hem 19H Q .0 (gm/Wm) L‘LI/SH area p983 em. fiq ‘PGPIIATECI ”nun JerumJ. E .10 w Height of a Transfer Unit H (cm) l000 00 00 700 600 500 400 3d; 200 100, . 90+ 804 70* 60‘ 50‘ 1+0« 30. ft—til T—TTTI' P p r V I I T 53 Legend Enriching Section Enriching Section RFXZCKD Stripping SeCtion LE = 0 Stripping Section EB El» 69+ 4| ‘- I. 2! L 4 t 1 Jp 4+ fib 1 .02 .03 .0A .06 . .l .2 .3 .4 .5 .7 1.0 2.0 FlOW'Humber 2Q .;_A LD G + LD + L“ V Figure 2A Height of a Transfer Unit Correlation. 5A An attempt was made to correlate tie overh ea: lizuid flow rate f“ Y to the gas flow rate and other variables. To accurate correlation could be found and so the overhead lic_uid flow rate Was assumed to be Hnoth r indepentent variable. ijur 25 and 26 are p“esented "If! ndicate some of the diii iculties encourtered and to rive ‘q H. here to a basis for sizing any future reflux purps. a very approxirate cor— rele ition between overhead foam den ity and gas flow rate was dlSCOVBTEQ for a one—stage separator as shown by Figure 25. Figure 26 is tne appro: ‘mate correlation for overhead foam density as a function 01 the foam densi y number. This last figure utiliz s data f1 on an enriching section, a stripping section, and a cumbifled C01“m”- A graphical solution was develOped for calculating tOp and bottom ractiondtion column with F’) product concentra Mo- in a continuous foa enriching and stripping sections. The solution Has fo*nd from the over-all material balance, and the tOp and bottom product concentra— tions for a set of assumed foam concentr tions at the feed point. (.0 These assumed concentrations were used to calculate driving force in the column which in turn permitted the calculation of a set of pos— sible tOp and bottom product concentrations for run .wz.. Figure 27 is the graphical solution to this set of equations. The CDC Digital(36CK3 Computer was used to make the calculations for a set of runs (Table 30) and the result: "“e given in Table Bl. This Digital Computer was also i used to calculate the slepe ardi tercent of the over—all m aterial bal- ance for the_combined column. A s mmarv 01 equations, which were de- rived in the section on theory and used in the computer program, is given below. Volumetric Fraction of Liquid in the Foam (Hy«}+-lap (cmB/cmB) 55 .lOv .Ogt .080- $ 007" E .064:- & .O5fi- .014.» Legend Bottom Product Concentra ion 03 (gm moles/cm3 solr. x lO ) 60C 607 5'6 507 002‘“. [4"1 500 3'1 305 d P = CG d = 3.02 _9 C = 8.06XJ_O 206 208 .01 4&7 : % 100 200 300 400 Gas Flow Rate G (cmB/min.) Figure 25 A Correlation Between the Amount of LiQuid in the Foam and the Gas Flow Rate for a 71" Cne Stage Separator. ) + L0 Fraction of the Overhead FOam Which is tiquid (G .08 .07 .05 o 0 IO b 69 Stripping Section di- - E Combined Column 56 Enriching Section h p— i be. \J‘( £ 2.0 C312 0:5 110 |._: \n Foam Density Number GB/Ca ( x lO‘lZ) :1in3 gyfilnolis Figure 26 A Correlation for the Cverhead Lifiuid Flow Rate in a Multi-Staged Separator. 57 0.&_ o ,'\ ' 4‘ 'xn‘n*\~“3=*'trl "““n {E} Ebgwiluu“ a uaua a, '33 d. CD ’1 F]. (1‘ H r [”1 £0 H p J O x 0 In = 1.0195 x 10 o 10“) V’ K H B Bottom Product hole Fraction (3 07—1— f" / ‘jfol' Calellattmi values using assumed foam concentrations (It the l-Cvd poinL om- 0.44. 0.; L I l L _l ‘ v- «1/ Y P to 21/” O.) 0.5 L'OO C07 KOO C). ,' m o . H . , A 10p Proguct hole rrzctiod (A, x 10’) Figure 27 Graphical Solution of Fun ALA. 58 The tOp product, LT’ and reflux liquid, LR’ flow rates were cal— culated from the definition of external reflux and a material balance. LR nX LT L0 = LR + LT (2) The bottom product liquid flow rate, LB’ was calculated from the over—all material balance. L = L + L (3) T .Lym The lepe Lm/LB and intercept XF(E: + l) of the over-all material balance for surfactant were calculated from known quantities \ _ LT ‘ LT X13 “ XFS (O) 59 The concentration of the foam at the feed point :UF was assumed along with the following set of driving forces for mass transfer: k 3% c Tfi a k D? c T jg'kl + : Dj ) (7) (‘1 + LF)MV CSoln. C V : C" soln. R )_/ ,2 as k Di, G 13F? (8) (Yet-13‘ " 1r ‘5"); = X'WWT‘ 1" ‘ 'r . - Y U; U1. .1 D 08013104036 UF [— U "rJ rm and ‘2 m k LA G i3 v" _ = _ V (‘UF YUF)E XDF egoln LCDQF ‘UF (9) Also, <1” 1) v (1”) X3? = '“i + YUF ‘ ‘UT _: LR LR <"" > NE“ <) r‘ - Y = ‘ c 10 m E ‘L *3 i U‘ UT CSoln. 03v T These driving forces were calculated by assuming bottom and tOp pro- duct concentrations and comparing trial numbers of transfer units to those calculated from the height of a transfer unit correlation. The circled experimental data point, shown in Figure 27, indicates how accurate this technique is. In Figure 28, the calculated bottom.pro- + duct mole fractions were in agreement to within - 6% and the calculated \‘l illi I! |I.I..ili 13". I lufl I'll .Illn.‘ Ill ii]! i .I h 0 ‘ 1 ' x " nxperimontal hole Fraction (K x 10‘) 1.1, 1.2 1.0 car 0.2 _-_-.‘ 60 Bottom Product hole Fraction "I lop Product hole Fraction 0.2 0.4 C) 1&- p— 0.6 0.8 alcu1atcd Hole Fraction (K x 10') .1 . ' ‘ t 18 Comb 1 ned (,0 .1 umn Mode l . 61 . . . + tOp product mole fractions were in agreement to within — 7.5% of the experimental values. Most of the calculated mole fractions were well within these lindts. 62 DISCUSSION CF ERRCF S The final test of the heiglt of a transfer ur it model, which was shown in Figure 28, was a pleasant surprise considering the amount of scatter in the equilibrium relationship. Rani error con— tributors, such as drainage and internal reflux, were partially can- celled out by the use of the height of a transfer nit correlation, Figire 2A. This correlation was determined by experiin wtal data and then it was used to predict experimental data, and hence much of the inherent error was voided. Internal reflux apparently had a negligible effect, since col— umn Operating conditions were adjusted so as to produce a uniform foam throughout the column and liquid distributors in the foam did not appear to coalesce the foam rising around them. If appreciable internal reflux had taken place, then it would have been acconzpanie ed by drainage because of the decreased amount of surface film area. The overall effect of this internal refluxing and its associated drainage would have been to increase the separations in the enrich— ing and stripping sections. If this ei fec t had talf en place, it would have been less prevalent in the conibined column than in the indivi- dual studies because of the thicker liquid films in the foam and short— er column sections in the combined column. Experimental evidence indicates that drainage was the lias negligible error encountered. Drainage can take place in the absence 63 of internal reflux ty tie thinning of foam liquid films without changing their surface area. The upflow liquid flow rate could have varied by as much as 20% due to foam drainage as shown in Firures 18 and 19. This effect would have been more pronounced in the individual studies than in the combined column, and hence the calculated separations should be on the average smaller than the experimental ones for a combined column. This last effect was observed in Figure 28; the experimental tOp product concen— trations were mostly higher and the bottom product concentrations mostly lower than the corresponding calculated ones. 61+ menmm Other two component surfactant systems should be studied in order to find out how the theory developed in this thesis applies to them. A general height of a transfer unit correlation might then be derivable which would predict the height of a transfer unit from the flow number and surfactant prOperties. A high purity two component surfactant system should be foah fractionated in order to determine the concentration regions where the Gibbs equation can be used to calculate surface excess from surface tension data. This would permit the calculation of equili— brium data from surface tension data. A three component surfactant system should be exan'ned to see whether the height of a transfer unit or the height equivalent to a theoretical plate is the best concept to apply to the foam frac— tionation of multi—component systems. The height of a transfer unit concept best approximates the continuous countercurrent mass trans— fer in a foam fractionation column but the mathematics may become unwieldy. In that case, the height equivalent to a theoretical plate would be the only usable concept even.though the height of a trans— fer unit is more theoretically correct. 65 CONCLUSIONS The height of a transfer unit model was found to be an accurate metho od for predictim separations in a foam fractionation column with enriching and strip1:ing sectio-s. 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HHJJE 106 TABLE XKXL* GRAPFLCAL RESULMS 153‘ Calculated Fottom MA 0 . 50’»; I?“ 'r: O .1103 hEC 0.527 -;: 5A 0 . 5.: 5 1: :.~;-A O . 572 a QB Q . 1400 MA 0 . 5:42 roamet mule :ractlog CJLCJLJted Top ProdJct $0.9 Bractio; O.Y[2 O . 721+ 0.79f 0.95; ;.0)o C 0 gill/v 0.922 1.0'. r.) m - Gram moles of sodium lauryl sulfate and water per cm 107 1 NORQNCL'TU; Ir Empirical constant from the surface excess equation (1.15 X In moles Interfacial area for mass transfer (cmz/cn3 ) Area of the column (15.52 cm2) Empirical constant from the surface excess equation (0.814 X ——6 m moles 10 5727—) PM meles Concentration of sodium lauryl sulfate in water (cx13 soln ) 0'?“ T". as , Concentration of bottom product straam 3 cm soln. *role 3 Concentration of feed stream (C .3 soln ) 3 of solu- o1 tion (W cm3s01n. m mol es 0 ’ F] ' Concentration of tOp proJuct stream (cm; soln.) Area averaged bubble diameter (cm) Driving force at the bottom of the column Logarithmic mean driving force Driving force at the tOp of the column Correction factor for sca1e readings from the Ceno—Dufiour Ten— - 3 siometer Flow number . (LE ‘J + 119 + LU Gas flow rate (cm3/min.) Height of a transfer unit (cm, in.) Height of a-transfer unit in an enriching section (cm, in.) L“ *11 O 108 Height of a transfer unit in an enriching section at total re- flux (cm, in.) Height of a transfer unit in a stripping section (cm, in.) Height of a transfer unit in a stripping section at total overhead (cm, in.) Area to volune constant for dodecahedron shaped bubbles (6.59) Conductivity cell constant (cm—l) Over—all mass transfer coefficient (cm/min.) Liquid flow rate (cmB/min.) Bottom product liquid flow rate (cmB/min.) Downflow liquid flow rate (cmB/min.) Feed liquid flow rate (c1113/min.) Overhead liquid flow rate (cm3/min.) Reflux liquid flow rate (cm3/nin.) TOp product liquid flow rate (cn3/min.) Upflow liquid flow rate (cmB/min.)i Number of transfer units Number of transfer units in an enriching section Humber of transfer units in an enriching section at total reflux Mass transfer rate of sodium lauryl sulfate ( .mmgles) Number of transfer units in a stripping section Number of transfer units in a stripping section at total over- head Average number of ions that sodium lauryl sulfate dissbciates into Universal gas constant (8.3144 x 107.0 1 ) External reflux ratio Scale reading (dynes/Cm) 109 Specific conductance of sodium lauryl sulfate in water (microm- h S/CIZ‘.) . . 0. Temperature of the liquid surface ( h) - 2 Surface excess of sodium lauryl sulfate (gm moles/cm ) C . 1 V . ,3 .y 2) Surface excess oased on XE (gm moles cm 2. Surface excess based on XDF (gm moles/cm ) . . ‘2 Surface excess based on ADP“ (gm moles/cm ) ID 2 Surface excess based on XF (gm moles/cm ) a . 2 Surface excess based on AT (gm moles/cm ) . 2 Surface excess based on KUB (gm moles/cm ) Mole fraction of sodium lauryl sulfate Mole fraction of the bovtom product stream Mole fraction of the downflow stream Mole fraction of downflow stream at the bottom of the column of foam Mole fraction of downflow stream just above the feed point Mole fraction of downflow stream just below the feed point Mole fraction of feed stream XDT = Mole fraction of the tOp product stream Mole fraction of bulk liquid in the upflow stream at the bottom of the column Mole fraction of soiium lau yl sulfate in broken down foam Mole fraction of foam at the bottom of the column hole fraction 01 foam at the feed point XT = Mole fraction of foam at the tOp of the column Equilibrium mole fraction of sodium lauryl sulfate in broken down foam Mole fraction of foam in equilibrium with XD‘ 110 .14 II Mole fraction of foam in equilibrium with either XDFB or XCF *4 II UT Mole fraction of foam in equilibrium with KT 2 = Height of column of foam (cm, in.) 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