This paper deals with the comparison of gas-liquid holdup and froth height on a perforated plate under various operational conditions such as liquid stagnant, cocurrent, countercurrent and crosscurrent gas-liquid flow system.
Tendency to foam is remarkable in countercurrent and crosscurrent flow system. The crosscurrent flow system is suitable for the operation of mass transfer from the point of view of gas-liquid holdup

Miyahara, Toshiro

Takahashi, Teruo

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Hydraulic Properties of Froth Layer on a Perforated Plate

Okayama University Scientific Achievement Repository

Memoirs of the School of Engineering, Okayama University Vol. 17, No.1, February 1983Hydraulic Properties of Froth Layer on a.Perforated PlateTeruo '!'akahashi* and Toshiro Mi.yahara*(Received November 13, 1982)SynopsisThis paper deals with the comparison of gas-liquidholdup and froth height on a perforated plate undervarious operational conditions such as liquid stagnant,cocurrent, countercurrent and crosscurrent gas-liquidflow system.Tendency to foam is remarkable in countercurrentand crosscurrent flow system. The crosscurrent flowsystem is suitable for the operation of mass transferfrom the point of view of gas-liquid holdup.IntroductionThe dispersion of gas through a perforated plate is of interestin the design of various plate columns and bubble columns employed inoperations involving distillation, absorption, stripping and otherseparations. The efficiency o~ contact related to mass transferbetween gas and liquid is o.ffected by operational conditions such asliquid stagnant, cocurrent, countercurrent and crosscurrent gas-liquidflow system. Therefore, gas-liquid holdup and froth height on a platein these flow systems are very important factors. The authors haveinvestigated these properties on a perforated plate under differentcontact systems between gas and liquid(l-7).This paper concerns the comparison of the difference between the* Department of Industrial Chemistry2 . Teruo TAKAHASHI and Tashiro MIYAHARAabove properties under each flow system.1. Summary of Previous Work1.1 Liquid HoldupFew researches have been reported about liquid holdup on a perforatedplate in cocurrent flow system.Hiratsuka et al. (9) have proposed the relationships predictingliquid holdup in countercurrent flow system. The correlationscontain a function of gas-liquid mass flow rate ratio and gas velocitythrough hole, whereas the effect of physical properties of liquidwas not found.Kamei et al. (10) have proposed the following equation in relationto froth height in crosscurrent flow system:Smith et al. (11) have given accounting for weir height,(1 - 1)H 0.725H - 1.84xlO-8H U ;p- + 9.3 x lO- 8Q/B + 0.0061,w w gc g (1 - 2)and Shono et al. (12) have given the following equation:H (0.333HW + d + 0.002 + 2U n )!/,og(lOOOU n Iu ).~c ~c gcF = 0.06-0.09, d = 0.005-0.015 m, Hw= 0.03-0.09 mUJI,c 0.0033-0.00'88 mis, Ugc = 0-1.38 mls(1 - 3)The above each relationship contains the effect of weir height, whilethe effect of physical properties of liquid is not noticed.1.2 Gas HoldupThe effect of gas distributor on gas holdup under liquid stagnantflow system has been reported by Houghton et a1. (13) as follows: gasholdup was affected by geometry of plate. On the other hand, Shulmanet al. (14) has reported that gas holdup was not affected by geometryof porous plate.For bubble column, where a deep pool of liquid is commonly used,Akita et al. (15) proposed the following equation:Hydraulic Properties of Froth Layer on a Perforated Plate 3Kato(8) has shown the gas holdup for bubble column with bothcocurrent and countercurrent gas-liquid flow. However, little hasbeen found about gas holdup in crosscurrent flow system.1.3 Froth HeightOnly a few studies have been made of froth height on a perforatedplate. Azbel(16) has analyzed theoretically the froth height with noliquid flow and given the following equation:h f = H (1 + ;pr). (1 - 5)However, few studies on froth height have been carried out fordifferent gas-liquid flow systems.2. Hydraulic Properties of Froth Layer on a Perforated PlateAs shown in Fig.l, when gas is dispersed through a perforated plateGast t tttFroth layer(Froth height)II--------i~J: (Liquid holdup)------------Perforated plateliquid fractionGaS void fractionGas liquid fractionratiomean valueyr = H/hf1- tf"= 1- H/hf=(hf-H)lhf(1- t£')/P"=(hf- H)/HFig.l Definition of gas-liquid fraction4 Teruo TAKAHASHI and Tashiro MIYAHARAGasLiquidI~III~ t(a) liquidstagnantflow(b)Gas-liquid (c)Gas-liquid (d)Gas-liquidcocurrent countercurrent crosscurrentflow flow flow·Fig.2 Froth layer on a perforated plateinto liquid, its liquid depth being H, froth, with the height of h f ,is formed. Gas holdup in the froth, ~, has a profile over a plate,and the integration of ~ from the plate to the top of the froth heightgives mean gas holdup,l-~.Figure 2 shows various flow systems. Characteristics of froth ona plate are as follows: (a)Liauid depth, H, becomes froth height, h f ,by the contact between gas and liquid. (b) Froth breaks down at thetop of the column, and liquid flows over a weir. (c) Liquid depth canbe determined mainly by gas flow rate, and liquid holds up on a plate.(d) Properties of froth are affected by weir height.Liquid depth for liquid stagnant flow system(a) is determinedspontaneously. Bubbles formed from a perforated plate are accompaniedby wakes on the rear sides. The wakes cause a circulation of liquidin froth. The liquid depth in the froth shown in Fig.2 (D), (c) and(d) is determined by operational conditions. h f , ~ and l-~ for eachflow system have inherent values respectively.Table 1 shows the operational conditions and the dimensions of theapparatus employed in the previous work(1,2,4-7) briefly.3. Liquid HoldupTable 2 shows the comparison of some empirical equations predictingliquid holdup obtained by the authors(1,2,5,7).H in liquid stagnant flow system is determined spontaneously.Hydraulic Properties of Froth bayer on a Perforated Plate 5Table 1 Experimental conditions4,7)o '" 1Flow Column Hole Plate Gas Liquidsystem diameter diameter perforation velocity velocity References-----------------~~~~------~~~~------~::~~_:~=~-----~g~~~~~~-----~!~~~~~~---------Liquid 0.00071'" 0.0011'"stagnant 0.04"'0.15 0.00306 0.0623cocurrent 0.06"'0.15 0.00071'" 0.0017'"0.00306 0.0535 o '" 1.16 o '" 0.35 5,7)counter-current 0.06"'0.150.0007]'" 0.0071'"0.0062 0.508 o '" 6 o '" 0.09 1.2,5)Cross-currentB=0.08"'0.15m 0.00073'" 0.0044'"L=O. 1"'0. 3m 0.0027 0.1087 o '" 1 Q=20XIO-6"'900XIO-6 6,7)m3/sTable 2 Liquid holdup,Ha LlqUld stagnsntH is determined spontaneously (2-1)b--~~~~~~~~~7)-----------------------------------------------------------------------------H/L ={l + 0.065(Fr 1/2/Fr 1/6)0.85)-1 (2-2)T 2 9 tc 2Frg=ugc /(gd), Frtc=Utc /(gLT)~--~~~~~~~~~~~~~~1~2r------------------------------------~---------------------------------1 ~d U h 2 40 ~t Uth 2HPt=(~){29(~) Pg+~Odg + Cl-~ht)2g(--t--) p t ) C2-3)kPgUgh2{t/Cl-t»3{3-2.4FCl-t»=2.2Pt(2-~ht)Uth2+8.68Xl0]CO.0316d-3/4 -O.87)X(10000-28.7)~tl/4Pt-l~ht3~t=2.2+{8.68xl03CO.03l6d-3/4-0.87)ClOOOO-28.7)~tl/4Pt-2/(Uth/t)2J,th=1,to=0.34B=1.34Ct2/Utc)1/250l/20~t-1/25+9.l5xlO-9{Ugc/(Utcl/2Ft1/4~tl/5»2; F=0.05"'0.2B=0.326{Fl / 5/CU. 1/12tl/15»o-2/9~.-1/50+1.18xlO-4{u leu. 1/3t l/5»2 ; F=0.2"'0.5~c ~ gc ~ct d=k[{1-FCl-t»2+ 0 . 4{1.25-F(1-t»], k is a function of tid C~btained byMcAllister et al. 17 »d--~~~~~~~~~~~~7r-------------------------------------------------------------------------.Fr =U 2/ (gd) ,9 gc;;, 3, n=l> 3, n=2Fr t ={Q/{BL)}2/(gHw)(2-4)However, the effect of physical properties of liquid is noticed incountercurrent flow system. Column height for cocurrent, weir heightfor crosscurrent and perforation ratio and hole diameter for counter-current are main factors controlling liquid holdup on a perforatedplate.6 Teruo TAKAHASHI and Toshiro MIYAHARACountercurrent,Ulc=O·OO2m1sd =0·00421 m,F=0·153d=0.004m,F=0·0896----------....- .. .-- --.....--- ~l-------------- I------ ....._~',,/ ---0-0-0·....0 --Hw=0.05mHw =O.l mCrosscurrent, Eq.(2-4)d::0·001m,Q/(BL)=0.1 m/sAir-water---26426410' Fi-----------------.:-::.:--::-.::..:-~--nEuI6424 6 10°Ugc Cm/s ]24 6Superficial gas. velocity,210-2 L_..I-....L.-.J.::t:!!~*-===:::!!.L._L..JL.L..Ll.LIJL___..I.._-L_LJ...L..u.LJ10-2Fig.3 Liquid holdup for each flow systemFigure 3 illustrates an example of the comparison of liquid holdupfor each flow system. The effects of column height in cocurrent andweir height in crosscurrent are remarkable, and liquid holdup increaseswith increasing column height or weir height, respectively. Llquidholdup in cocurrent and crosscurrent decreases with increase of gasvelocity, while that in countercurrent increases, and decreases withperforation ratio. These could be interpreted due to the simultaneouspassage of gas and liquid through holes of a perforated plate.4. Gas HoldupGas holdup shows a profile over a plate. Figure 4 representsvertical profiles of liquid fraction on a perforated plate obtainedby means of y-ray technique in liquid stagnant flow system. Fromthis chart, the vertical profile is div~ded into three regions.i) Bubble formation regionHydraulic Properties of Froth Layer on a Perforated Plate 7In this region, burbles are formed at the surface of the plateand stagnant near here as dependent on the growing velocity.Liquid fraction decreases abruptly. This is remarkable at highgas velocity.ii) Middle. regionThis is observed remarkably at high liquid depth and a constantliquid fraction is found.iii)Foam layer regionThis region, which is found at the upper section of the froth layer,shows an abrupt. decrease of liquid fraction, and an increase ofthis region is noticeable at higher gas velocity, while bubbleformation region decreases.ZCm]0 0.1 0·2 0 0·1Ugc= 0.36 m/s Ugc= O· 74 m/s Ke H[ mJ0 0·03• 0·050·070·10c 0·150ti 0·5 0·20~];!:J.~...J0 0.10 0·1 0;2 0 0·2Z Cm J Distance Z Cm J(a) (b) (c) (d)d =0·0008 m , m = 974 , tid = 1 F=0.0623. D =0·1 mAir - waterFig.4 Vertical profile of liquid fraction on aperforated plateEach flow system shown in Fig.2(b), (c) and (d) has a similar tendency.Figure 5 shows an example of vertical profile of liquid fractionin cocurrent and crosscurrent flow system. In cocurrent flow system(a),vertical profile has a similar tendency to the case of liquid stagnantflow system, while profile in crosscurrent flow syste~ is affectedby weir height. Vertical profile of liquid fraction in countercurrentflow system is not shown here because of the difficulty of themeasurement by means of y-ray technique for very low froth height.Table 3 includes the relationships of mean gas-liquid fractionratio, (l-~)/~, obtained by the authors previously with each flow system.8 Teruo TAKAHASHI and Tashiro MIYAHARA1·0r-----r--'T"""-""""T--:----....,Fig.5 Vertical profile of liquidfraction on a perforated1·4Key H CmJ0·2 0·4 0·6 0.8 1·0 1·2Distance z C m J(a) CoturrentAir-waterd=0·00084 mm=3036=0.1 mo 0.053• 0.075~~'3m"<t ~ ~'.~~\ ~ \ Ugc=O.l1 m/s\Q=573Xl0-6m3 /s00L.,__.L..._..lo.oI.L. ~~~~~__..10·05Distance z(b) CrosscurrentAir-water60.5....u~-nIU~Mean gas holdup decreaseswith increasing stream velocityin cocurrent flow, whereas thatin countercurrent flow increases.No significant effect of liquidflow is found in crosscurrent,although that of perforationratio is noticed. In each flowsystem, mean gas holdup increaseswith gas velocity.(l-~)/~ for each flow system isillustrated in Fig.6. In thischart, (l-~)/~ is plottedagainst Fr(=U 2/(gH» which isgcthe Froude number based on liquiddepth. (l-~)/~ for cocurrentflow is smaller than that forliquid stagnant flow, while thatfor countercurrent flow is larger.(l-~)/~ for crosscurrent flowis also larger. We can findtransitional points in liquidstagnant, cocurrent and counter-current flow system at aboutFr=8.5xlO-4 • On the other hand,the transitional Froude numberin crosscurrent flow decreaseswith perforation ratio, F, and(l-~)/~ exhibits the effect of F.Further, gas holdup shows a platedifferent behavior dependent on whether liquid is foaming materialor not. The above results are those for non-foaminq materials.5. Froth HeightFroth height can be calculated from the relationships of gasholdup and liquid holdup. According to the analysis of Azbel(16)and the results of the authors, it is found that froth height becomesa function of the Froude number, Fr based on liquid depth.Hydraulic Properties of Froth Layer on a Perforated PlateTable 3 Gas liquid fraction ratio. (l-~)/~=(hf-H)/H9a Liquid stagnant4 , 7)(1-'1') /'1'=6. slFr(1-'1') /'1'=2 31Fr-4; Fr<8.SxI0= -4; Fr>8.SxI0(3-1)b CocurrentS)(1-'I')/'I'=6.SIfr/{1+6.slFr(U. /u )}",c gc(1-'1')/'1'=2 31F:r/{1+2 31F:r(u. /u )}",c gcc CountercurrentS )(1-'1') /'1'=6. slF:r/ (l-6. SIFr"(Uj,c/Ugc) }(1-'1')/'1'=2 3,1fi""/{l-2 3,1fi""(U. /u )}",c gc-4Fr~8.SxI0Fr>8.Sxl0-4Fr~8.sxl0-4Fr>8.Sxl0-4(3-2)(3-4)d Crosscurrent6 )(1-'I')/'I'=8.S,Ifi""(1_'I')/'I'=1.2SFrl/4F-O.14Fr~4.68xl0-4F-O.S6Fr>4.68xl0-4F-O• S6(3-4)10- 2 2Froude number, Fr (= ~~c ) [- ]Fig.6 Meari gas liquid fraction ratio for each flow system10 Teruo TAKAHASHI and Toshiro MIYAHARATable 4 Froth height, hfa Liquid stagnant4 , 7)hf=H (1+6. Sm)hf=H (1+2 3m )-4Pr~8.Sx10-4Pr>8.Sx10(4-1)b CocurrentS)-4h f =HI1+6.SIFr/{1+6.S!F:r(U. /U )Ij 1 Pr<8.Sx10",c gc =h f =HI1+2 31Fr/{1+2 3!F:r(U. /U )Ij 1 pr>8.S x10-4",c gc(4-2)c CountercurrentS). -4hf=HI1+6.SIFr/{1-6.SIFr(UJI,c/Ugc)Ij 1 Pr~8.Sx10 (4-3)h f =HI1+2 31Fr/{l-2 3,1fi"(U. /U ) Ij 1 pr>8.S x10-4",c gcd CrosscurrentG, 7)hf=H(1+8.S~) 1 pr;4.68x10-4p-O.56hf=H(1+1.2spr1/4p-O.14) 1 pr>4.68x10-4p-O. 56(4-4)32Countercurrent,Eq.(4-3H=O·l m Ule= 0·1 m/sLiquid stagnant,Eq.(4 -1 )H =0·1 m••••o 0·1• 0·05Key H [m]75vol% aqueousglycerine solutionliquid stagnant2642Crosscurrent, Eq.(4-4)H=0·lm,F=0.056 C--.:t~::::t=f:J:Jm:I=-=~~~=i;;i;D::i::;~....l.......J10-2 2 4 6 10- 1 2 4 6 10°-~QIc::,-.cen.~.c.c"0...-nIU::r:--L:.Superficial gas velocity, Ugc Cm/s ]Fig.? Relative froth height for each flow systemHydraulic Properties of Froth Layer on a Perforated Plate 11In any flow systems, froth height increases with gas velocity.Table 4 shows the relationships of froth height obtained from theresults of liquid holdup shown in Table 2 and those of gas holdupshown in Table 3. The transitional Froude number, Fr, is found ineach flow system. This is probably due to the transition from bubbleto froth flow systems.Figure 7 compares the relative froth height, hf/H, against gasvelocity in each flow system. From this figure, it is found thatthe tendency to foam is remarkable in countercurrent and crosscurrentflow system. As liquid holdup increases with gas velocity in counter-current as shown in Fig.3, it is considered that the crosscurrent flowsystem is most effective for the operation of mass transfer. The resultsof aqueous glycerine solution, which is a foaming material, underliquid stagnant flow are plotted in Fig.7.At small gas velocity,hf/H shows the maximum and becomes independent of species of liquidsat higher gas velocity. At that point, we can notice a cellular foam,though the phenomenon could not be explained by static propertiesof liquid such as density, viscosity and surface tension. Thisis perhaps due to dynamic properties such as surface tension gradientand surface viscosity.Conclusions1) Liquid holdup in cocurrent and crosscurrent gas-liquid flowsystem decreases with gas velocity, whereas that in countercurrentincreases.2) Mean gas liquid fraction ratio in each flow system is correlatedwell with the Froude number based on liquid depth. Mean gasholdup decreases with liquid velocity in cocurrent and increases incountercurrent, while that in crosscurrent is not affected byliquid flow.3) Froth height in each flow system increases with gas velocity, andcan be determined mainly by liquid holdup and the Froude numberbased on liquid depth.4) Tendency to foam is remarkable in countercurrent and crosscurrentflow system.S) Crosscurrent flow system is suitable for the operation of masstransfer.12 Teruo TAKAHASHI and Toshiro MIYAHARANomenclatureSd,Sg"sa,Sh = resistance coefficients duesurface tension and liquid holdupPg,Pg,= density of gas and liquida surface tensionBDdFFrFrgFrg,Frg,cgHmweir widthcolumn diameterhole diameterperforation ratioFroude number(=U 2/ (gH}}gC 2Froude number(=U I(gd}}gc 2Froude number (={Q/(BL}} l(gH }}2 wFroude number(=ug,c l(gLT )}gravitational accelerationliquid holdupweir heightfroth heightcoefficientliquid flow path lengthcolumn heightplate thicknesshole numberliquid flow J;'atesuperficial gas velocitygas velocity through holesuperficial liquid velocityliquid velocity through holeaeration factor[ m ][ m ][ m ][ - ][ - ][ - ][ - ][ - ]2 ]m/s[ m ][ m ][ m ][ - ][ m ][ m ][ m ][ - ][ m3/s ][ m/s ][ m/s ][ m/s ][ m/s ]- ]to gas, liquid,[ - ]kg/m3 ][ N/m ]ratio of hole area of dropping liquid flow per totalhole area of a perforated plateviscosity of liquidkinematic viscositygas holdupmean liquid holdupReferences[ - ]Pa.s ]m2Is ][ - ][ - ](I) T.Takahashi, M.Tanaka and S.Sudo: Kagaku Kogaku, 34 (1970), 744.Hydraulic Properties of Froth Layer on a Perforated Plate 13(2) T.Takahashi and M.Tanaka: ibid., ~ (1971), 595.(3) T.Takahashi, R.Matsuno and T.Miyahara: J. Chern. Eng. Japan, 6(1973),38.(4) T.Takahashi, T.Miyahara and K.Shimizu: ibid., 7 (1974) ,75.(5) idem: ibid., I (1974), 312.(6) T.Takahashi, T.Miyahara and T.Sato: ibid., 12 (1979),269.(7) T.Miyahara: Doctoral Dissertation, Kyoto University, (1982).(8) Y.Kato: Kagaku Kogaku, ~ (1962), 1068.(9) K.Hiratsuka, S.Masuda and N.Hashimoto: Kagaku Kogaku, 30 (1960),38.(10) S.Kamei, T.Takamatsu, S.Mizuno and Y.Tomizawa: Kagaku Kogaku,18 (1954),108.(11) B.D.Smith: "Design of Equilibrium stage Processes", McGraw-Hill,New York, (1963).(12) H.Shono, T.Suzuki and M.Hirata: Kagaku Kogaku, 31 (1967), 886.(13) G.Houghton, A.M.Mclean and P.D.Ritchie: Chern. Eng. Sci., 7(1957), 40.(14) H.L.Shulman and M.C.Molstad: Ind. Eng. Chern., 42 (1950), 1058.(15) K.Akita and F.Yoshida: Ind. Eng. Chern., Process Des. Dev.,12 (1973), 76.(16) D.S.Azbel: Khim. Prom., No.ll (1962), 854; idem: Intern. Chern.Eng., l (1963), 319.(17) G.A.McAllister, P.H.McGinnis and C.A.Plank: Chern. Eng. Sci.,9 (1958), 25.

Hydraulic Properties of Froth Layer on a Perforated Plate

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