OF SIEVE TRAY EFFICIENCY
OF SIEVE TRAY EFFICIENCY
S. R. Syeda, A. Afacan, and K. T. ChuangS. R. Syeda, A. Afacan, and K. T. Chuang
Ã
Ã
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada.
Abstract:
Abstract: A phenomenological model for froth structure is proposed based on the analysis of A phenomenological model for froth structure is proposed based on the analysis of froth images of an active sieve tray taken from a 0.153 m distillation column. Froth is defined froth images of an active sieve tray taken from a 0.153 m distillation column. Froth is defined as
as a a comcombinbinatiation on of of bubbubblebles s and contiand continuonuous us jetjets s that that brebreak ak the the sursurfacface e of of frofroth th proprojecjectintingg liq
liquid uid splsplashashes es and and drodrops ps aboabove ve the the sursurfacface. e. TTo o estestimaimate te the the frafractiction on of of smasmall ll bubbubblebles s inin froth, a fundamentally sound theoretical expression is derived from turbulent break-up theory. froth, a fundamentally sound theoretical expression is derived from turbulent break-up theory. A
A new new modmodel el for for prepredicdictinting g poipoint nt efefficificiencency y of of crocross-ss-flow flow siesieve ve tratrays ys has has beebeen n devdeveloelopedped based on the hydrodynamics of an operating sieve tray represented by the proposed froth based on the hydrodynamics of an operating sieve tray represented by the proposed froth struc-ture model. This efficiency model is applicable for both froth and spray regime. Fraction of ture model. This efficiency model is applicable for both froth and spray regime. Fraction of by-passed or uninterrupted gas jet is considered as the determining factor for froth to spray by-passed or uninterrupted gas jet is considered as the determining factor for froth to spray tran-sition. The net efficiency is estimated by adding up the contributions of both bubbles and jets sition. The net efficiency is estimated by adding up the contributions of both bubbles and jets present in the dispersion. The model is tested against the efficiency data of cyclo-hexane present in the dispersion. The model is tested against the efficiency data of cyclo-hexane// n-heptane and i-butane
n-heptane and i-butane//n-butane mixtures.n-butane mixtures.
Keywords:
Keywords: distillation; tray efficiency; froth; turbulent break-up; bubble sizedistillation; tray efficiency; froth; turbulent break-up; bubble size
INTRODUCTION
INTRODUCTION
The
The simsimultultaneaneous ous masmass s and and heaheat t tratransfnsfer er com
combinbined ed witwith h the the comcompliplicatcated ed twotwo-ph-phasease fluid dynamics make distillation formidable to fluid dynamics make distillation formidable to conduct any fundamental analysis of conduct any fundamental analysis of distilla-tion. Furthermore, distillation became a tion. Furthermore, distillation became a well-estab
establishelished d indusindustry try long before long before the the theortheoryy of
of tratranspnsport ort phephenomnomena ena was was estestablablishished.ed. Th
Thusus, , ththe e cocommmmon on trtrenend d of of didiststilillalatitionon resea
research rch to to date mostly date mostly remairemains ns empirempirical,ical, se
semi mi emempipiriricacal l or or memechchananisistitic c in in nanatuturere.. Ma
Mass ss trtranansfesfer r efefficficieiencncy y in in didiststilillalatition on isis as
assosociciatated ed wiwith th ththe e flufluid id dydynanamimics cs on on aa sie
sieve ve tratray y thathat t detdetermermineines s the the disdisperpersiosionn str
structucture ure or or the the concontactact t arearea a betbetweeween n thethe gas and liquid phases. The flow regimes on gas and liquid phases. The flow regimes on a sieve tray influence the efficiency directly a sieve tray influence the efficiency directly by
by affeaffecting the cting the interinterfaciafacial l area. Numerouarea. Numerouss studies on flow regimes have been done to studies on flow regimes have been done to unde
understanrstand d the the hydrohydrodynadynamic mic behabehaviour of viour of sieve trays. Most of these studies are mainly sieve trays. Most of these studies are mainly focussed on the transition from froth to spray focussed on the transition from froth to spray reg
regimeime. . The definiThe definitiotion n of of frofroth th itsitself is elf is stistillll very vague in the literature. In froth regime, very vague in the literature. In froth regime, th
the e prpresesenence ce of of pupulslsatatining g jejets ts rarangnges es of of bub
bubblebles, s, liqliquid uid splsplashashes es and and drodropleplets ts givgivee rise to a highly complex dispersion structure. rise to a highly complex dispersion structure. The
The tratraditditionionallally y perperceiceived ved picpicturture e of of thethe froth regime consists of bubbles in a liquid froth regime consists of bubbles in a liquid co
contntininuouous us phphasase e anand d ththat at of of ththe e spsprarayy regime consists of droplets in a gas regime consists of droplets in a gas continu-ous
ous phaphase. se. TheThese se defidefinitnitionions s of of frofroth th andand spr
spray ay regregime ime sugsuggesgest t a a sudsudden changden change e inin th
the e nanatuture re of of twtwo-o-phasphase e mimixtxturure e in in ththee tra
transnsititioion n zozone ne anand d ask ask fofor r twtwo o sesepapararatete ex
exprpresessisionons s of of ininteterfarfacicial al ararea ea to to prprededicictt th
the e trtray ay efefficficieiencncy y in in ththesese e twtwo o reregigimemes.s. Zu
Zuididererweweg g (1(198982) 2) and and StSticichlhlmamair ir (1(197978)8) developed their tray efficiency models based developed their tray efficiency models based on this approach.
on this approach.
The FRI efficiency data of commercial sieve The FRI efficiency data of commercial sieve trays, on the other hand, show smooth trays, on the other hand, show smooth tran-sition of tray efficiency from the weeping to sition of tray efficiency from the weeping to flo
flooodidinng g ppoiointnt. . ThThis is cocompmpeelllleed d mamanyny res
researearchechers rs to to resresort ort to to a a sinsingle gle efefficificiencencyy mo
modedel l fofor r boboth th frfrototh h anand d spspraray y reregigimemes.s. Mos
Most t of of the the exiexististing ng tratray y efefficificiencency y modmodelsels (AI
(AIChEChE, , 1951958; 8; ChaChan n and and FaiFair, r, 1981984; 4; CheChenn and Chauang, 1993) are of this type.
and Chauang, 1993) are of this type.
None of the abovementioned models took None of the abovementioned models took into account the
into account the strucstructure of ture of the two-phasthe two-phasee mixture that is generated on the tray in mixture that is generated on the tray in differ-ent regimes. The only major attempt that ent regimes. The only major attempt that con-sid
siders ers the the disdisperpersiosion n strstructucture ure in in the the frofrothth regime was made by Prado and Fair (1990) regime was made by Prado and Fair (1990) for the air
for the air //water system. They treated the dis-water system. They treated the dis-persion as three regions: a region near the persion as three regions: a region near the tray where the gas can either be jetting or tray where the gas can either be jetting or bubbling, a bulk froth region which contains bubbling, a bulk froth region which contains bubbl
bubbles es with with bimobimodal dal distrdistributiibution on dispedispersedrsed in the liquid and a spray region at the top. in the liquid and a spray region at the top. How
Howeveeverr, , thethey y ignignoreored d the the sprspray ay regregion ion inin the
their ir detdetailailed ed masmass s tratransfnsfer er modmodel. el. LatLaterer,, Ga
Garcrcia ia anand d FaFair ir (2(200000a0a, , b) b) exextetendnded ed ththisis mod
model el to to othother er syssystemtems. s. TheTheir ir modmodel el waswas sh
showown n to to agagreree e fafavovoururabably ly wiwith th a a wiwidede range of
range of data. Howeverdata. However, , severseveral al adjusadjustabletable
Ã
ÃCorrespondence to:Correspondence to: Dr K.T. Chuang, Department Dr K.T. Chuang, Department of Chemical and Materials of Chemical and Materials Engineering, University of Engineering, University of Alberta, Edmonton, AB, Alberta, Edmonton, AB,
Canada, T6G 2G6. Canada, T6G 2G6. E-mail: karlt.chuang@ E-mail: karlt.chuang@ ualberta.ca ualberta.ca DOI: 10.1205/cherd06111 DOI: 10.1205/cherd06111 0263–8762/07/ 0263–8762/07/ $30.00 $30.00
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0.000.00 Chemical Engineering Chemical Engineering ResearcResearch h and Designand Design Trans IChemE, Trans IChemE, Part A, February 2007 Part A, February 2007 # #2007 Institution2007 Institution of Chemical Engineers of Chemical Engineers
parameters needed to be introduced at different stages of the parameters needed to be introduced at different stages of the model to emphasize its mechanistic nature. Bennett model to emphasize its mechanistic nature. Bennett et al.et al.
(19
(1997)97), , devdeveloeloped ped a a poipoint nt efefficificiencency y modmodel el basbased ed on on thethe mechanistic analysis of sieve tray froth height. The model mechanistic analysis of sieve tray froth height. The model considers the fluid on the tray to be contained in a considers the fluid on the tray to be contained in a liquid-con-tinuous region near the tray deck and a vapour-conliquid-con-tinuous tinuous region near the tray deck and a vapour-continuous region on top of the liquid-continuous region. The finial region on top of the liquid-continuous region. The finial simpli-fied model takes into account the mass transfer of the liquid fied model takes into account the mass transfer of the liquid continuous region only and thus has limited applicability in continuous region only and thus has limited applicability in spray regime. A recent study of van Sinderen
spray regime. A recent study of van Sinderen et al.et al. (2003),(2003), tha
that t deadeals ls witwith h ententrairainmenment nt and and maxmaximuimum m vapvapour our loaload d of of tr
trayays s prpresesenented ted a a twtwo o or or threthree e lalayeyer r momodedel l of of ththe e twtwo- o-phase mixture on the tray. This study, although provides a phase mixture on the tray. This study, although provides a detai
detailed insight into led insight into the dynamics of the dynamics of the froth, the froth, particparticularularlyly the mechanisms of entrainment formation but was unrelated the mechanisms of entrainment formation but was unrelated to mass transfer efficiency.
to mass transfer efficiency.
From the above discussions it is evident that most existing From the above discussions it is evident that most existing correlations for point efficiency are highly empirical and do correlations for point efficiency are highly empirical and do not deal with froth dynamics on a sieve tray. The very few not deal with froth dynamics on a sieve tray. The very few studies, which consider the nature of the dispersion structure studies, which consider the nature of the dispersion structure in their models generally, ignore the contribution of drops and in their models generally, ignore the contribution of drops and sprays. These models agree with a wide range of data when sprays. These models agree with a wide range of data when using adjustable parameters, but are less applicable in spray using adjustable parameters, but are less applicable in spray regime on theoretical ground.
regime on theoretical ground.
In this study, the froth regime is modelled based on the In this study, the froth regime is modelled based on the analysis of froth images taken from a 0.153 m diameter analysis of froth images taken from a 0.153 m diameter distil-lation column. The model describes the froth as a lation column. The model describes the froth as a combi-nation of bubbles and continuous jets. At higher gas load, nation of bubbles and continuous jets. At higher gas load, the
the jetjettinting g frafractioction n domdominainates tes and gives rise and gives rise to to the spraythe spray reg
regimeime. . ThiThis s frofroth th modmodel el is is furfurthether r adoadoptepted d to to devdeveloelop p aa fundamental model for predicting sieve tray efficiency. The fundamental model for predicting sieve tray efficiency. The efficiency model takes into account the contribution of both efficiency model takes into account the contribution of both bubbles and jets to the net mass transfer.
bubbles and jets to the net mass transfer.
MODEL STRUCTURE
MODEL STRUCTURE
Froth images taken in a 0.153 m diameter distillation column Froth images taken in a 0.153 m diameter distillation column are shown in Figures 1 and 2. Based on a careful study of are shown in Figures 1 and 2. Based on a careful study of these kinds of froth images, a froth structure has been these kinds of froth images, a froth structure has been sche-matically presented in Figure 3, where froth is shown as a matically presented in Figure 3, where froth is shown as a com
combibinanatiotion n of of jejets, ts, bububbbbleles s anand d liliququid id spsplalashshes. es. ThThee images (Figures 1 and 2) show that the liquid droplets and images (Figures 1 and 2) show that the liquid droplets and
splashes constitute a major part of the froth. A portion of the splashes constitute a major part of the froth. A portion of the droplets is formed when bubbles break out of the surface of droplets is formed when bubbles break out of the surface of the froth. However, the presence of liquid splashes confirms the froth. However, the presence of liquid splashes confirms that some of the gas jets manage to penetrate through the that some of the gas jets manage to penetrate through the froth without forming bubbles and generates liquid splashes froth without forming bubbles and generates liquid splashes at
at the end the end of of liliququid id concontintinuouous us zonzone. e. FigFigurure e 4 4 is is a a momorere detailed representation of the froth model, showing both jetting detailed representation of the froth model, showing both jetting and bubbling zones. The jetting zone elaborates how some of and bubbling zones. The jetting zone elaborates how some of the gas jets formed at the sieve tray holes, cross the froth the gas jets formed at the sieve tray holes, cross the froth uninterrupted and throw liquid splashes above by tearing up uninterrupted and throw liquid splashes above by tearing up the liquid surface. The bubbling zone shows the process of the liquid surface. The bubbling zone shows the process of large and small bubble formation in the froth. Both zones are large and small bubble formation in the froth. Both zones are present and remain intimately mixed with each other in real present and remain intimately mixed with each other in real fro
frothth. . No No jejettitting ng is is achachievieved ed at at a a relrelatiativevely ly lolow w liliququid id flowflow rate
rate. . This regime is This regime is callcalled ed bubbubblinbling g regregime, which ime, which occoccursurs close to the weeping limit and is
close to the weeping limit and isof limited signiof limited significance for com-ficance for com-mercial sieve tray operation. As the gas load is increased, an mercial sieve tray operation. As the gas load is increased, an increa
increasingly greater proportiosingly greater proportion of n of gas passes the gas passes the disperdispersion insion in the form of jets. The spray regime occurs when most of the the form of jets. The spray regime occurs when most of the gas jets formed at the orifice, reach the liquid surface gas jets formed at the orifice, reach the liquid surface uninter-rupted and project the liquid up to form small drops. Unlike in rupted and project the liquid up to form small drops. Unlike in froth regime, where bubble
froth regime, where bubbles form s form a major part a major part of the of the interfainterfacialcial area, in spray regime drops are the only contributor to the area, in spray regime drops are the only contributor to the interfa
interfacial area. cial area. The point The point efficefficiency is iency is estimateestimated by d by combinicombiningng Figure 1.
Figure 1.Froth image of pure methanol on a sieve tray in a 0.153 mFroth image of pure methanol on a sieve tray in a 0.153 m distillation column.
distillation column.
Figure 2.
Figure 2.Froth image of 67 wt% methanolFroth image of 67 wt% methanol//water mixture on a sievewater mixture on a sieve tray in a 0.153 m distillation column.
tray in a 0.153 m distillation column.
Figure 3.
Figure 3. Schematic representation of froth on an operating sieveSchematic representation of froth on an operating sieve tray.
the
the concontribtributioutions ns from both from both bubbbubbling and ling and jettjetting ing zonzones es thatthat exist on a tray.
exist on a tray.
E
E OGOG
¼
¼
(1(1À
À
f f ii))E E BBþ
þ
f f iiE E j j (1)(1)where
where f f j j is the volume fraction of the gas that bypasses theis the volume fraction of the gas that bypasses the
bubbles as continuous jets,
bubbles as continuous jets,E E BBandandE E j jare contributions of bub-are contributions of
bub-bling and jetting zone, respectively, to the net point efficiency. bling and jetting zone, respectively, to the net point efficiency. Due to incomplete break up of the large (primary) bubbles both Due to incomplete break up of the large (primary) bubbles both large (primary) and small (secondary) bubbles coexist in large (primary) and small (secondary) bubbles coexist in bub-bling zone. Thus
bling zone. Thus E E BB has contributions from both large andhas contributions from both large and
small
small bubblebubbles,s,
E
E BB
¼
¼
(1(1À
À
FSBFSB))E E LBLBþ
þ
FSBFSBÃ
Ã
E E SBSB (2)(2)where
where FSBFSBis the fraction of small bubbles.is the fraction of small bubbles.
THEORY OF MASS TRANSFER
THEORY OF MASS TRANSFER
Fol
Followlowing ing expexpresressiosions ns can can be be obtobtainained ed frofrom m twotwo-fil-filmm theory, theory, N N GG
¼
¼
aaiGiGk k GGt t GG (3)(3) N N LL¼
¼
aaiLiLk k LLt t LL (4)(4) where where a aiLiLt t LL¼
¼
r r LLGGf f r r GGLLf f a aiGiGt t GG (5)(5) HereHereaaiGiGandandaaiLiLrepresent the geometrical interfacial area per represent the geometrical interfacial area per
unit volume of gas and liquid phases, respectively. Assuming unit volume of gas and liquid phases, respectively. Assuming that the liquid composition does not change vertically and that the liquid composition does not change vertically and va
vapopour ur papasssses es as as plplug ug floflow w withwithouout t mimixixingng, , ththe e ovovereralalll mass transfer unit can be related to point efficiency as mass transfer unit can be related to point efficiency as fol-lows:
lows:
E
E OGOG
¼
¼
11À
À
exp(exp(À
À
N N OGOG)) ((66))In the present study,
In the present study,E E OGOGis obtained from the published Mur-is obtained from the published
Mur-phree efficiency,
phree efficiency, E E mvmv, data as outlined by Garcia and Fair , data as outlined by Garcia and Fair
(2000a). (2000a).
MODEL DEVELOPMENT
MODEL DEVELOPMENT
In the following sections a method to estimate point In the following sections a method to estimate point effi-ciency
ciency E E OGOG from equations (1) and (2) has been discussed.from equations (1) and (2) has been discussed.
Bubbling Zone
Bubbling Zone
Bub
Bubblibling ng zonzone e is is conconsidesidered red to to havhave e bimobimodal dal size distri-size distri-bution of bubbles as reported in many studies (Porter bution of bubbles as reported in many studies (Porter et al.et al.,, 196
1967; 7; AshAshley ley and and HaseHaseldenlden, , 1971972; 2; LocLockettkett et et alal.., , 19197979;; Kaltenbacher, 1982; Hofer, 1983; Klug and Vogelpohl, 1983). Kaltenbacher, 1982; Hofer, 1983; Klug and Vogelpohl, 1983). The small bubbles are the secondary bubbles formed by the The small bubbles are the secondary bubbles formed by the turbulent break-up of the primary bubbles originated from the turbulent break-up of the primary bubbles originated from the orifice. The large bubbles are the unbroken primary bubbles orifice. The large bubbles are the unbroken primary bubbles that remain in the froth due to incomplete break-up.
that remain in the froth due to incomplete break-up. The
The specispecific fic interinterfaciafacial l area,area, aaiGiG and residence time,and residence time, t t GLBGLB
for the
for the larlarge ge bubbubblebles s in in froth froth can be can be estestimaimated from ted from thethe following equations, respectively:
following equations, respectively:
a aiGiG
¼
¼
6 6 d d 32L32L (7) (7) t t GLBGLB¼
¼
h hf f U U LBLB (8) (8) Due to complex nature of the process, there are few analytical Due to complex nature of the process, there are few analyticalexpre
expressionssions s for for any design in any design in distildistillatiolation n literliteratureature. . The gen-The gen-era
eral l tretrend nd is is to to use use corcorrelrelatiationsons, , whiwhich ch are suppoare supporterted d byby rel
reliabiable le expexperierimenmental tal datdata. a. The The folfollowlowing ing equequatiations ons areare used to estimate the Sauter mean diameter and raise velocity used to estimate the Sauter mean diameter and raise velocity of the large bubbles formed at the orifice.
of the large bubbles formed at the orifice.
d
d 32L32L
¼
¼
00::887887DDH00H::846846u u 00HH::2121 (9)(9)U
U LBLB
¼
¼
22::5(5(V V LBLB))11==66þ
þ
u u aa (10)(10)Where
Where DDHH andand u u HH are the hole diameter and velocity;are the hole diameter and velocity; V V LBLBisis
the large bubble volume and
the large bubble volume and u u aa is the gas velocity basedis the gas velocity based
on the tray active (bubbling) area. Equation (9) based on on the tray active (bubbling) area. Equation (9) based on the
the bubbubble ble sizsize e datdata a meameasursured ed by by eleelectrctronionic c proprobes bes jusjustt above the sieve tray (Prado
above the sieve tray (Prado et al.et al., 1987). Thus the equation, 1987). Thus the equation estimates the unbroken primary bubbles in froth. Three estimates the unbroken primary bubbles in froth. Three differ-ent liquid systems with nine differdiffer-ent tray geometries were ent liquid systems with nine different tray geometries were used to generate the bubble size data. This is by far the used to generate the bubble size data. This is by far the only correlation for primary bubbles on a sieve tray. Equation only correlation for primary bubbles on a sieve tray. Equation (10) was originally developed for estimating rise velocity of (10) was originally developed for estimating rise velocity of bubble swarms through a porous bed (Nicklin, 1962). Later bubble swarms through a porous bed (Nicklin, 1962). Later Burgess and Calderbank (1975) showed that this equation Burgess and Calderbank (1975) showed that this equation adequately predicts rise velocity of large bubbles in froth on adequately predicts rise velocity of large bubbles in froth on sieve trays. This is again the only study done on this topic. sieve trays. This is again the only study done on this topic.
The mass transfer coefficient for the liquid phase,
The mass transfer coefficient for the liquid phase, k k LLBLLB, , isis
modelled with Higbie penetration theory (Higbie, 1935), modelled with Higbie penetration theory (Higbie, 1935),
k k LLBLLB
¼
¼
11::1313 D DLL t t GLBGLB
00::55 (11)(11)This is a well-established model used previously by This is a well-established model used previously by
numer-ous
ous stustudiedies. s. The The masmass s tratransfnsfer er coecoeffifficiecient nt for for gas gas phaphase,se,
k
k GLBGLB, of the large bubbles is estimated from the numerical, of the large bubbles is estimated from the numerical
sol
solutiution on prepresensented ted by by ZarZaritzitzky ky and and CalCalvelvelo o (Za(Zaritritsky sky andand Calveio, 1979). This solution was developed for mass Calveio, 1979). This solution was developed for mass trans-port models in distillation. It was tested against experimental port models in distillation. It was tested against experimental data and was applied in efficiency models such as those by data and was applied in efficiency models such as those by Pra
Prado do and Fair and Fair (19(1990) and 90) and GarGarcia and cia and FaiFair r (20(2000b00b). ). TheThe solution is presented as a plot of Peclet number (
solution is presented as a plot of Peclet number (PePeGG) ) of of
Figure 4.
the
the gas gas phaphase se verversus sus the the asyasymptmptotiotic c SheSherworwood od numnumber ber (
(ShSh//). Within the range 40). Within the range 40 ,,PePeGG,,200 the following poly-200 the following
poly-nomia
nomial l proviprovides an des an excelexcellent fit lent fit for the for the experexperimenimental data:tal data:
Sh
Sh//
¼ À
¼ À
1111::878878þ
þ
2525::879879((loglogPePeGG))À
À
55::64(log64(logPePeGG))22 (12)(12)For the
For the ranrangege PePeGG..20200, 0, It It wawas s fofoununf f ththatat ShSh11 hahad d anan
essentially constant value of 17.9. essentially constant value of 17.9.
Froth height,
Froth height, hhf f , is estimated from Bennett, is estimated from Bennett et al.et al.’s (1983)’s (1983)
correlation for effective froth height, correlation for effective froth height,
h hf f
¼
¼
hhwwþ
þ
C C Q QLL W W aaee
00::6767 (13)(13) where where aaee
¼
¼
expexpÀ
À
1212::5555 u u ss r r GG r r LLÀ
À
r r GG
00::55
!
!
00::91912
2
4
4
3
3
5
5
(14)(14) and and C C¼
¼
00::55þ
þ
00::438exp(438exp(À
À
137137::88hhww) ) ((1155))There are a number of correlations available in literature to There are a number of correlations available in literature to estimate the froth height on a sieve tray. The unique estimate the froth height on a sieve tray. The unique charac-teristic of equation (13), proposed by Bennett
teristic of equation (13), proposed by Bennett et al.et al.(1983), is(1983), is that unlike any other correlations it gives effective froth height that unlike any other correlations it gives effective froth height i.e., the height of the liquid continuous region. Since in the i.e., the height of the liquid continuous region. Since in the present model, froth height is used to estimate the residence present model, froth height is used to estimate the residence time of bubbles in froth, the height of liquid continuous region time of bubbles in froth, the height of liquid continuous region cal
calculculateated d by by equequatiation on (13(13) ) givgives es the the appappropropriariate te valvalue.ue. Other correlations, which give total froth height i.e., the Other correlations, which give total froth height i.e., the com-bined height of liquid and vapour continuous region, would bined height of liquid and vapour continuous region, would over estimate the residence time of bubbles.
over estimate the residence time of bubbles. Using the above information,
Using the above information, N N GLBGLBandandN N LLBLLBcan be calcu-can be
calcu-lated from equations (3) and (4). Equation (4) is then used to lated from equations (3) and (4). Equation (4) is then used to get the overall mass transfer unit,
get the overall mass transfer unit, N N OGLBOGLB, from which the con-, from which the
con-tribution of the large bubbles,
tribution of the large bubbles, E E LBLB, to the net efficiency is, to the net efficiency is
obtained by using the equation (6). obtained by using the equation (6).
The portion of small bubbles in froth is considered to reach The portion of small bubbles in froth is considered to reach equ
equiliilibribrium um whewhen n masmass s tratransfnsfer er ratrate e is is highigh h (Lo(Lockeckett tt andand Plaka, 1983). Kaltenbacher (1982) also suggested that the Plaka, 1983). Kaltenbacher (1982) also suggested that the small bubbles get trapped in the froth and leave the froth small bubbles get trapped in the froth and leave the froth practically saturated. In this case, because equilibrium practically saturated. In this case, because equilibrium pre-vai
vails ls betbetweeween n the vapouthe vapour r and the and the liqliquid phase of uid phase of smasmallll bubbles, the efficiency of small bubbles becomes unity, i.e., bubbles, the efficiency of small bubbles becomes unity, i.e.,
E
E SBSB
¼
¼
11 ((1166))In order to estimate the contribution of small bubbles to the In order to estimate the contribution of small bubbles to the total efficiency, we need to determine the fraction of small total efficiency, we need to determine the fraction of small bubbles
bubbles, FSB, FSB, , in froth. Due in froth. Due to to lack lack of of expexperierimenmental datatal data and reliable method to estimate this parameter, expression and reliable method to estimate this parameter, expression for
for FSBFSB has been derived from turbulent break-up theory of has been derived from turbulent break-up theory of bubbles.
bubbles.
In any flow field, the
In any flow field, the FSBFSBis governed by the bubble break-is governed by the bubble break-age rate and the bubble residence time in turbulent zone. age rate and the bubble residence time in turbulent zone. Previous theoretical studies (Valentas
Previous theoretical studies (Valentas et al.et al., 1966; Valentas, 1966; Valentas and
and AmuAmundsndson, on, 1961966) 6) deadealinling g witwith h drodrop p sizsize e disdistritributbutionion assumed that the breakage rate of a drop is of first order with assumed that the breakage rate of a drop is of first order with respect to the number of drops. Later Hesketh
respect to the number of drops. Later Hesketh et al et al . (1991). (1991)
use
used d thithis s conconcepcept t for for bubbubble ble brebreak-ak-up up in in pippipelielinesnes. . TheThe sam
same e appapproaroach ch is is appapplielied d here here for for siesieve ve tratray y anaanalyslysis,is, where a first order bubble breakage rate is assumed. The where a first order bubble breakage rate is assumed. The breakage rate of large bubbles in froth is given by
breakage rate of large bubbles in froth is given by
dN dN dt
dt
¼ À
¼ À
kN kN (17)(17)Here
Herek k is the breakage rate constant andis the breakage rate constant and N N is the number of is the number of large bubbles. Two additional assumptions are made to keep large bubbles. Two additional assumptions are made to keep the calculation simple.
the calculation simple.
(1) All large bubbles are bigger than the maximum stable (1) All large bubbles are bigger than the maximum stable bubble size and are equally susceptible to the break-up bubble size and are equally susceptible to the break-up process.
process. (2)
(2) The numbeThe number of r of large and small bubblarge and small bubbles at any les at any partiparticular cular cross section of the froth is constant.
cross section of the froth is constant.
Let us consider that the number of large bubbles entering the Let us consider that the number of large bubbles entering the
froth at
froth att t ¼¼0 is0 isN N ii. Due to turbulent break-up,. Due to turbulent break-up,N N iireduces toreduces toN N f f
at
att t ¼¼DDt t . Here. HereDDt t is the residence time of large bubbles in theis the residence time of large bubbles in the
flow field. Therefore, by integrating equation (17) from flow field. Therefore, by integrating equation (17) from N N ii atat
t
t ¼¼0 0 toto N N f f atat t t ¼¼DDt t , the following expression is obtained:, the following expression is obtained:
N
N f f
¼
¼
N N iieeÀ
À
k k DDt t (18)(18)Let us consider that the fractions of large and small bubbles Let us consider that the fractions of large and small bubbles
at
at t t
¼
¼
DDt t represent the average fraction of large and smallrepresent the average fraction of large and small bubbles in the froth. The number of unbroken large bubbles bubbles in the froth. The number of unbroken large bubbles atat t t
¼
¼
DDt t is given byis given byN
N f f
¼
¼
N N iieeÀ
À
k k DDt t (19)(19)For binary breakage, For binary breakage,
N
N ss
¼
¼
2(2(N N iiÀ
À
N N f f )) ((2200))where
where N N ss is the number of small bubbles formed atis the number of small bubbles formed at t t
¼
¼
DDt t ..Thus the volume fraction of small bubbles in froth can be Thus the volume fraction of small bubbles in froth can be estimated as follows: estimated as follows: FSB FSB
¼
¼
N N ssV V ss N N ssV V ssþ
þ
N N f f V V LL¼
¼
2( 2(N N iiÀ
À
N N f f )) 2( 2(N N iiÀ
À
N N f f ))þ
þ
N N f fð
ð
V V LL==V V ssÞ
Þ
(21) (21) HereHereV V SSandand V V LLare the volumes of small and large bubbles,are the volumes of small and large bubbles,
respectively. Assuming bubbles have spherical shapes, we respectively. Assuming bubbles have spherical shapes, we get the
get the follofollowing expresswing expression for ion for FSBFSB from from equaequations (19)tions (19) and (21): and (21): FSB FSB
¼
¼
2(12(1À
À
eeÀ
À
k k DDt t )) 2(1 2(1À
À
eeÀ
À
k k DDt t ))þ
þ
((d d 32L32L==d d 32S32S))33eeÀ
À
k k DDt t (22) (22) The ratio of large bubble diameter to small bubble diameter, The ratio of large bubble diameter to small bubble diameter,d
d 32L32L//d d 32S32S, , is is obobtatainined ed frfrom om ththe e exexisistiting ng liliteteraratuturere. . ThThee
reported diameter ratios are summarized in Table 1. reported diameter ratios are summarized in Table 1.
From the above table, we find that the most probable value From the above table, we find that the most probable value of the ratio
of the ratio d d 32L32L//d d 32S32Sis 5. The breakage rate constantis 5. The breakage rate constant k k is is aa
function of the turbulent flow field and the fluid physical function of the turbulent flow field and the fluid physical prop-erties. Hesketh
erties. Heskethet al.et al.(1991) showed that the measured defor-(1991) showed that the measured defor-ma
matition on titimemes s anand d brbreaeakakage ge titime me of of bububbbbleles s cacan n bebe characterized by the natural mode of oscillation of a sphere characterized by the natural mode of oscillation of a sphere given by Lamb (1932) and proposed the following given by Lamb (1932) and proposed the following functional-ity of the rate constant
k k
¼
¼
33::88 We We00::99 cr cr
r r L00L::11r r GG00::33v v 00::66 s s 00::44 (23)(23) Here,Here,v v is the rate of energy dissipation in unit mass;is the rate of energy dissipation in unit mass; WeWecr cr isis
the critical Weber number given as the critical Weber number given as
We Wecr cr
¼
¼
r r u u 22d d maxmax
s
s (24)(24)
where
whereu u 22isisthe mean squarthe mean square velocity of turbulene velocity of turbulent flow field andt flow field and
d
d maxmax is is the the maximaximum mum stastable ble bubbubble size ble size agaagainst inst turturbulebulentnt
break-up;
break-up; r r andand s s are the density and surface tension of theare the density and surface tension of the
liquid phase, respectively. The values of reported
liquid phase, respectively. The values of reported WeWecr cr rangerange
over an order of magnitude depending on the flow pattern over an order of magnitude depending on the flow pattern responsible for the deformation of the bubble. In distillation, responsible for the deformation of the bubble. In distillation, there is no
there is no reportereported value for d value for WeWecr cr . The rate of energy dissipa-. The rate of energy
dissipa-tion, howe
tion, howeverver, is, isapproapproximatelyximatelyestimateestimated byd byv v
¼
¼
u u ssg g (Kawase(Kawaseand Moo-Young, 1990); thus the rate constant becomes and Moo-Young, 1990); thus the rate constant becomes
k k
¼
¼
33::88 We We00::99 cr cr
r r LL00::11r r 00GG::33 s s 00::44 (( u u ssg g ))00::66 (25)(25)The breakage time
The breakage time DDt t can be expressed ascan be expressed as
D
Dt t
¼
¼
nt nt GLBGLB (26)(26)here,
here, nnis any value between 0 and 1. Since bothis any value between 0 and 1. Since both nnandandWeWecr cr
are unknowns, we can combine them into single constant: are unknowns, we can combine them into single constant:
C C
00
00
¼
¼
nn We We00::99 cr cr (27) (27) By multiplying equations (25) and (26) we getBy multiplying equations (25) and (26) we get
k k DDt t
¼
¼
C C00
00
33::88r r 0 0::11 L L r r 00GG::33 s s 00::44
((u u s sg g ))00::66 (28)(28) The constantThe constantC C
00
00
will be estimated by comparing the model withwill be estimated by comparing the model with the measured efficiency data.the measured efficiency data.
Jetting Zone
Jetting Zone
In
In frofroth th regregimeime, , it it is is difdifficuficult lt to to invinvestestigaigate te jetjettinting g zonzonee separately as jets are intimately mixed with bubbles. No separately as jets are intimately mixed with bubbles. No infor-mation is available in literature on the size of jets or droplets mation is available in literature on the size of jets or droplets prese
present in nt in froth. In this froth. In this studystudy, we , we will treat the jetting zone aswill treat the jetting zone as spray and use the correlations of spray regime to estimate spray and use the correlations of spray regime to estimate the contribution of jets in froth regime. Although numerous the contribution of jets in froth regime. Although numerous studies have been done to determine the onset of spray, studies have been done to determine the onset of spray, very few studies have been focussed exclusively on mass very few studies have been focussed exclusively on mass transfer efficiency in this regime. Fane
transfer efficiency in this regime. Fane et al.et al. (1977) achieved(1977) achieved some success in predicting efficiency in spray regime on a some success in predicting efficiency in spray regime on a
small tray by using free trajectory model. However, Raper small tray by using free trajectory model. However, Raper
et al.
et al. (1979) showed that Fane(1979) showed that Fane et al.et al.’s model under-predicts’s model under-predicts the
the tratray y efefficiencficiency y whewhen n appapplielied d for for indindustustriarial l sizsize e tratrayy.. Another important attempt to predict mass transfer efficiency Another important attempt to predict mass transfer efficiency in spray regime was made by Zuiderweg (1982). His in spray regime was made by Zuiderweg (1982). His semi-emp
empiriirical cal modmodel el is is basbased ed on on the the FRI FRI expexperierimenmental tal datdata.a. This is the only model so far that is not case sensitive and This is the only model so far that is not case sensitive and is readily applicable for spray regime. In this study, we have is readily applicable for spray regime. In this study, we have ch
chososen en ZuZuididererweweg’g’s s spspraray y reregigime me momodedel l [e[eququatatioionsns (29–34)] to estimate the contribution of jetting zone to the (29–34)] to estimate the contribution of jetting zone to the total mass transfer efficiency in froth regime;
total mass transfer efficiency in froth regime;
k k GjGj
¼
¼
0 0::1313 r r GGÀ
À
0 0::065065 r r 22GG (1 (1,,r r GG,,80kgm80kgmÀ
À
33) ) ((2299)) k k LjLj¼
¼
2 2::66Â
Â
1010À
À
55 m m 00LL::2525 (30) (30) EE j j
¼
¼
11À
À
expexpÀ
À
ah ahf f K K OGjOGj u u ss
(31)(31) ah ahf f¼
¼
40 40 F F 00::33 F F bbabba22 hhLLFP FP s s
00::3737 (32)(32) where,where,F F bbabbais vapour rate based on active area,is vapour rate based on active area, F F is the ratiois the ratio
of hole area to active area,
of hole area to active area, hhLL is the clear liquid height andis the clear liquid height and
expressed as expressed as h hLL
¼
¼
00::66hhWW p p b bFP FP
00::2525 (33)(33) and at total refluxand at total reflux
FP FP
¼
¼
r r GG r r LL
00::55 (34)(34)The experimental data obtained by Raper
The experimental data obtained by Raper et al.et al. (1982) are(1982) are used to evaluate the volume fraction of gas that bypasses used to evaluate the volume fraction of gas that bypasses the bubbles formation and forms jets,
the bubbles formation and forms jets, f f j j and to estimate theand to estimate the
net
net concontritributbution ion of of jetjettinting g zone. zone. FolFollowlowing ing equequatiation on is is anan excellent fit for the average value of jetting fraction,
excellent fit for the average value of jetting fraction, f f j j as as aa
function of
function of F F -factor,-factor, F F bbabba..
f
f j j
¼ À
¼ À
00::17861786þ
þ
00::9857(19857(1À
À
eeÀ
À
11::43F 43F bbabba) ) ((3355))DETERMINING CONSTANT
DETERMINING CONSTANT
C C00
00
Constant
Constant C C
00
00
is determined by comparing the model withis determined by comparing the model with seven sets of FRI data (Sakata and Yanagi, 1979; Yanagi seven sets of FRI data (Sakata and Yanagi, 1979; Yanagi and Sakata, 1982). These data sets cover two hydrocarbon and Sakata, 1982). These data sets cover two hydrocarbon systemsystems, s, cyclocyclo-hexa-hexanene//n-hepn-heptane tane and and i-buti-butaneane//n-butane,n-butane, at five different pressures in two different tray geometries. at five different pressures in two different tray geometries. The cyclo-hexane
The cyclo-hexane//n-hepn-heptane system is tane system is widelwidely y used for used for test- test-ing distillation tray performance. The properties of this system ing distillation tray performance. The properties of this system are representative of many hydrocarbon systems operated at are representative of many hydrocarbon systems operated at 400 kPa pressure or below. The data sets for this system are 400 kPa pressure or below. The data sets for this system are taken at two different pressures, 34 kPa and 165 kPa. The taken at two different pressures, 34 kPa and 165 kPa. The data sets for i-butane
data sets for i-butane//n-butane cover three different pressuren-butane cover three different pressure le
levevelsls. . ThThe e memeasasurured ed efefficieficiencncieies s at at high high prpresessusureress (2068
(2068 kPa kPa and and 2758 2758 kPa) have kPa) have been corrected for been corrected for vapouvapour r entra
entrainmeninment t with the with the down flow down flow liquiliquid d (Hock and (Hock and ZuideZuiderwegrweg,, 1982). Figure 5 presents the effect of different values of 1982). Figure 5 presents the effect of different values of con-stant
stantC C
00
00
on the estimated point efficiency for the seven setson the estimated point efficiency for the seven sets of FRI data. The average absolute error was calculated by of FRI data. The average absolute error was calculated by Table 1.Table 1.Reported bubble size distribution on an Reported bubble size distribution on an operating sieve trayoperating sieve tray.. S
Soouurrcce e SSmmaalll l bbuubbbblle e LLaarrgge e bbuubbbblle e RRaattiioo H
Hooffeer r ((11998833) ) 5 5 mmm m 225 5 mmm m 55 Ashley and Haselden
Ashley and Haselden (1972) (1972) 5 5––110 0 mmm m 4400––880 0 mmm m 88 K Kaalltteennbbaacchheer r ((11998822) ) 4 4 mmm m 225 5 mmm m 66 Porter
Porter et al.et al.((11996677) ) 5 5 mmm m 220 0 mmm m 44 Lockett
the following equation, the following equation,
Error%
Error%
¼
¼
P
P
j
j
EstimatedEstimatedÀ
À
ExperimentalExperimentalj
j
==ExperimentalExperimentaln
nnumber of datanumber of data
(36) (36) The minimum error was obtained at
The minimum error was obtained at C C
00
00
¼¼0.16. The reported0.16. The reportedtheoretical values of
theoretical values of WeWecr cr range from 1 to 4.7 (Hinze, 1955;range from 1 to 4.7 (Hinze, 1955;
Lew
Lewis is and and DavDavidsidson, on, 1981982). 2). WitWithin hin thithis s ranrange,ge, DDt t variesvaries from 0.16
from 0.16 t t GLBGLB to 0.644to 0.644 t t GLBGLB atat C C
00
00
¼¼0.16. The values are0.16. The values arereasonable for obtaining the average bubble size distribution reasonable for obtaining the average bubble size distribution withi
within n the the frothfroth..
PREDICTION OF POINT EFFICIENCY
PREDICTION OF POINT EFFICIENCY
The present model introduces a new method to estimate The present model introduces a new method to estimate sieve tray efficiency based on a froth structure that describes sieve tray efficiency based on a froth structure that describes the hydrodynamics of an operating sieve tray. The predicted the hydrodynamics of an operating sieve tray. The predicted point
point efficefficiencieiencies,s, E E OGOG, , frofrom m the propthe propososed ed momodedel l arare e cocom-
m-pared with the FRI data in Figures 6–12. In all cases, pared with the FRI data in Figures 6–12. In all cases, predic-tions from two earlier models of Chen and Chuang (1993) and tions from two earlier models of Chen and Chuang (1993) and Garcia and Fair (2000b) are also compared with the proposed Garcia and Fair (2000b) are also compared with the proposed model. The unique characteristics of the new model is that model. The unique characteristics of the new model is that unlike the two other models it predicts the trend of efficiency unlike the two other models it predicts the trend of efficiency change from weeping to flooding point more closely (Figures change from weeping to flooding point more closely (Figures 7–9). The steady decrease in both fraction of small bubbles 7–9). The steady decrease in both fraction of small bubbles and bypassed jets results in gradual decrease of the
and bypassed jets results in gradual decrease of the point effi-point effi-ciency,
ciency,E E OGOGas theas theF F -fac-factor approtor approachachesesthe weepithe weepingngpoinpoint.t.TheThe
model also predicts the smooth transition of
model also predicts the smooth transition of E E OGOGfrom froth tofrom froth to
spray regime. Under high operating pressures (Figures 10 and spray regime. Under high operating pressures (Figures 10 and 11), the breakage rate constant
11), the breakage rate constant k k is high enough to causeis high enough to cause bre
breakagakage e of of all large all large bubbubblebles. s. This makes the This makes the fracfractiotion n of of small bubbles
small bubblesFSBFSBunity and gives rise to high point efficiencyunity and gives rise to high point efficiency under such operating condition. The experimentally measured under such operating condition. The experimentally measured fraction of bypassed gas is 0.8 at
fraction of bypassed gas is 0.8 atF F -factor 2 (Fane-factor 2 (Faneet al.et al.1977).1977). Beyond this point froth is dominated by spray and the model Beyond this point froth is dominated by spray and the model red
reduces to uces to ZuidZuiderweerweg’s model g’s model for for sprspray ay regregimeime. . ThuThus s anyany Figur
Figure e 5.5. Effect of constantEffect of constant C C 0000 on point on point effiefficiency; expresseciency; expressed d asas average absolute
average absolute errorerror..
Figure 6.
Figure 6. Comparison of measured and predicted point efficienciesComparison of measured and predicted point efficiencies for the cyclo-hexane
for the cyclo-hexane//n-heptane system at 34 kPa (open hole-arean-heptane system at 34 kPa (open hole-area 14%).
14%).
Figure 7.
Figure 7. Comparison of measured and predicted point efficienciesComparison of measured and predicted point efficiencies for the cyclo-hexane
for the cyclo-hexane//n-heptane system at 165 kPa (open hole-arean-heptane system at 165 kPa (open hole-area 14%).
14%).
Figure 8.
Figure 8.Comparison of measured and predicted point efficiencies for Comparison of measured and predicted point efficiencies for the iso-butane
the iso-butane//n-butane system at 1138 kPa (open hole-area 14%).n-butane system at 1138 kPa (open hole-area 14%).
Figure 9.
Figure 9. Comparison of measured and predicted point efficienciesComparison of measured and predicted point efficiencies for
for the the isoiso-but-butaneane//n-bun-butane tane systsystem em at at 11138 138 kPa kPa (ope(open n holehole-are-areaa 8.3%).
error in
error in predicpredictingting E E OGOG beyondbeyond F F -fac-factor 2 tor 2 is is inhinheriterited fromed from
Zuiderweg’s model. Zuiderweg’s model.
The prediction of Chen and Chuang (1993) model is The prediction of Chen and Chuang (1993) model is satis-fa
factoctory ry fofor r all all six sets six sets of of dadata. ta. The The ininterterfafaciacial l arearea a in in ththisis model is
model is estimateestimated from d from the bubble size the bubble size distribdistribution. Howeverution. However,, since the vapour
since the vapour //liquid disperliquid dispersion in sion in spray regime mostly con-spray regime mostly con-sists of drops, the model is applicable only to froth regime. sists of drops, the model is applicable only to froth regime.
The
The GarGarcia cia and Fair and Fair (20(2000b00b) ) modmodel el prepredicdicts ts the the lowlow- -pressure tray efficiency data adequately. However, it predicts pressure tray efficiency data adequately. However, it predicts significantly lower tray efficiency than the measured values at significantly lower tray efficiency than the measured values at hig
high h prepressussuresres. . ThiThis s disdiscrecrepanpancy cy resresultults s frofrom m the the highighlyhly em
empipiriricacal l nanatuture re of of ththe e momodedel. l. ThThe e momodel del ininvovolvlves es aa number of equations and at least four adjustable parameters number of equations and at least four adjustable parameters tha
that t matmatch ch aboabout ut 22 22 setsets s of of tratray y efefficificiencency y datdata, a, mosmostlytly measured under low or moderate pressures. The under measured under low or moderate pressures. The under pre-diction of three sets of data out of 22 sets, did not affect the diction of three sets of data out of 22 sets, did not affect the fin
final form of al form of ththe e momodedel. l. ThThusus, , ththe e momodedel l is is fofounund d to to bebe suitable at low and moderate pressures only.
suitable at low and moderate pressures only.
Figure 13 compares the overall performance of the three Figure 13 compares the overall performance of the three models. The proposed model predicts within
models. The proposed model predicts within ++10% for all10% for all the
the syssystemtems s and shows betteand shows better r perforperformanmance ce thathan n the twothe two oth
other er modmodelsels. . The The agragreemeement ent betbetweeween n the the expexperierimenmentaltal data and predictions of the new model proves the validity of data and predictions of the new model proves the validity of the proposed approach.
the proposed approach.
DISCUSSION
DISCUSSION
Tray hydrodynamics is considered to be the key factor in Tray hydrodynamics is considered to be the key factor in determining the nature of two-phase mixture in distillation. determining the nature of two-phase mixture in distillation.
Th
The e ununiqique ue featfeaturure e of of ththe e proppropososed ed momodedel l is is ththat at it it isis based on the analysis of tray hydrodynamics (Figures 1–4) based on the analysis of tray hydrodynamics (Figures 1–4) that describes the real situation on a sieve tray. The model that describes the real situation on a sieve tray. The model includes both bubble and jet contribution to the total point includes both bubble and jet contribution to the total point effi-ciency. The often reported bimodal distribution of bubbles in ciency. The often reported bimodal distribution of bubbles in froth is explained as the result of incomplete break-up of froth is explained as the result of incomplete break-up of pri-mar
mary y bubbubblebles s in in turturbulbulent flow ent flow fielfield. d. The fractiThe fraction on of of smasmallll bubbles,
bubbles, FSBFSB, is directly estimated by theoretical analysis, is directly estimated by theoretical analysis of the rate of bubble breakage in froth. The only other similar of the rate of bubble breakage in froth. The only other similar effort to estimate
effort to estimateFSBFSBwas done by Garcia and Fair (2000b).was done by Garcia and Fair (2000b). Although their final model agreed with the database Although their final model agreed with the database
favour-ab
ablyly, , ththe e ststududy y fafaililed ed to to ididenentitify fy ththe e sosource urce of of bibimomodadall bubble size distribution observed in froth, which made their bubble size distribution observed in froth, which made their semi-theoretically obtained
semi-theoretically obtained FSBFSBexpression rather arbitrary.expression rather arbitrary. The present model has been developed to incorporate both The present model has been developed to incorporate both the froth and spray regimes. The fraction of gas that forms the froth and spray regimes. The fraction of gas that forms continuous jets,
continuous jets,f f j j, is the determining factor of the contribution, is the determining factor of the contribution
fro
from m eaceach h of of the regithe regimesmes. . For exampFor example, in le, in frofroth th regregimeime,, 0
0,,f f j j,,1. As1. As f f j j increases with higher a gas load, transitionincreases with higher a gas load, transition
to spray regime occurs gradually and
to spray regime occurs gradually and f f j j becomes unity asbecomes unity as
spray regime is reached. No sudden change in dispersion spray regime is reached. No sudden change in dispersion st
struructcturure e ococcurs curs duduriring ng ththis is trantransisititionon, , anand d ththerere e is is aa smooth transition of FRI efficiency data from froth to spray smooth transition of FRI efficiency data from froth to spray regime. Thus the effect of the present approach of regime. Thus the effect of the present approach of consider-in
ing g ththe e efeffefect ct of of ththe e floflow w regiregimemes s on on ththe e tratray y efefficficieiencncyy ado
adoptepted d in in the the proproposposed ed modmodel el difdifferfers s frofrom m thathat t resresultultinging from the two previous approaches of the existing models. from the two previous approaches of the existing models. On
One e of of ththe e apapprproaoachches es is is to to apapplply y ththe e same same efefficficieiencncyy model for both froth and spray regimes without considering model for both froth and spray regimes without considering Figure 12.
Figure 12. Comparison of measured and predicted point efficienciesComparison of measured and predicted point efficiencies for
for cyclo-hcyclo-hexaneexane//n-hen-heptanptane e systsystem em at at 165 165 kPa kPa (ope(open n holehole-are-areaa 8.3%).
8.3%).
Figure 13.
Figure 13.Overall comparison of the proposed model with two other Overall comparison of the proposed model with two other existing models.
existing models. Figure 10.
Figure 10. Comparison of measured and predicted point efficienciesComparison of measured and predicted point efficiencies for
for the the iso-iso-butabutanene//n-bun-butane tane system system at at 2068 2068 kPa kPa (ope(open n holehole-are-areaa 8.3%).
8.3%).
Figure 11.
Figure 11.ComComparisparison ofon ofmeameasuredsuredandandpredpredictedictedpointpointefefficienficiencies for cies for the iso-butane
the effect of change of the dispersion structure (AICHE, 1958; the effect of change of the dispersion structure (AICHE, 1958; Chan and Fair, 1984; Chen and Chuang, 1993) The other Chan and Fair, 1984; Chen and Chuang, 1993) The other approach is to use two completely different models for froth approach is to use two completely different models for froth and spray regime (Zuiderweg, 1982). Since the dispersion and spray regime (Zuiderweg, 1982). Since the dispersion str
strucuctuture re in in frofroth th reregigime me is is jujust st ininveversrse e to to ththat at of of spsprarayy regime, applying the same efficiency model for both regimes regime, applying the same efficiency model for both regimes without considering the change in the dispersion structure is without considering the change in the dispersion structure is the incorrect way to estimate the tray efficiency. On the other the incorrect way to estimate the tray efficiency. On the other ha
handnd, , whwhen en twtwo o sesepapararate te momodedels ls arare e usused ed fofor r ththe e twtwoo regim
regimes es difdifficultficulties ies arise in arise in idenidentifyintifying g the the exact transitionexact transition point. By including the fraction of jetting, dependent on gas point. By including the fraction of jetting, dependent on gas flow rate, the new model takes into account the difference flow rate, the new model takes into account the difference in
in disdisperpersiosion n strstructucture ure betbetweeween n the the coecoexisxistinting g frofroth th andand spray regimes. Thus the model provides a logical solution spray regimes. Thus the model provides a logical solution tha
that t can be can be appapplielied d concontintinuouuously over sly over the range of the range of flowflow rates, without resorting to an arbitrary selection of the use rates, without resorting to an arbitrary selection of the use of
of ththe e sasame me or or sesepapararate te momodedels ls fofor r boboth th ththe e fofortrth h anandd spr
spray ay regregimeimes, s, and and thetherebreby y fulfully ly desdescricribes bes the the smosmoothoth transition between the regimes.
transition between the regimes.
The inclusion of physical properties considered in the The inclusion of physical properties considered in the esti-mat
mation ion of of frafractiction on of of smasmall ll bubbubblebless FSBFSB [equ[equation ation (28)](28)] makes the model applicable to systems with wide range of makes the model applicable to systems with wide range of phy
physicsical al proproperpertieties s and and undunder er difdifferferent ent prepressussure re levlevelsels,, where physical properties of the same systems can vary where physical properties of the same systems can vary sig-nifica
nificantlyntly. . MoreMoreoverover, , the the calcucalculatiolation n steps of steps of the the propoproposedsed mod
model el are much are much simsimplepler r and less and less rigrigoroorous us thathan n thothose se of of other similar models (Garcia and Fair, 2000a, b).
other similar models (Garcia and Fair, 2000a, b).
The present model fully incorporates the jetting fraction of The present model fully incorporates the jetting fraction of the dispersion as spray. Due to lack of definitive data on the the dispersion as spray. Due to lack of definitive data on the stru
structurcture e of of the the sprspray ay regregimeime, , this study utilizethis study utilized d the the semsemi- i-empiric
empirical spray regime model of al spray regime model of ZuiderwZuiderweg to eg to estimaestimate the te the jet- jet-ting contribution. Thus the current level accuracy of predicjet-ting ting contribution. Thus the current level accuracy of predicting usi
using ng the the proproposposed ed modmodel el is is limlimited by ited by the the semisemi-emp-empiriciricalal nature from Zuiderweg’s model and is not applicable for nature from Zuiderweg’s model and is not applicable for sys-tems with vapour density less than unity. More fundamental tems with vapour density less than unity. More fundamental studies of drop dynamics and quantification of point efficiency studies of drop dynamics and quantification of point efficiency in spray regime will
in spray regime will improve the model and enhance the corre-improve the model and enhance the corre-lation between the model and experimental data.
lation between the model and experimental data.
CONCLUSIONS
CONCLUSIONS
A fundamental model to predict point efficiency has been A fundamental model to predict point efficiency has been pro
proposposed ed basbased ed on on the the hydhydrodrodynaynamicmics s of of an an opeoperatratinging sieve tray. The new model predicts the FRI efficiency data sieve tray. The new model predicts the FRI efficiency data of hydrocarbon systems within
of hydrocarbon systems within ++10%. It is also able to pre-10%. It is also able to
pre-dict the trend of tray efficiency from weeping to the flooding dict the trend of tray efficiency from weeping to the flooding po
poinint t momore re clclososelely y ththan an anany y otheother r momodedel. l. ThThe e prpresesenentt mo
modedel l is is babasesed d on on ththe e ananalalysysis is of of rereal al frfrototh, h, anand d so so isis based on sound empirical data, and so the model is more based on sound empirical data, and so the model is more adoptable to the diversified conditions than any other existing adoptable to the diversified conditions than any other existing models.
models.
The model can be used throughout the froth and spray The model can be used throughout the froth and spray reg
regimeimes s and the and the tratransinsitiotion n betweebetween n thethem, m, and so and so wilwill l bebe more applicable for the prediction of distillation tray efficiency. more applicable for the prediction of distillation tray efficiency. Furthe
Further r fundafundamentamental l researesearch rch on on poinpoint t efefficienficiency cy in in sprayspray regime, however, would make the model more universal. regime, however, would make the model more universal.
NOMENCLATURE
NOMENCLATURE
a
a interfacial area per volume of two-phase mixture, minterfacial area per volume of two-phase mixture, m22mm2233
a
aiGiG geometrical interfacial area per volume of gas, mgeometrical interfacial area per volume of gas, m22mm2233
a
aiLiL geometrical interfacial area per volume of liquid, mgeometrical interfacial area per volume of liquid, m22mm2233
b
b weir length per unit bubbling area, mweir length per unit bubbling area, m2211
C
C constant defined by equation (13)constant defined by equation (13)
d
d maxmax maximum stable bubble diameter in turbulent flowmaximum stable bubble diameter in turbulent flow
field, m field, m d
d 32L32L sauter mean bubble diameter of large bubbles, msauter mean bubble diameter of large bubbles, m
d
d 32S32S sauter mean bubble diameter of small bubbles, msauter mean bubble diameter of small bubbles, m
D
DGG moleculamolecular r diffudiffusion coefficiension coefficient t for for gas, mgas, m22ss2211
D
DHH orifice diameter, morifice diameter, m
D
DLL moleculamolecular r diffudiffusion coefficiension coefficient t for for liquid, mliquid, m22ss2211
E
E BB overall point efficiency for bubbling zoneoverall point efficiency for bubbling zone
E
E j j overall point efficiency for jetting zoneoverall point efficiency for jetting zone
E
E LBLB overall point efficiency for large bubblesoverall point efficiency for large bubbles
E
E OGOG overall point efficiency (gas composition basis)overall point efficiency (gas composition basis)
E
E SBSB overall point efficiency for small bubblesoverall point efficiency for small bubbles
f
f j j volume fraction of gas bypasses the froth bubbles asvolume fraction of gas bypasses the froth bubbles as
continuou continuous s jetjet F
F ratio of hole to active (bubbling) arearatio of hole to active (bubbling) area F
F bbabba vapour rate based on active area (vapour rate based on active area (u u aa
p
p
ffiffiffiffiffiffi
ffiffiffiffiffiffi
r r GG),),(kg m
(kg m2233))0.50.5m sm s2211
FP
FP flow parameter, (flow parameter, (r r GG==r r LL))00::55 at total refluxat total reflux
FSB
FSB fraction of small bubblesfraction of small bubbles g
g gravitatigravitational constant, onal constant, 9.8 m s9.8 m s2222
G
Gf f gas mass flow rate, kg sgas mass flow rate, kg s2211
h
hf f froth height, mfroth height, m
h
hLL clear liquid height, mclear liquid height, m
h
hWW weir height, mweir height, m
k
k first order bubble breakage rate constant, sfirst order bubble breakage rate constant, s2211
k
k GG gas-phase mass transfer coefficient, m sgas-phase mass transfer coefficient, m s2211
k
k GjGj k k GGfor jetting zonefor jetting zone
k
k GLBGLB k k GGfor large bubblesfor large bubbles
k
k LL liquid-phliquid-phase mass ase mass transfer coefficitransfer coefficient, m ent, m ss2211
k
k LLBLLB k k LLfor large bubblesfor large bubbles
k
k LjLj k k LLfor jetting zonefor jetting zone
K
K OGjOGj K K OGOGfor jetting zonefor jetting zone
L
Lf f liquid mass flow rate, kg sliquid mass flow rate, kg s2211
N
N the number of large bubblesthe number of large bubbles N
N ii the number of large bubbles formed at the orifice at anythe number of large bubbles formed at the orifice at any
instant instant N
N f f the number of unbroken large bubbles leaving the froth atthe number of unbroken large bubbles leaving the froth at
any instant any instant N
N f f number of unbroken large bubbles remained fromnumber of unbroken large bubbles remained fromN N ii atat
t t
¼
¼
DDt t NN GG number of gas-phase mass-transfer unitsnumber of gas-phase mass-transfer units
N
N GLBGLB N N GGfor large bubblesfor large bubbles
N
N LL number of number of liquid-pliquid-phase mass-transfer unitshase mass-transfer units
N
N LLBLLB N N LLfor large bubblesfor large bubbles
N
N OGOG number of overall gas-phase mass-transfer unitsnumber of overall gas-phase mass-transfer units
N
N OGLBOGLB N N OGOGfor large bubblesfor large bubbles
N
N ss number of secondary bubbles formed fromnumber of secondary bubbles formed fromN N ii atatt t
¼
¼
DDt tp
p pitch of holes on sieve plate, mpitch of holes on sieve plate, m Pe
PeGG Peclet number (Peclet number (d d 32L32LU U LBLB//DDGG))
Q
QLL liquid flow rate, mliquid flow rate, m33ss2211
Sh
Sh// asymptotic Sherwood number (asymptotic Sherwood number (k k GLBGLBd d 32L32L//DDGG))
t
t GG mean residence time of gas in dispersion, smean residence time of gas in dispersion, s
t
t GLBGLB mean residence time of large bubbles in dispersion, smean residence time of large bubbles in dispersion, s
t
t LL mean residence time of liquid in dispersion, smean residence time of liquid in dispersion, s
D
Dt t the time when half of the total secondary bubbles arethe time when half of the total secondary bubbles are formed in froth from the initial
formed in froth from the initialN N iinumber of bubbles, snumber of bubbles, s
u
u aa gas velocity based on active(bubbling) area, m sgas velocity based on active(bubbling) area, m s2211
u
u HH gas velocity based on total open hole area, m sgas velocity based on total open hole area, m s2211
u
u ss gas velocity based on total column cross-sectionalgas velocity based on total column cross-sectional
area, m s area, m s2211
U
U LBLB rise velocity of large bubbles, m srise velocity of large bubbles, m s2211
u
u 22 mean square velocity of turbulent flow field, (mean square velocity of turbulent flow field, (v v d d
max max))22//33, m, m
V
V LBLB volume of large bubbles, mvolume of large bubbles, m33
W
W weir height, mweir height, m We
Wecr cr critical Weber number critical Weber number
Greek symbols Greek symbols
a
aee froth density defined by equation (14)froth density defined by equation (14) m
m LL liquid viscosityliquid viscosity, , Pa sPa s2211 r
r GG gas density, kg mgas density, kg m2233 r
r LL liquid density, kg mliquid density, kg m2233 s
