chemical engineering research and design 9 2 ( 2 0 1 4 )
471480Contents lists available at
ScienceDirectChemicalEngineeringResearchandDesignj our nal
homepage: www. el sevi er . com/ l ocat e/ cher
dAnewmodelforbubblinguidizedbedreactorsM.P. Jaina,, D.
Sathiyamoorthya, V. Govardhana RaobaBhabha Atomic Research Centre,
Mumbai 400085, IndiabIndian Institute of Technology Bombay, Mumbai
400076, IndiaabstractVarious mathematical models have been proposed
in the past for estimating the conversions of reactant gases
inuidized bed reactors. A newmathematical model is being proposed
in this paper that gives relatively better resultscompared to the
prevailing models for bubbling uidized bed reactors utilizing
Geldart B particles. The new modelisnamed as JSR (Jain,
Sathiyamoorthy, Rao) model and it is a modied version of bubble
assemblage model of KatoandWen (1969). This paper discusses the
development of JSR model and its verication by using data
fromchemicalengineering literature on uidization and also
experimental data fromhydrochlorination of silicon in a uidized
bedreactor. The new model is tested for ve processes having
operating temperatures from 130C to 450C, operatingvelocities
from0.019ms1to 0.19ms1and solid particle sizes from65 to 325 mesh.
2013 The Institution of Chemical Engineers. Published by Elsevier
B.V. All rights reserved.Keywords: Fluidization; Modelling;
Reactors; Powder; Particles; Compartments1.IntroductionInitially
twophase models consisting of bubble and emul-sion phases and then
three phase models having one moreadditional phase called cloud
phase were proposed. Exam-ples of twophase models are Davidson and
Harrison (1963)and Patridge and Rowe (1966) models, and examples of
threephase models are Kunii and Levenspiel model (1968) and Katoand
Wen model (1969). Davidson and Harrison model had lim-itations with
respect to high interphase mass transfer, andPatridge and Rowe
model due to excess bubble-cloud areathan actual. Therefore, both
the two phase models could notprovide satisfactory results. Models
by Fryer and Potter (1972)and Werther (1980) were proposed. Fryer
and Potter modelis known as countercurrent back-mixing model
(CCBM). TheCCBM model did not become popular because of the
dif-culties associated with numerical solutions of the
governingequations. The model used constant size bubble while it is
afact that bubble diameter changes as it rises in the uidizedbed.
Werther (1980) model took an analogy from gasliquidbehaviour. In
the this model the reactant gas from the gasphase to solid phase is
assumed to be transported in a man-ner similar to the diffusion of
a gas through a thin lm intothe bulk of a liquid in a gasliquid
interacting system. Kuniiand Levenspiel (1968) and Kato and Wen
(1969) models haveCorresponding author. Tel.: +91 22
25592537.E-mail address: [email protected](M.P. Jain).Received3
December 2012; Receivedinrevisedform3 September 2013; Accepted15
September 2013been popularly used for design of bubbling uidized
bed reac-tors. There is still some scope for improvement for both
thesemodels as reported by Chavarie and Grace (1975).
Anewmodel(JSR, i.e., Jain, Sathiyamoorthy and Rao) has been
proposedto improve and scale up the gassolid bubbling uidized
bedreactors. The JSR model has been further tested using
fourreaction systems, viz. ammoxidation of propylene,
hydro-genationof ethylene, oxidationof ammonia,
decompositionofnitrous oxide by using data fromchemical engineering
litera-ture. All the four reactions are conrmed to have rst order
asthat of hydrochlorination of silicon metal. Experiments
werecarried out by us on hydrochlorination of silicon in a
uidizedbed reactor in order to verify the predictions of the new
JSRmodel. Silicon powder used in our experimental work belongsto
classication Geldart B. The conversions of reactant gasesin uidized
bed conditions are predicted utilizing JSR, Kuniiand Levenspiel,
and Kato and Wen models and
compared.1.1.MinimumuidizationvelocityMinimum uidization velocity
for classication Geldart Bparticles can be evaluated with a good
accuracy fromthe cor-relation of (Delebarre, 2004)24.5Rc2m
+29.4003m(1 m)Rcm = Ar (1)0263-8762/$ see front matter 2013 The
Institution of Chemical Engineers. Published by Elsevier B.V. All
rights
reserved.http://dx.doi.org/10.1016/j.cherd.2013.09.006472chemical
engineering research and design 9 2 ( 2 0 1 4 ) 471480NomenclatureA
reactant gasAr Archimedes number, (d3p, (,s,)g,jg2),
CAconcentration of reactant gas in cloud
phase,kgmolm3Ceconcentration of reactant gas in emulsionphase,
kgmolm3Cbconcentration of reactant gas in bubble
phase,kgmolm3CEconcentration of reactant gas at reactor
exit,kgmolm3Coconcentration of reactant gas at entry of reac-tor,
kgmolm3Cbhconcentration of reactant gas in bubble phaseat height h,
kgmolm3Cbhiconcentration of reactant gas in bubble phaseat height h
in ith compartment, kgmolm3CEnconcentrationof reactant gas at exit
of nthcom-partment, kgmolm3CEn1concentration of reactant gas at
exit of (n1)thcompartment, kgmolm3D molecular diffusion coefcient
of gas, m2s1dbiinitial bubble diameter, mdbbubble diameter,
mdpparticle diameter, mdtreactor ID, mdbmmaximumbubble diameter, mF
a parameter used in Eq. (5), g gravitational acceleration,
ms2Lhiheight of ith compartment, mID internal diameter of reactor,
mKbcvolume rate of gas exchange between bubbleand cloud phases per
unit bubble volume, s1Kbevolume rate of gas exchange between
bubbleand emulsion phases per unit bubble volume,s1Kbeivolume rate
of gas exchange between bubbleand emulsion phases in ith
compartment perunit bubble volume, s1Kcevolume rate of gas exchange
between cloud-wake and emulsion phase per unit bubblevolume,
s1Krapparent xed bed reaction rate constant,m3/m3catalyst
s1Kfapparent uidized bed reaction rate constant,m3/m3catalyst
s1Lmfinitial height of the solid bed, mM a parameter dened by Eq.
(20)t time, sRemfReynolds number at minimum uidizationvelocity
(Remf=(dpUmf,f/jg)), Uo, supercial velocity of uidizing gas,
ms1Umfsupercial gas velocity at incipient uidization,ms1Ubbubble
velocity, ms1Ubrbubble rise velocity, ms1x a parameter dened by Eq.
(35) in appendixXAconversion of reactant gas, XAJSRconversion of
reactant gas by JSR model, XAKLconversion of reactant gas A by
Kunii and Lev-enspiel model, XAKWconversion of reactant gas A by
bubble assem-blage model, a parameter dened by Eq. (9), a parameter
dened by Eq. (12), ,cratio of volume of solids in cloud-wake
regionto volume of bubbles in bed,eratio of volume of solids in
emulsion phase tovolume of bubbles in bed,bratio of volume of
solids in bubble phase to vol-umeof bubbles in bedIbubble fraction
of the HCl gas in the ith com-partment[ a parameter dened by Eq.
(14), a parameter dened in Eq. (22), ,sdensity of solid particle,
kgm3,fdensity of the reactant gas, kgm3Afractional change in volume
between nil andcomplete conversion of reactant Amffraction of bed
at incipient uidizationjgviscosity of the reactant gas,
kgm1s1or,Rcm = [{6003m(1 m)}2+0.0408Ar]0.56003m(1 m) (2)The above
equation includes bed voids at minimumuidiza-tion and helps better
prediction of minimum
uidizationvelocity.2.DevelopmentofanimprovednewmathematicalmodelVarious
phases in a bubbling bed model are shown in Fig. 1,and it is
similar to Kunii and Levenspiel model. Three phaseshave been
considered in the bubbling bed model. The modelconsiders all
bubbles of equal size throughout the bed and nocounter-diffusion in
the estimation of predicted conversionof the reactant. Kato and Wen
(1969) have proposed a modelin which a bubbling bed is divided into
several hypotheticalcompartments of different sizes based on
factors like particledensity, gas velocity and particle diameter.
New model bringsimportant concepts of both Kunii and Levenspiel,
and Katoand Wen models together.Assumptions for new model1. The
model assumes bubbles of perfectly spherical shape.2. It is assumed
that in the cloud zone, wake is not a separateentity.3. The
reactant is assumed to diffuse from bubble phase toemulsion
phase.4. In any compartment the mass transfer is assumed to
occurfroma bubble of diameter equivalent to the compartmentheight.
The emulsion phase is considered to be at incipientstate of
uidization and considered to be well mixed upwith constant voids.5.
The solid particles present in the bubble are neglected andhence
the reaction with the gas in the bubble phase isassumed to be
nil.The model is discussed here in ve steps as follows,(i)
Derivation of equation for compartment heightchemical engineering
research and design 9 2 ( 2 0 1 4 ) 471480 473Fig. 1 Transport of
reactant froma bubble to emulsion with a hypothetical compartment
of partitioned gas uidized.The uidized bed is assumed to be made up
of severalhypothetical compartments of size Lhiwhich is same as
thediameter of a single bubble in that compartment. Kato andWen
(1969) have mentioned in their paper that they are apply-ing
Kobayashi et al. (1965) correlation with possibility of someerror
in the calculation of compartment height and this cor-relation can
be used till a better correlation is found out.Vishwanathan et al.
(1982) also analysed and expressed thesimilar views.Empirical
equation by Mori and Wen (1975) correlated bub-ble diameter and
reactor tube diameter for Geldart B and Dpowders as given below,dbi
= dbm(dbmdo) exp_0.3ndt_(3)The range of conditions are
dt1.3m,0.005Umf0.20ms1, 60dp450m,(UoUmf) 0.48ms1.Bubble diameter is
calculated for ithcompartment fromEq.(3). Maximumlimit for reactor
diameter is 1.3mbut accordingto GOLFERS (1982) Eq. (3) can be used
for higher diameters alsofor designing and scaling up purposes.
This equation will beused to nd out compartment height as the
bubble diameterhas been considered to be equal to the height of ith
com-partment at a particular level in the uidized bed.
Therefore,dbi = Lnifor i = 1toNcompartmentsPutting the value of dbi
in Eq. (3), rearranging and integrat-ing1 =_nini1_1_dbm(dbmdo)
exp_0.3ndt___dn (4)Taking, (0.3/dt) =p and (1(do/dbm))exp(phi1)
=F.On simplifying (details are given in the appendix),Zni =_1p_ln[F
+(1 F) exp(pdbm)] (5)(ii) Developing anexpressionfor mass transfer
of reactant gasA frombubble to cloud and cloud to emulsion(a) Mass
balance of reactant gas A over the cloudphase in a particular
compartment: Transfer of A to cloudwake=reaction in cloud
wake+transfer of A to emulsionKbc(CbCc) = ,cKrCc+Kcc(CcCc)
(6)Symbols have their usual meaning and have beendescribed in
nomenclature.No counter diffusion and no bulk ow are considered
herein the above equation.(b) Mass balance of A over the emulsion
phase in a particu-lar compartment: Transfer of A to
emulsion=reaction of A inemulsionKcc(CcCc) = ,cKrCc(7)orCc
=KccCc(,cKr +Kcc)(8)or,Cc = Cc(9)FromEq. (6),KbcCb = Cc{,cKr +Kcc(1
) +Kbc} (10)Therefore,Cc =CbKbc{,cKr +Kcc(1 ) +Kbc}(11)orCc =
Cb(12)Therefore,Cc = Cb(13)Taking, =[Cc = [Cb(14)474chemical
engineering research and design 9 2 ( 2 0 1 4 ) 471480The terms and
are calculated fromthe values of Kbc, Kce,,c, ,e and Kr.Kbc and Kce
are calculated similar to the model of Kunii andLevenspiel and
correlations are given below,Kbc =
4.5Umdb+5.85_D0.5g0.25d1.25b_(15)andKcc = 6.77_UmDUbrd3b_(16)(iii)
Estimation of bubble phase exit concentration of AMass balance in
bubble phase in Lhi size compartmentRateof changeof reactant
concentrationinthebubbles= Loss of reactant
byexchangetoemulsionSolid particles inside the bubbles are
neglected and it isit is assumed that no reaction takes place in
bubbles. Onlybubble to emulsion reaction takes place for reactant
gas A inthe compartment idCbdt= Kbc(CbCc) (17)(Here, for a
particular compartment i, (1/Kbe) =(1/Kbc) +(1/Kce))dCb =
Kbc(CbCc)dt (18)Putting the value of Cefrom Eq. (14) and value of
dt by itsdenition in Eq. (18)dCb = Kbc(Cb[Cb)dnUbr(19)Integrating,
and taking, ((Kbe(1[))/Ubr) =MCbCo= exp(M Lni) (20)(iv) Exit
concentration for reactant A from the ith compart-mentReferring to
Fig. 2 mass balance for reactant gas A is givenbelow. Only bubble
and emulsion phases are considered hereand gas volume in cloud
phase is negligibleUoCECo=UmCcCo+(UoUm)CbCo(21)Taking, ((UoUmf)/Uo)
=CECo{(1 )[ +}_CbCo_(22)For each compartmentCEiCo= {(1 )[
+}_CbiCo_(23)Fig. 2 Reactant gas ow through a compartment in
auidized bed.or,CEiCo= {(1 )[ +} exp(MLni) (24)(v) Evaluation of
overall conversionConcentration of reactant A exiting after all the
n numberof compartments, i.e., whole reactor is estimated
asCECo=_CE1Co__CE2CE1__CE3CE2_ _CEnCEn1_(25)Then conversion of
reactant gas A is found out as given below,XA =_1 CECo_(26)Eq. (26)
is to be used along with other equations given abovefor nding out
overall conversion of a gaseous reactant in auidized bed
reactor.The model can be used for gassolid bubbling uidizedbed
reactors involving Geldart B particles. Data from litera-ture for
four processes utilizing uidized bed reactors havebeen tested
particularly oxidation of ammonia, ammoxida-tion of propylene,
hydrogenation of ethylene and nitrousoxide decomposition and also
our experimental data forhydrochlorination of silicon. It was found
that JSR model givessatisfactory results compared to other
prevailing
models.3.VericationofnewmodelbytakingexperimentaldatafromliteratureData
for four chemical reactions published in literature hasbeen picked
up to study the universality of JSR model. Theproperties of the
materials used and owrates of reactants areconverted from standard
conditions to operating conditions.Data fromexperimental work for
hydrochlorination of siliconis used as a fth case for testing JSR
model.chemical engineering research and design 9 2 ( 2 0 1 4 )
471480 475Table 1 Comparison of experimental and
predictedconversions of propylene to acrylonitrile.S. no. U/UmfBed
height,mXAexpXAJSRXAKLXAKW1 2.94 0.175 0.83 0.847 0.35 0.142 4.9
0.175 0.62 0.586 0.21 0.123 2.97 0.276 0.88 0.927 0.134 0.0944 4.88
0.276 0.72 0.741 0.185 0.175 6.86 0.276 0.53 0.525 0.301
0.23.1.AmmoxidationofpropyleneThis is a well known process for
manufacturing acryloni-trile which is used for production of
acrylic bre, styreneco-polymers andnitrile rubber. JSRmodel is
testedfor ammox-idation of propylene in a uidized bed reactor. The
exothermicreaction takes place as follows,CH2CH CH3+NH3+ 32O2
CH2CHCN+3H2O+136.2kcal (27)A streamfromrenery is introduced along
with ammoniaand air into a catalytic uidized bed reactor. The
catalyst usedis molybdenum-bismuth. The temperature of the reaction
is400500Cand pressure 1.53atm. Afewseconds contact timeis
available. The reactor afuent is scrubbed with water toremove the
desired products in an aqueous solution whichis further
fractionated to give wet acrylonitrile and acetoni-trile. Both are
further puried by azeotropic and
conventionaldistillation.Experimental work of Stergiou et al.
(1984) is taken for test-ing of JSRmodel. Reactionrate constant for
xedbedconditionis reported to be 0.38s1at 450C by Sawyer and Martel
(1992).The data for owrates and conversion of propylene and
otherparameters are given below,Bulk density of catalyst
=1000kgm3.Minimumuidization velocity=0.025ms1.Number of holes per
unit area=1.4.Reaction temperature=450C.Reaction
pressure=1.53atm.The JSR model is applied and the results are
giveninTable 1and Fig. 3.3.2.HydrogenationofethyleneHeidel et al.
(1965) carried out hydrogenation of ethylene ina uidized bed
reactor. Nickel coated solid catalyst is used inthe reactor. The
reaction takes place as given below,C2H4+H2 C2H6(28)This experiment
was carried out when hydrogen is inexcess to maintain the supercial
gas velocities in the u-idized bed reactor. Copper on silicaalumina
is used as acatalyst in three sizes from 042, 4260 and
6090m.Inletcomposition of the feed is 70% hydrogen and 30%
ethylene.The reactiontakes place between130Cand150C. The
exper-imental data taken from a paper by Werther (1980) is
shownalong with results in Table 2. The analysis of the data has
beencarried out and results are shown in Fig. 4.Table 2 Comparison
of experimental and predictedconversions on hydrogenation of
ethylene.S. no. Uo, ms1k, s1XAexpXAmodelJSRXAKLXAKW1 0.025 0.27
0.94 0.997 0.705 0.1452 0.05 0.27 0.74 0.83 0.401 0.1233 0.075 0.27
0.61 0.667 0.284 0.1054 0.10 0.27 0.51 0.56 0.222 0.01035 0.04 0.16
0.85 0.97 0.38 0.013.3.OxidationofammoniaMassimila and Johnson
(1961) have worked on the oxidationof ammonia reaction for
uidization studies. The solid cata-lyst used was manganusbismuth
oxide on alumina spheres.The solids particles size was 100325 mesh.
The temperatureand pressure of the reaction were 250C and 1.1atm,
respec-tively. Inlet composition of the gas was 10%ammonia and
90%oxygen. The reaction takes place as follows,2NH3+2O2 N2O + 3H2O
(29)The equipment consists essentially of a heated
reactor,cylinders of air, oxygen and ammonia, ow metres for
gases,thermocouples, sample valves etc. The reactor had 0.1143mFig.
3 Model versus experimental conversion ofpropylene.Fig. 4 Model
versus experimental conversion of ethylene.476chemical engineering
research and design 9 2 ( 2 0 1 4 ) 471480Fig. 5 Model versus
experimental conversion of ammoniabed.ID and 1.09mheight and was
made up of stainless steel. Thelower ange was connected to an inlet
plenumsection and astainless steel perforated plate (distributor)
placed betweenthe reactor and the inlet section, was used to
support thebed and disperse the gas uniformly. The ange
supportedthe cyclone separator used to remove the catalyst
particlesfromthe gas stream. The catalyst collected in the cyclone
wasreturned to the reactor at the end of each series of runs.The
reactor was heated electrically by four chromel resis-tance ribbons
wound on alundum insulation around thereactor. The temperature of
the bottom and upper sectionswere controlled manually with variacs
and the temperatureof sections immediately above the porous plate
was regulatedby an automatic controller. The experimental data and
pre-dicted results are given in Table 3 and results are depicted
inFig. 5.3.4.DecompositionofnitrousoxideCatalytic decomposition of
nitrous oxide gas has been chosenas a reaction to test the new
model in uidized bed reac-tors. This experimental work was carried
out by Shen andJohnstone (1955). The catalyst activity remains
substantiallyconstant over a long period of time. The rate of
decompositionis measured in xed and uidized beds in the
temperaturerange from 343C to 426C. Nitrogen, air or oxygen
streamscontaining 12.5% nitrous oxide are used. The reaction is
rstorder. This reaction in uidized bed reactor is used to verifythe
JSR model and it is given as,2N2O 2N2+O2(30)The individual gases
are own through lters, pressureregulators and ow metres. The
reactor had 0.1143m ID and1.09 height. The reactor is made up of
SS310. One thermo-couple is embedded in the perforated stainless
steel supportplate (distributor) and two others are mounted through
thecolumn wall in the uidized bed itself. The reactor is
heatedelectrically by chromel resistance ribbon which is wound
inall the three sections around the reactor. The temperaturesof the
top and bottom sections are controlled manually withvariable
transformers and the temperature of the middle sec-tion which
covers the entire catalyst bed is regulated with anautomatic
controller. The data obtained from literature andalso predicted
conversions are presented in Table 4. A plotFig. 6 Model versus
experimental conversion of nitrousoxide.showing experimental
conversion of nitrous oxide versus pre-dicted conversion is drawn
and depicted in Fig.
6.3.5.HydrochlorinationofsiliconHydrochlorination of silicon is
carried out in a uidized bedreactor as per the following
reaction,Si +3HCl321C1.0atmSiHCl3+H2LH = 115kcal,mol(31)The
experimental set-up is made up of SS316L. It consistedof a reactor
having 0.026m ID and 0.47m height. The reactorhad a perforated
plate distributor with 9 holes at the bottomthrough which HCl gas
was supplied and it had a pressuregauge at the top for knowing the
internal pressure of the reac-tor. Approximately 0.056kg dried
silicon powder of requiredsize was introduced from the top of the
reactor up-to an ini-tial height of bed equal to 0.1m.The gaseous
products onexiting the reactor were condensed by a dry ice cooled
con-denser (working at 78C). The reactor was heated by
electricresistance coil and controlled by an ONOFF controller.
Tem-perature of the reactor was measured by a thermocouple.Glass
wool was used to insulate the reactor. The temperatureof the
reaction was 321C at atmospheric pressure. Heat gen-erated due to
reaction was removed by air owing througha copper coil brazed
externally around the reactor. Siliconpowder was added to the
reactor from a silicon bin so asto keep the bed height constant
while the bed gets depleteddue to reaction. Condensed reaction
product (trichlorosilanemainly) was weighed after the reaction was
over. Some quan-tity of trichlorosilane still escaped the condenser
whichwas at78C. Vapours of uncondensed trichlorosilane were
reactedwithNaOHsolutionina trapping vessel and the contents
wereanalysed and the amount of SiO2was estimated to ascertainthe
extent of trichlorosilane escaping condenser using thestoichiometry
of the reaction. Silica was estimated as per thefollowing
reaction.SiHCl3+3NaOH SiO2+3NaCl + H2+H2O (32)Silica thus obtained
was washed with hot distilled waterseveral times and dried in an
electric oven. The amount of sil-ica obtained and quantity of
condensed trichlorosilane werechemical engineering research and
design 9 2 ( 2 0 1 4 ) 471480 477Table 3 Comparison of experimental
and predicted conversion on catalytic oxidation of ammonia.S. no.
Uo, ms1Bed height, m XAexpXAmodelJSRXAKLXAKW1 0.023 0.19 0.27 0.27
0.287 0.0522 0.046 0.19 0.14 0.136 0.146 0.0453 0.069 0.19 0.081
0.09 0.0985 0.0454 0.023 0.38 0.4 0.43 0.414 0.0785 0.046 0.38 0.24
0.27 0.228 0.0786 0.069 0.38 0.15 0.16 0.16 0.072Table 4 Conversion
of experimental and predicted conversions of catalytic
decomposition of nitrous oxide.S. no. Temp., C Umf, ms1k, s1Uo, m
Bed height, m XAexpXAmodelJSRXAKLXAKW1 427 0.00317 0.0152 0.112
0.524 0.16 0.155 0.023 0.0542 427 0.00317 0.0152 0.056 0.524 0.277
0.264 0.046 0.0633 427 0.00317 0.0152 0.037 0.524 0.36 0.355 0.07
0.0764 427 0.00317 0.0152 0.036 0.35 0.28 0.282 0.046 0.0295 427
0.00317 0.0152 0.022 0.524 0.54 0.54 0.078 0.07786 427 0.00317
0.0152 0.019 0.524 0.64 0.64 0.144 0.105used to back calculate HCl
utilized during reaction for esti-mating conversion of HCl. The
total quantity of HCl fed wasknown by using a rotameter.Packed bed
reaction rate constant was estimated bykeeping the supercial gas
velocity lower than minimumu-idization velocity and then for
calculation of reaction rateconstant inuidizedbedconditionsupercial
gas velocity waskept above the minimumuidization velocity.The dry
hydrogen chloride gas used was 99.5% pure. Thevalue of silicon
powder minimum bed voids (mf) was foundto be 0.5 for all particle
sizes used in the experiment except208m for which it was 0.47.
Density of the silicon particlesused was 2065kgm3. A sample of
tricholorosilane producedwas checkedina gas
chromatographandshowed94.4%, purityof trichlorosilane. Other than
trichlorosilane it was assumedto be tetrachlorosilane present in
the liquid mixture pro-duced.Experimental data obtained for the
hydrochlorination ofsilicon in uidized bed conditions at
optimumtemperature of321C is presented in Table 5 for bed of
silicon metal powderof size 88208m.The initial bed height in all
the cases is keptat 0.1m.Jain et al. (2011) carried out experiments
for the reac-tion of silicon powder with HCl in the temperature
rangeof 250340C at atmospheric pressure to nd out
optimumtemperature for operation of the reactor to yield near
theo-retically maximum rate of production of trichlorosilane.
Thistemperature was found to be 321C for maximum rate ofproduction
of trichlorosilane. Hence, subsequently the exper-iments were
carried out at 321C and atmospheric pressure.The value of packed
bed condition reaction rate constant, Krwas obtained utilizing
separate experimental data and it wasfound to be approximately
0.7s1. In homogeneous reactionsrate constant is temperature
dependent but in heterogeneousreactions interphase mass transfer
coefcients are also takeninto consideration to nd out uidized bed
condition reactionrate
constant.3.5.1.ConversionsofHClgasinuidizedbedreactorMinimum
uidization velocity was calculated for differentsize of particles
used in the experiment. Flow rates weremeasured at room temperature
and corrected to 321C byassuming the gases to be ideal and
considering reductionin overall volumetric ow due to reaction.
Conversions ofHCl were estimated for various particle sizes using
theconventional popular models, i.e., Kunii and Levenspiel, andKato
and Wen models, and also the newly proposed JSR modeland compared
with the experimental values. Values of wakefraction, fw (0.23),
and ratio of volume of solids in bubblephase tovolume of bubbles
inthe uidizedbed,b (0.005) weretaken fromLevenspiel (1991) for
Kunii and Levenspiel model.The calculated value of diffusivity of
pair of trichlorosilaneand HCl was 0.243104m2s1. The reduction in
volume ofthe dry HCl feed gas due to reaction (A=1/3 for
completeconversion) was considered as well as temperature effect
forvolume increment of the gas in supercial gas velocity wasalso
considered in all the models presented here for calcula-tion of
conversion of HCl to trichlorosilane.The predicted results by
models and experimental resultsare shown in Table 6 and Fig. 7 and
it shows that maximumnumber of newmodel conversions points are
falling onor neary =x line to show that the new JSR model is a
comparativelybetter model for hydrochlorination of
silicon.4.DiscussionIt is found fromcalculations that the choice of
bubble growthequation critically affects the value of compartment
sizes.Mori and Wen (1975) have analysed well and also proposedtheir
correlation for maximum bubble and initial bubbleFig. 7 Model
versus experimental conversion of HCl gas.478chemical engineering
research and design 9 2 ( 2 0 1 4 ) 471480Table 5 Fluidized bed
experimental data and off gas analysis for hydrochlorination of
silicon metal using HCl gas fordifferent size particles at 321C.S.
no. Particlediameter, mHCl gas owrate, lpmConc. of NaOH,in trap,
%TCScondensed, kg103Av. wt. of silicaprecipitated intrap, kg 103HCl
reactiontime, s1 88 1.6 10 4.364 0 1202 124 0.6 10 0 2.587 3003 141
1.3 6.25 0 3.788 3004 141 0.6 10 0 2.736 3005 160 1.9 10 23.01 4.9
9006 160 0.85 10 0 10.896 9007 208 3.2 15 18.449 2.263 3908 208 1.7
10 17.962 4.112 7209 208 2.8 1015.805 3.513 45010 208 4.0 1011.51
7.049 480Table 6 Comparison of HCl conversion at 321C by model
prediction and experimental results for different particle size.S.
no. dp, m Uo, ms1Umf, ms1Uo/UmfXAexpXAJSRXAKLXAKW1 88 0.073 0.0034
21.35 0.68 0.74 0.29 0.52 124 0.0238 0.0067 3.55 0.97 0.98 0.68
0.383 141 0.0243 0.0087 2.8 0.93 0.96 0.72 0.364 141 0.0596 0.0087
6.85 0.65 0.75 0.37 0.345 160 0.0892 0.0112 7.96 0.60 0.63 0.28
0.266 160 0.0339 0.0112 3.03 0.96 0.96 0.60 0.297 208 0.0776 0.0214
3.62 0.66 0.67 0.36 0.178 208 0.1334 0.0214 6.23 0.56 0.38 0.22
0.179 208 0.1524 0.0214 7.12 0.56 0.41 0.19 0.1810 208 0.1935
0.0214 9.04 0.52 0.30 0.16 0.14diameter. Their correlation gives
morerealistic bubble sizeand hence the compartment size also as
compared to thevalue obtained by Kobayashis correlation
(1965).Bubble diameter calculation takes care of gas ow
rates,minimum uidization velocity, particle density, particle
size,gas density, gas viscosity, temperature of the gas, etc. In
JSRmodel both mass transfer coefcients for bubble to cloud andcloud
to emulsion have been considered rather than exchangecoefcient
value as 11/db in Bubble Assemblage (KW) model.Kato and Wen (1969)
have used exchange coefcient based onwork of (Kobayashi et al.,
1965). Toei et al. (1965) have reportedexchange coefcient to be in
the range of (2/db) to (6/db) intheir studies. Therefore, it would
be better to go for Kunii andLevenspiel method of nding exchange
coefcient which is awell established concept. It is important that
the new mathe-matical model utilizes Mori and Wen correlation for
bubblediameter and also combined exchange coefcient for reac-tants
in bubble and emulsion phases. Volumetric gas owrate change due to
temperature and reaction are taken intoconsideration. Minimum
uidization velocity of reactant gasis calculated by Delebarre
correlation or experimental valueused. These are important criteria
for nding supercial gasvelocities. Therefore, all the above
improvements provide agood solution to the problemof modelling for
all the reactionsystems chosen for the present study.The data for
ammoxidation of propylene, hydrogenationof ethylene, oxidation of
ammonia, decomposition of nitrousoxide and hydrochlorination of
silicon were tested for JSRmodel and it is found that the model
works well for all thesereaction systems as shown from Figs. 38.
Also it can beseen from Fig. 8 that the conversions of gaseous
reactants inuidized bed by JSR model very closely agree with
experimen-tal results. Kunii and Levenspiel and Kato and Wen
modelspredict conversions lower than the experimental values inmost
of the cases. Reasons for predicting low conversions byFig. 8
Conversion of reactant by model versusexperiments (all cases
together).the two models may be attributed to consideration of
cor-rect mass transfer resistance from bubble to emulsion onlyin
case of Kunii and Levenspiel model and accounting forchange in
bubble size only in the case of Kato and Wen model.JSR model
utilizes both these concepts together along withvolume change due
totemperature andreactionandalsoDele-barre correlation for minimum
uidization velocity. Majorityof the points obtained by utilizing
JSR model are either on ornear the y =x line in all the gures. In
Fig. 8 goodness of tshows the value of R2to be 0.876 for JSR model.
It indicatesthat new model is working well.5.ConclusionA new model
named as JSR model has been mathematicallydeveloped and proved by
matching theoretical (model) andexperimental conversions of
reactant gases for uidizationchemical engineering research and
design 9 2 ( 2 0 1 4 ) 471480 479of Geldart B particle of sizes
65325 mesh. The reactant gasbubbles grow as they rise in the
uidized bed. The calcula-tion of size of the bubbles in
hypothetical compartments isan important factor which was achieved
by employing Moriand Wen correlation as compared to Kobayashi et
al. correla-tion earlier used in Kato and Wen model. Interphase
exchangecoefcient Kbe is obtained by Kunii and Levenspiel methodin
JSR model. In Kato and Wen model exchange coefcient isassumed to be
11/db which is not a perfect assumption as Toeiet al. have
reportedmass interchange exchange coefcient dif-ferently intheir
studies. Rening of the calculations withthesetwoparameters, i.e.,
bubble diameter and interphase masstransfer coefcients and other
parameters such as tempera-ture correction for gas ow, volume
change due to reactions,calculation of minimumuidization velocity
by Delebarre cor-relation improve the results. It is found that the
JSR modelpredicts the conversion of reactant gases better than the
twoprevailing models for solid particles of classication Geldart
Band size 65325 mesh.AcknowledgmentAuthors are grateful to Dr. A.K.
Sharma, Head, Food Technol-ogy Division, BARC for his help and
permission for carryingout work on hydrochlorination of
silicon.AppendixA.AppendixThe equation for nding compartment height
is further sim-plied fromEq. (4) as follows,1 =_nini11{dbm(dbmdo)
exp(pn)}dn (33)Therefore,dbm =_nini11__1 _1 dodbm__exp(pn)_dn
(34)Taking,_1 _1 dodbm__exp(pn) = x (35)Therefore,_1
dodbm_exp(pn)(p)dn = dx (36)ordn =dx__1 dodbm_exp(pn)_ (37)ordn
=dxp(1 x)(38)dbm =_xixi1dxp(1 x)(39)wherexi1 = 1 _1
dodbm_exp(pni1)Put_1 dodbm_exp(pni1) = Fxi1 = 1 Fpdbm
=_1F{exp(pLn)}1Fdx(1 x) +_1F{exp(pLn)}1Fdxx(40)pdbm =[ln(1
x)]1F{exp(pLni)}1F+[lnx]1F{exp(pLni)}1F_lnx1
x_1F{exp(pLni)}1F(41)pdbm = ln_1 F{exp(pLni)}_[1 {1 F exp(pLni)}]
ln(1 F)[1 (1 F)](42)pdbm = ln {(1 F(exp(pLni)))}F[F(1 F)
exp(pLni)](43)exp(pdbm) = {(1 F(exp(pLni)))}[F(1 F)
exp(pLni)](44)exp(pdbm){(1 F) exp(pLni) = {1 F{exp(pLni)}
(45)exp(pLni)[F +(1 F) exp(pdbm)] = 1 (46)exp(pLni) = [F +(1 F)
exp(pdbm)] = 1 (47)pLni = ln[F +(1 F) exp(pdbm)] (48)Lni =_1p_ln(F
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