Multiphase CFD Modeling of Trickle-Bed Reactor Hydrodynamics

Transcription

1 Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA Mulphase CFD Modelng of Trckle-Bed Reacor Hydrodynamcs Rodrgo J.G. Lopes and Rosa M. Quna-Ferrera Absrac Ths sudy ams o ncorporae mos recen mulphase models n order o nvesgae he hydrodynamc behavor of a TBR n erms of pressure drop and lqud holdup. Takng no accoun ranspor phenomena such as mass and hea ransfer, an Euleran k-flud model was developed resulng from he volume averagng of he connuy and momenum equaons and solved for a 3D represenaon of he caalyc bed. Compuaonal flud dynamcs (CFD) model predcs hydrodynamc parameers que well f good closures for flud/flud and flud/parcle neracons are ncorporaed n he mulphase model. Moreover, caalyc performance s nvesgaed wh he caalyc we oxdaon of a phenolc polluan. Index Terms CFD, Euler-Euler model, Hydrodynamcs, Mulphase Flow. I. INTRODUCTION Mulphase flow sysems are descrbed by he cocurrenly downward flow of gas and lqud hrough a packed bed and s commercal applcaons arses n processng of fuels and chemcals such as desulfurzaon, hydroreang, hydrocrackng, dsllaon and flraon. Over he las hree decades, he research conduced for he desgn of such mulphase sysems sll reles on smplfed emprcal models raher han on a heorecal bass. The lack of knowledge abou he dealed flow pcure n packed beds reles n he complex mechansms governng he flud flow so ha plo scale expermens s ofen carred ou o perform scale-up sudes. Therefore, n reacor desgn, he couplng beween dfferen flow regmes as well as mass and hea ransfer raes are drecly lnked wh he hydrodynamcs of mulphase reacors such as rckle-bed reacors (TBR). The success of he modelng of mulphase flow processes s vrually relaed wh recen advances acheved n compuaonal flud dynamcs (CFD) gven ha nowadays compuers offer unprecedened numercal power o address Manuscrp receved July 22, Ths work was suppored by REMOVALS 6 h Framework Program for Research and Technologcal Developmen FP06 Proec no and Fundação para a Cênca e Tecnologa, Mnséro para a Cênca, Tecnologa e Ensno Superor, Porugal under gran SFRH/BD/19933/2004/WM59. R.J.G. Lopes and R. M. Quna-Ferrera are wh Chemcal Engneerng Deparmen, Faculy of Scences and Technology, Unversy of Combra, COIMBRA PORTUGAL (e-mal: rodrgo@eq.uc.p; rosaqf@eq.uc.p). complex chemcal process operaonal and desgn ssues. Our case sudy oulnes an alernave CFD modelng mehod o nvesgae he hydrodynamc behavor of a TBR n erms of pressure drop, lqud holdup and caalys weng effcency. Afer a bref revew of modelng approaches, furher deals of an Euleran wo-flud model s provded dscussng velocy 3D maps and caalys surface emperaure profles evaluaed n unseady sae afer performng he CFD valdaon. II. STATE OF THE ART The large number of sudes ha have been repored n he leraure on varous hydrodynamc aspecs of rckle-bed reacors rely on several correlaons and models of pressure graden and lqud holdup. The exsng hydrodynamc models can be broadly classfed no wo dfferen caegores [1]-[9]. The frs caegory uses an emprcal approach based on dmensonal analyss o produce explc correlaons for pressure drop and holdup. These correlaons have several parameers for fng he expermenal resuls n whch he predced values of pressure graden and lqud sauraon vary consderably. The second caegory nvolves he developmen of models resulng from equaons of moon and consders deermnaon of drag forces of gas and lqud phases a varous operang regmes. In hs caegory has been used hree dsnc approaches: he relave permeably model, he fundamenal force balance model and he sl model [4]. More recenly, he effor has been roued for advanced CFD models based on macroscopc mass and momenum conservaon laws, n whch he drag force has a conrbuon o boh parcle-lqud and gas-lqud neracons [5]. The presen rend s o develop models based on he fundamenal approach o explo her wder range of applcably unlke he correlave models, whch are sysem specfc. Therefore, our model s based on he fundamenal physcs based approach conanng he mechansc deals of he sysem coupled wh reacon knecs for he caalyc degradaon of lqud polluans performed elsewhere [10] and aemps o model pressure drop and lqud holdup a hgh-pressure operaon for he rckle-bed reacor. The CFD model was hen developed focusng a unfed approach n modelng of he hydrodynamcs wh ncdence for he downflow mode o presen a more realsc pcure of he complex hydrodynamcs prevalng n he reacor.

2 Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA III. CFD MODEL In he presen work, he flow n he rckle-bed reacor was modeled usng a mulphase CFD approach ncorporaed n he FLUENT 6.1 (FLUENT INC. USA) [11] sofware ha s he Euleran mulphase model. In he Euleran wo-flud approach, he dfferen phases are reaed mahemacally as nerpenerang connua. The dervaon of he conservaon equaons for mass, momenum and energy for each of he ndvdual phases s done by ensemble averagng he local nsananeous balances for each of he phases. The curren model formulaon specfes ha he probably of occurrence of any one phase n mulple realzaons of he flow s gven by he nsananeous volume fracon of ha phase a ha pon where he oal sum of all volume fracons a a pon s dencally uny. Fluds, gas and lqud, are reaed as ncompressble, and a sngle pressure feld s shared by all phases. In mulphase flows, he connuy (1), momenum (2) and speces connuy equaons (3) are solved for each phase and he momenum ransfer beween he phases s modeled hrough a drag erm [12]. U U x y U z = 0 y z (1) r r r ( αρu ) ( α ρu U ) = α p ˆ τ n r r r r r α ρ g ( R m& U m& U ) F (2) p= 1 ρ r r ρ U w = 0 r = ρ D α ρ s densy, U he mass average velocy, h s specfc enhalpy and g s gravy; subscrps and k represens dfferen speces. The arrow overbar sgnfes a vecor, and ˆ s a second-order ensor. μ and b are he frs and second coeffcens of vscosy, respecvely. κ s he hermal conducvy, and D s he mul-componen dffuson coeffcen and α s he mass fracon. In urbulen flows, he ncompressble ranspor equaons are gven by (4)-(6). ρ k C ρu k = τ ρ ε ε1 ε k ρε ρu ε = τ τ = μ 2 Cε 2ρε k ( μ μ ) k ( μ 0.77μ ) ε (3) (4) (5) 2 U k δ ρk μ (6) 3 k δ s Kronecker dela and k subscrp ndcaes a summaon over he x k Caresan coordnaes. The hermal energy balance and he hea flux are expressed n (7) and (8), respecvely. ρ h C U '' ρu h P = ' P τ T q = κ p μ T Pr n m = 1 n = 1 q μ α h Sc P U '' τ m μ α h = Sc ρu '' IV. NUMERICAL METHOD The numercal smulaon was performed on a cylndrcal grd (L 1m, ID 0.05m) and he mesh adoped n he TBR reacor s erahedral around and over he caalys parcles and hexahedral elsewhere wh 800,000 cells wh he frs en caalyc layers shown n Fg. 1. Caalyc bed grd generaon for he rckle-bed reacor was creaed usng he negraed sold modelng and meshng program Gamb (Fluen Inc., USA) [14]. The approach consss n dvdng he doman n subdomans, each of whch s represened by a boundary-fed coordnae mappng o a specfc regon n whch a unform grd s generaed. In order o manage wh he geomerc complexy of he caalyc bed, he subdoman decomposon was unsrucured, leadng o mulblock block-srucured grds. The local grds for a sample caalys parcle are srucured and he flexbly of hs knd of grd was covered for rckle flow n whch boundary pars move relavely o each oher. Furhermore, hs s a way o nclude adapvy n he srucured grd conex. The dscrezaon akes place on boundary-fed srucured grd and he flow s governed by he ncompressble Naver-Sokes equaons. The dscrezed connuy equaon serves as an algebrac consran and ofen a sem-heursc urbulence model s used o predc me-averaged flow varables based on a compromse beween accuracy, memory requremens and compung me. The local refnemen and coarsenng of unsrucured erahedral meshes n our case sudy requre local grd modfcaons o effcenly resolve soluon feaures for compung hree-dmensonal problems ha arses n TBR. However, repeaed ansoropc subdvson can sgnfcanly deerorae he qualy of a erahedral mesh demonsrang ha soropc subdvson s mandaory f mesh qualy s o be conrolled effecvely for arbrary refnemen levels n erahedral meshes, whou resorng o local mesh regeneraon. Expermenally, s observed ha rckle-bed reacors presen random dreconal flow felds mposng serous lmaons o erahedral meshes ha could m (7) (8)

3 Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA lead o an neffcen dsrbuon of grd pons n he fnal mesh. The momenum equaons are solved wh he couplng SIMPLE algorhm and he second upwnd dscrezaon scheme. The pressure s compued by means of he PRESTO scheme. Model equaons were solved n a ransen fashon wh a me sep of 1 s for he Euleran smulaons and a number of sub-eraons were performed whn each me sep o ensure connuy. The resduals convergence was acceleraed by under-relaxaon parameers, 0.4 for pressure and 0.8 for velocy vecor feld. Inle boundary condons are assgned a he op dsrbuor and oule condons a he free surface. velocy nle. Pressure nle was also esed bu he resuls seem o be well descrbed by he frs whch specfy more realsc boundary condons a he nle. I should be poned ha nle urbulence can sgnfcanly affec he downsream flow as observed n hgh pressure rckle-bed reacor [15]. In he rckle-bed smulaons performed, he fdely of he resuls for urbulen flows s largely deermned by he urbulence model beng used and n order o enhance he qualy of urbulen flow smulaons, he mesh generaon accouns for wall-bounded flow, a leas on caalys parcle, snce he wall s expeced o sgnfcanly affec he flow. Fg. 1 Trckle-bed reacor compuaonal mesh The urbulen flow s modeled hrough a se of modfed k-ε equaons wh erms ha nclude nerphase urbulen momenum derved from he nsananeous equaon of he connuous phase and nvolves he velocy covarance. The equaons dscussed above are solved usng an exenson of he SIMPLE algorhm. The momenum equaons are decoupled usng he full elmnaon algorhm avalable n FLUENT n whch he varables for each phase are elmnaed from he momenum equaons for all oher phases. The pressure correcon equaon s obaned by summng he connuy equaons for each of he phases. The equaons are hen solved n a segregaed, erave fashon and are advanced n me. A each me sep, wh an nal guess for he pressure feld, he prmary- and secondary-phase veloces are compued. These are used n he pressure correcon equaon and based on he dscrepancy beween he guessed pressure feld and he compued feld, he veloces, L/G holdups and fluxes are suably modfed o oban convergence n an erave manner. In he frs sage, several runs were compued wh suffcenly fne meshes o evaluae hs dependency. A hs pon, was possble o check he near-wall mesh n he pos-processng reamen. The soluon ndependency was hen esablshed afer several assays wh he defnon of urbulence boundary condons avalable n k-ε model. The boundary condons a he walls are nernally aken care by FLUENT, whch obvaes he need for boundary condon npus for k and ε suppled by nle boundares, specfcally V. HYDRODYNAMIC VALIDATION Snce he CFD mehodology s no specfcally desgned for applcaon n consraned geomeres, such as parcle packed beds, s necessary o verfy f he smulaed resuls are vald. Alhough he CFD code s based on fundamenal prncples of flow and hea ransfer, some of he boundary ssues are modeled usng emprcal daa no necessarly approprae for fxed bed applcaons. Valdaon of CFD flow feld calculaons has generally aken one of he wo forms. In he frs, nonnvasve velocy measuremens nsde he packed bed have been made, and compared o veloces compued from a model of eher he enre expermenal bed or a represenave par of. In he second form, compued pressure drops have been compared o eher measured values or esablshed correlaons for pressure drop n fxed beds, such as he Ergun equaon. The presen case sudy employed he las mehod o assess he Euleran model. Therefore, he numercal mehodology s valdaed agans expermenal daa avalable from leraure relaed o he hydrodynamc nformaon for TBR operaon. Indeed, he acual sraegy s o compare CFD resuls n erms of well known parameers such as lqud holdup and pressure drop ha are he wo mos employed characerscs n TBR developmen sudy. The expermenal condons and he parameers commonly measured n hgh pressure TBRs are evaluaed exensvely n opcs such as: pressure effec on physcochemcal properes, phenomenologcal analyss of wo-phase flow, flow regme ranson, sngle-phase pressure drop, wo-phase pressure drop, lqud holdup, gas-lqud nerfacal area and mass ransfer, caalys weng effcency as well as caalys dluon wh ner fnes n laboraory scale TBRs. In hs conex, he mesh was valdaed by checkng he mesh sensvy and by comparng he numercal resuls agans he sngle-phase and wo-phase expermenal daa. The valdaon of CFD codes usng pressure drop s mos relable when acual expermenal daa are aken n equpmen dencal o he suaon ha s beng smulaed. Exsng leraure correlaons such as he Ergun equaon are known o have shorcomngs wh respec o wall effecs, parcle shape effecs, applcaon o ordered beds and valdy a hgh Reynolds numbers (Re). The applcably of leraure correlaons o ypcal CFD smulaon geomeres needs o be examned crcally before fruful comparsons can be made because pressure drop

4 Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA measuremens can provde an ndrec means of checkng on he compuaons a hgher flows, alhough mos comparsons have been made a relavely low flow raes. Therefore, pressure graden and lqud holdup was he wo fundamenal hydrodynamc parameers evaluaed for he desgn, scale-up, and performance sudes of TBR. Pressure drop s an mporan parameer n he desgn of wo-phase concurren reacors because f affecs he energy supply and has been use o correlae he gas-lqud and sold-lqud mass ransfer whereas lqud holdup s he lqud volume conaned n a un column volume. I should be poned ha n he model valdaon was aken no consderaon ha almos all he holdup daa avalable n open leraure refers o laboraory columns [15]. Several runs smulang operang pressures n he range 10 o 30 bar runs were carred ou for he vecor feld of lqud and gas velocy and for lqud hold up and pressure drop usng sphercal caalyss wh 2 mm dameer. Smulaed CFD lqud holdup and pressure drop are represened n Fgs. 2 and 3 by lnes as a funcon of lqud mass flux waer when he reacor operaes wh ar as he gas phase a dfferen gas flow raes. The expermenal daa ploed were obaned wh one reacor wh dmensons descrbed by Nemec and Levec [15]. In he hgh neracon regme modeled for he gas and lqud phases, he predcons are n good agreemen wh expermenal values whch enables he valdaon of our CFD model. In fac, he compuaonal flud dynamc model valdaon was carred ou frs n sngle-phase pressure drop smulaons wh only he gas phase flowng downward he bed; aferwards, wo-phase flow s smulaed o perform he fnal comparson beween predced hydrodynamc parameers and expermenal daa. In he whole range of Re numbers for gas phase, pressure drop predcons are whn 10% error when comparng wh he leraure measuremens. The resulng pressure drop s gven by he addon of lamnar flow local losses wh frconal losses. A very low veloces, exclusvely lamnar or vscous conrbuons o pressure drop are observed bu a hgher veloces he lamnar erm from Blake-Kozeny-Carman equaon and he neral erm from Burke-Plummer equaon are addve. Ths muual conrbuon ha represens he rao beween he sac pressure and he hydrosac pressure s ploed n Fg. 2. The operaonal regon of flow raes (10<Re G <400) s ha of parcular neres o TBR and n hs amb Euleran model fs he pressure drop daa as well as lqud holdup que well whn accepable lms of 10%. Furhermore, akng no accoun ha he dealed knowledge of lqud holdup s essenal for safe processng o preven ho-spo formaons and possble runaways ha could have sgnfcan nfluence on he lqud resdence me dsrbuon, mass- and hea-ransfer processes as well as weng effcency, our resuls n erms of lqud holdup were also successfully valdaed n Fg. 3 avodng many correlaons ha have been publshed n mulphase reacors ΔP/L (Pa/m) 1000 G = 0.10 kg/m 2 s G = 0.30 kg/m 2 s G = 0.50 kg/m 2 s G = 0.70 kg/m 2 s L / (kg/m 2 s) Fg. 2 Comparson of smulaed pressure drop as a funcon of lqud mass flux a consan gas flow raes wh expermenal daa [15] εl 0,1 0, L / (kg/m 2 s) G = 0.10 kg/m 2 s G = 0.30 kg/m 2 s G = 0.50 kg/m 2 s G = 0.70 kg/m 2 s Fg. 3 Comparson of smulaed lqud holdup as a funcon of lqud mass flux a consan gas flow raes wh expermenal daa [15] Accordng o Fg. 3, lqud holdup decrease when he pressure was ncreased for gven gas and lqud superfcal veloces. Ths decrease s nerpreed as due o a shf n he reacor flud dynamcs from a sae predomnanly conrolled by gravy o a sae conrolled by gas-lqud shear sress or pressure drop. Comparng Fgs. 2 and 3, where he pressure graden per un reacor lengh has been ploed as a funcon of lqud mass flux, we see ha for very low values of pressure drop he lqud holdup are equally small. Wh he ncrease of pressure drop due o hgher reacor pressures, he oal drvng force enlarges noceably and, hence, he lqud holdup growh rae reduces when he lqud mass flux ncreases. On he oher hand, he nvesgaon of lqud dsrbuon n he cocurrenly gas/lqud sysem a elevaed pressures could also be relaed o he resuls ploed n Fgs. 2 and 3, n whch can be seen ha lqud holdup values a elevaed gas flow raes are much lower n comparson wh hose accouned n lower gas flow raes condons. Ths effec can be explaned by means of he rao beween he drvng forces, shear and gravaonal forces, and he reardng vscous force. As he vscosy of lqud ncreases

5 Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA exponenally wh ncreasng pressure, he rao of drvng forces and vscous force ncreases also. Ths causes a gradual reducon of he lqud sauraon n he packed bed. Moreover, he comparson beween he hydrodynamc parameers deermned a 10 and 40 bar shows ha he effec of he reacor pressure has greaer nfluence on he pressure drop han has on he lqud holdup, as expeced. Furhermore, CFD model resuls sae ha lqud holdup s slgh nsensve o low gas flow raes. Ths fac could be nerpreed by he evoluon of lqud holdup as a funcon of gas densy by plong lqud holdup as a funcon of superfcal mass lqud velocy demonsrang ha he heorecal model s able o predc que well he sgnfcan nfluence of he gas flow rae on he hydrodynamc parameers when comparng he heorecal resuls wh he expermenal daa ses. I should be also emphaszed ha he fxed-bed modeled n hs work had he ube o parcle dameer rao hgher han 10 so he avalable geomery and daa aken from leraure should no be affeced by he reacor column wall. In accordance o Fg. 3, when he lqud mass flux ncreases, he lqud holdup also ncreases for L hgher han 8 kg/m 2 s beng he growh rae smaller for he same oal pressure value whereas an ncrease of he oal pressure resuls n a consderable decrease of lqud holdup. The nfluence of he gas flow deermned by a dfferen operang pressure on he lqud holdup s less pronounced a low values of lqud mass fluxes. For example, n case he reacor operaes wh a gas flow rae a 0.7 kg/m 2 s, he lqud holdup s subsanally lower when compared wh he case operaes a 0.1 kg/m 2 s. These hgher dfferences a hgher lqud flow raes resul from he fac ha a furher ncrease of he reacor pressure a a consan gas velocy corresponds o a hgher drvng force. The heorecal predcons from he model correcly accoun for he srong nfluence of he gas flow on he hydrodynamc behavor of he rckle-bed reacors, as saed by several auhors [1]-[4]. The mporan nfluence of he gas flow s arbued o he neracons phenomena exered by he gas phase on he lqud phase. These neracons clearly appear o be sgnfcan a hgh superfcal gas mass veloces. Fnally, n order o address CFD flow sreamlnes, he 3D map aken wh a vercal caalys layer llusraed n Fg. 4 ndcae ha he velocy s hgher a pons where he flow s processed downward n axal drecon. In accordance o hese resuls, he maxmum gas velocy s abou 0.5 cm/s (whereas he lqud velocy s abou cm/s) whch s n he range of well acceped rckle flow maps revewed n he leraure [1]. In fac, he TBR hydrodynamcs are affeced dfferenly n each flow regme and he operang condons ha are of parcular neres n he ndusry s he exensvely used rckle flow encounered a low gas and lqud superfcal veloces. In he 3D map, s shown he unformy n packng srucure wh sphercal parcles, bu he gas/lqud dsrbuon depends no only on he superfcal gas and lqud veloces bu also n parcle shape and parcle equvalen dameers n order o sudy he effec of parcle geomery. Spheres were used by vrue of her unque shape and are ncapable of nfluencng he srucure of he bed by her orenaon. Some addonal dfferences beween he poroses of beds, despe he same packng procedures were due o wall effec, whch as menoned before dd no affec he overall pressure drop. Wh regards o he porosy dependence whn he neral regme, should be repored n he bass of heorecal smulaons of flow hrough random arrays of spheres ha he porosy funcon s also well aken no accoun as long as he porosy s around 0.4 as s ndeed he case for packed bed reacors when made up of spheres. The values of porosy dsrbuon funcon for he presen CFD Euleran model were appled n he range from 0.38 o I should be also poned ha when he superfcal velocy of gas s suffcen o nerac comparavely wh ha of lqud, lqud dsrbuon mproves sgnfcanly and he pressure drop arses as descrbed elsewhere [13]. In our smulaon acves, was assumed ha he rckle-bed reacor has a unform dsrbuor a he op and we can sae ha lqud dsrbuon do no depends on he desgn of he dsrbuor. Fg. 4 Gas sreamlnes colored by axal velocy (cm/s) VI. REACTION STUDIES Amng o assess he TBR reacon behavor, he caalyc we oxdaon of a model phenolc acd soluon was smulaed n connuous mode by means of CFD codes. The knec expressons of a mxure of sx phenolc acds prevously calculaed [10] were hen negraed n he TBR compuaonal model where was assumed ha chemcal reacon occurs namely on he caalys surface. Ths assumpon s expeced o be mosly reasonable because of he hydrodynamc neracon regme acheved by he Euleran model. The CFD model has also aken no accoun exernal mass ransfer lmaons whch s he mos suable when operang a large scale plo plan uns. Accordng o Fg. 5, a emperaure color map was aken wh a flow me of wo hours. As he operaon s modeled n unseady sae, afer evaluang successve emporal emperaure color maps s possble o conclude ha seady sae of TBR un s acheved n hs me.

6 Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA he lqud mass flux ncreases. The nfluence of operang pressure on lqud holdup s less pronounced han n pressure drop. Fnally, CFD runs performed n unseady sae for he caalyc we ar oxdaon of one phenolc soluon demonsraed he effec of emperaure llusraed by caalys surface emperaure 3D map. ACKNOWLEDGMENT The auhors graefully acknowledged he fnancal suppor of REMOVALS 6 h Framework Program for Research and Technologcal Developmen FP06 Proec no and Fundação para a Cênca e Tecnologa, Porugal. Fg. 5 Caalys surface emperaure (K) Furhermore, as he lqud holdup s drecly relaed o he caalys weng effcency ha also mgh affec he reacon yeld, n accordance o Fg. 5, he dfferen emperaures rangng from 470 o 474 K aaned n dfferen locaons of he caalys parcles ndcae dfferen reacon raes. These resuls n erms of caalys surface emperaure for he exohermc oxdaon process of he polluans reflec dfferen weng levels of he sold by he lqud effluen. Therefore, n he TBR desgn and scale-up sudes exernal caalys weng effcency s also a hydrodynamc parameer ha ndcaes he ulzaon degree of caalys surface area. However, he couplng naure of ranspor phenomena and knecs n TBR s far from beng compleely undersood so ha general scale-up and scale-down rules for he quanave descrpon of mulphase flows depends on how phenomenologcal analyss s correlaed wh avalable numercal power o address complex chemcal process operaonal and desgn ssues. VII. CONCLUSION A unque physcs-based model has been proposed for modelng rckle-bed reacors a elevaed pressures amng o predc he hydrodynamc parameers. The unfed approach ncludes fundamenal pon force balance and akes no accoun he nfluence of gravy n he force balance. The model consss n an Euler-Euler reamen for he flud phases coupled wh he energy equaon. The numercal smulaons are compared agans expermenal daa o valdae he predced pressure drop and lqud holdup. Operang condons were smulaed wh bar of reacor pressure whle gas and lqud mass flow rae were n he range and kg/m 2 s, respecvely. The novel hydrodynamc model has been found o predc wh a reasonable accuracy he expermenal daa, ponng ou ha he lqud holdup ncreases as he lqud mass flux ncreases and decreases for hgher operang pressure values. A low values of pressure drop he lqud holdup s small bu wh an ncreasng value of pressure drop due o an ncrease of he reacor pressure, he lqud holdup growh rae reduces when REFERENCES [1] M. H. Al-Dahhan, F. Larach, M. P. Dudukovc, and A. Lauren, Hgh pressure rckle-bed reacors: A Revew Ind. Eng. Chem. Res. 36 (8), 1997, [2] R.G. Carbonell, Mulphase flow models n packed beds Ol & Gas Scence and Technology Revue de l IFP 55, 2000, [3] M. P. Dudukovc, F. Larach, and P. L. Mlls, Mulphase caalyc reacors: A perspecve on curren knowledge and fuure rends Caal. Rev. 44 (1), 2002, 123. [4] A. Lakoa, J. Levec, R. G. Carbonell, Hydrodynamcs of rcklng flow n packed beds: relave permeably concep A.I.Ch.E. J., 48, 2002, 731. [5] P. R. Gunal, M. N. Kashd, V. V. Ranade, and R. V. Chaudhar, Hydrodynamcs of rckle-bed reacors: expermens and CFD modelng Ind. Eng. Chem. Res. 2005, 44, [6] S. T. Se and R. Krshna, Process developmen and scale up: III. Scale-up and scale-down of rckle bed processes Rev. Chem. Eng. 14, 1998, [7] S. Goo and J. M. Smh, Trckle bed reacors performance: I hold-up and mass ransfer effecs A.I.Ch.E. Journal 21, 1975, 706. [8] R. A Holub, M. P. Dudukovc, and P. A. Ramachandran, Pressure drop, lqud hold-up and flow regme ranson n rckle flow A.I.Ch.E. Journal 39, 1993, 302. [9] A. E. Saez and R. G. Carbonell, Hydrodynamc parameers for gas lqud cocurren flow n packed beds A.I.Ch.E. J. 31, 1985, 52. [10] R. J. G. Lopes, A. M. T. Slva, and R. M. Quna-Ferrera, Screenng of caalyss and effec of emperaure for knec degradaon sudes of aromac compounds durng we oxdaon Appl. Caal B: Envronmenal, 73 (1), 2007, [11] FLUENT 6.1., User s Manual o FLUENT 6.1. Fluen Inc. Cenrera Resource Park, 10 Cavendsh Cour, Lebanon, USA. [12] A. Aou and G. A. Ferschneder, Two-flud model for flow regme ranson n gas lqud rckle-bed reacors Chem. Eng. Sc. 54 (21), 1999, [13] R. J. G. Lopes, A. M. T. Slva, and R. M. Quna-Ferrera, Knec Modellng and Trckle-Bed CFD Sudes n he Caalyc We Oxdaon of Vanllc Acd Ind. Eng. Chem. Res., 2007, n press. [14] GAMBIT 2, User s Manual o GAMBIT 2. Fluen Inc. Cenrera Resource Park, 10 Cavendsh Cour, Lebanon, USA. [15] D. Nemec and J. Levec, Flow hrough packed bed reacors: 2. Two phase concurren downflow Chem. Eng. Sc. 60 (24), 2005,