IMPROVING THE MATHEMATICAL MODEL OF A HETEROCATALYTIC TUBE REACTOR

Transcription

1 HUNARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPRÉM Vol. 36(1-) pp (008) IMPROVIN THE MATHEMATICAL MODEL OF A HETEROCATALYTIC TUBE REACTOR T. VARA,. RÁDI, T. CHOVÁN Unversty of Pannona, Department of Process Engneerng, H-800 Veszprém Egyetem u. 10., HUNARY E-mal: vargat@fmt.un-pannon.hu In recent decades the applcablty and usefulness of mathematcal models n the soluton of many ndustral problems have been shown. There are many cases when the correct answer can not be gven because of the complexty of the problem however CFD approaches can be appled to dg deeper and mprove the relablty of results. In ths work the mprovement of the frst-prncple model of a tubular fxed-bed reactor s shown applyng COMSOL Multphyscs. Mathematcal models of tubular fxed bed catalytc reactors to smulate ther operaton are well known and the formulaton of such models s well documented. In most cases the am of modelng s the development of the smplest model whch can be appled to solve the modelng task. However, nowadays these modelng problems can be more complcated and requre more accurate models, e.g. n case of model based dagnostc systems, early detecton systems. After the model wth the adequate complexty was developed t must be solved wth the necessary accuracy. In general, as the complexty of the model ncreases, so does the chance of encounterng numercal dffcultes. Our purpose s to apply the most approprate software methodology to solve problems at each level of the model herarchy, therefore a proccess model of an ndustral heterocatalytc reactor has been extended wth ntegratng transport processes on mcro level. The dea s the ntegraton of a model of a sngle catalyst pellet mplemented n COMSOL Multphyscs nto the steady-state process smulator of the reactor developed n MATLAB. The proposed approach makes possble to develop the model of a whole catalyst bed from the partcle models. The frst step to accomplsh our purpose s the mplementaton of the pellet model n the appled CFD code. Then the pellet model can be ntegrated nto the process smulator at the hgher model herarchy level. Keywords: heterocatalytc tube reactor, mechanstc modelng, computatonal flud dynamcs, catalyst pellet Introducton The am of all producton technologes s formaton of a more valuable materal through some chemcal reactons. The reactor s a place reactons generally take place. Hence, a reactor must be able to convert the necessary amount of raw materals nto products wth desred qualty n gven amount of tme. A chemcal technology can not be magned wthout a reactor consequently the desgn process of a reactor has a really mportant role n generatng a well proftable technology. Furthermore the planng of nstrumentaton and optmzaton of operatng varables s also crucal. Man steps n development of a well functonng reactor are the followng: defnng desred performance of reactor operaton; collectng all a pror nformaton and physcal constrants; determnng and/or nvestgatng velocty feld n the reactor; assgnng all operatng varables. Nowadays development of flow feld n process equpments s a key ssue n plannng of process unt. Wth a well desgned flow feld the overall process performance and safety of operaton can be ncreased at the same tme. To support ths step, dfferent modelng softwares and flow sheet smulators have been developed n last decades. As computatonal capacty of computers has beng ncreased the role of computatonal flud dynamcs (CFD) n appled modelng techncs and methods has sgnfcantly grown snce the frst computer was swtched on [1]. CFD s a collecton of numercal solvers for partal dfferental equatons. Wth applyng CFD codes more complcated problems n more complex structures can be nvestgated n detals than wth other modelng techncs. Couplng of mathematcal models of dfferent physcal and chemcal processes wth effcent numercal solvers makes possble to analyze chemcal engneerng and other knd of engneerng problems n much more detals. Of course, as n other modelng techncs, CFD models must be valdated before t can be used to predct the behavor of nvesgated system. Valdaton of models s based on comparng smulaton results wth measured varables,.e. developng an adequate CFD model, because of the complexty of model, needs welldesgned and precsely carred out experments.

2 144 In recent years many papers applyng CFD techncs to analyze some phenomenon or to desgn a reactor have been publshed. The most frequently nvestgated phenomenon are the transport processes between a statonary and a movng phase, or two movng phases, such as heat transfer [] and mass transfer [3] n a fludzed bed. Another nterestng feld of applcaton of CFD models s the modelng of bubble columns [4-8]. CFD models can be appled not only n reactor and column desgn but n solvng other knd of engneerng problems, e.g. desgnng a protectve sut [9]. These examples show that CFD s capable to smulate transport processes and t can be appled as a part of complex mathematcal model. In ths paper the concept of a detaled mathematcal model of an ndustral used heterocatalytc reactor wll be ntroduced. The former verson of reactor model was appled n a Operator Support System [10] to support process operators n choosng approprate values of mportant operatng varables to keep the producton n safe and effcent regme. To mprove the accuracy of our reactor model mass and heat transfer processes between sold catalyst pellets and movng gas are consdered. In prevous nvestgatons a small dfference was notced between the characterstc of measured and calculated temperature profles but model relablty couldn t be furher mproved wthout ncreasng model complexty. However, to mprove our quas-sngle phase model sold phase and all coupled transport processes are consdered. Our dea s the ntegraton of the model of a sngle catalyst pellet mplemented n COMSOL Multphyscs nto the steady-state process smulator of the reactor developed n MATLAB. The proposed approach makes possble to buld up catalyst bed from partcles whch have dfferent sze. The frst step to accomplsh our purpose s the mplementaton of the pellet model n the appled CFD code. Then pellet model can be ntegrated nto the process smulator at the hgher model herarchy level. After short ntroducton regardng the most frequently appled CFD codes and some CFD applcaton examples n model development the nvestgated case study s presented, than smulaton results obtaned at ths level of work are evaluated and fnally conclusons are drawn and future steps are outlned. Case study Our approach s to apply the most approprate software to solve problems at each level of model herarchy, therefore a mathematcal model of an ndustral heterocatalytc reactor was developed wth ntegratng processes at the level of thermodynamc phases. Reactor model The nvestgated, vertcally postoned reactor contans a large number of tubes flled wth catalyst as shown n Fg. 1. A hghly exothermc reacton takes place as reactants are rsng up n tubes passng through the fxed bed of catalyst partcles whle generated heat by reacton s removed through tube walls by coolng meda. The reacton has equalbrum and snce temperature s ncreasng n reactor more and more product decomposed. Due to the hghly exothermc reacton t has a great chance to develop hot spots some n catalyst bed whch ncrease the rate of catalyst ageng. Drecton of the flow of coolng meda s not mportant n ths process because there s only 7-8 K dfference between the nlet and outlet temperature of coolng meda. Selecton of approprate operatng condtons s mportant to avod the development of reactor runaway and to ncrease lfetme of catalyst. The nvestgated reactor s a heterocatalytc tube reactor gas phase s the movng phase whle catalyst s the statonary phase. In our prevous work a quas-sngle phase mathematcal descrpton of the reactor was ntroduced [10]. Snce model accuracy couldn t be mproved wthout ncreasng model complexty the quas-sngle phase must be dvded nto sold and gas phases as t shown n Fg.. State varables are calculated n both phases whch are coupled by mass and heat transport processes. As t can be seen at components level n Fg. the reacton s consdered only n sold phase so the produced heat by the hghly exothermc reacton s removed by coolng meda n jacket. coolant out W,out W ( T, B ) coolant n W,n W ( T, B ) product,out T, B,out,out,out (, c, p ) reagents,n T, B,n,n,n (, c, p ) Fgure 1: Smplfed scheme of reactor x = L x = 0 As t can be seen n the model structure n Fg. process varables calculated n two phases n the tubes. Thermodynamc phases are coupled by mass and heat transport processes. Steps of the assumed overal process are summarzed n Fg. 3. Frst steps, the adsorpton of reagents take place smultanously and t s called compettve adsorpton because two components are competng to get to the same actve stes on the surface

3 145 of the catalyst. After both reagents adsorb a second order reacton takes place and generates the product whch leaves the surface of catalyst by desorpton process. Developed model calculates changes only along the reactor,.e. model s one dmensonal and t doesn t consder the dffusvty along the radus of catalyst bed. Before the ntroducton of model equatons some smplfcatons must be consdered to smplfy the real problem. These smplfcatons are summarzed as follows: gas and sold phases are consdered n tubes, whch are connected by the mass and heat transport processes; hghly exothermc, second order reacton takes place n sold phase; dffusvty along radus of the reactor s neglected; all catalyst pellets have the same sze and sphercal shape; to calculate pressure drop n catalyst bed a modfed Ergun-equaton s appled. A steady-state model based on the overall rate of all mass transport processes and reacton wth detaled descrpton of appled smplfcatons can be found n [10]. That model was solved n MATLAB and calculated temperature profles were compared to measured ones n order to determne mssng model parameters. It was concluded that accuracy of developed model was approprate, although some mnor dfferences could be experenced between characterstcs of calculated and measured profles. To further mprove model accuracy, overall rate was substtuted for by a CFD model of a catalyst pellet to smulate basc steps ntroduced n Fg. 3. Steady-state reactor model s not ntroduced n ths paper, a detaled descrpton can be found n [10]. Sold phase Tube(s) Mass&Heat transport Reactor A B C X A B C Reacton(s) Heat transport as phase Fgure : Structure of two phases model Jacket Lqud phase Our concept s the ntegraton of a catalyst pellet model mplemented n COMSOL Multphyscs nto the reactor smulator developed n MATLAB. The frst step to accomplsh our objectve s the mplementaton of pellet model n the appled CFD code. As t can be seen n Fg. processes at the mcro level can be smulated and developed CFD model can be ntegrated nto hgher herarchy level. COMSOL s more than just a software whch uses a CFD code because mathematcal models of many processes n dfferent area of scence are collected and classfed; consequently the necessary tme to solve an W engneerng problem s less than wth applyng other CFD software. COMSOL apples the fnte element method [1] to dscretze the nvestgated object and to solve model. Fgure 3: Basc steps of the assumed overall process Catalyt pellet model n COMSOL Multphyscs The frst step of model buldng n COMSOL s the selecton of the necessary correlatons from the model collecton. Of course there s a possblty to ntroduce new correlatons. To nvestgate complex geometres an nteractve graphcal nterface helps the user to defne t or the user can mport t from a CAD software. Our COMSOL model contans only one catalyst pellet wth the narrow surroundngs of the partcle. The surroundng s flowng around the pellet and the transport processes make the connecton between two phases. MATLAB smulator runs ths smulator and bulds the whole catalyst bed. Dfference between each pellet s consdered by changng boundary condtons before solvng the pellet model. To descrbe the whole catalyst bed the MATLAB smulator of the reactor evaluates boundary condtons based on the poston of the acual pellet n the catalyst bed. Because of the axal symmetry of tubes and the sphercal symmetry of the catalyst pellet the COMSOL model s two dmensonal. Based on the ntroduced smplfcatons and the ntroduced pellet model the followng equatons were appled to calculate the state varables n both phase. All component mass balances n the gas phase contan terms to calculate convectve and conductve transport processes and naturally the mass transport process between the sold and gas phase: d ( B c ) = D d c + A β S ( c c ), B flow rate of gas phase; c concentraton of -component n gas phase; = {A; B; C}; x reactor length; D dffuson coeffcent of -component n gas phase; A nterface area between the gas and sold phase; β mass transfer coeffcent between the gas and sold phase of -component; c S concentraton of -component n sold phase.

4 146 Of course the convectve term n sold phase s mssng: S S d c S S D = A β ( c c ) + V ν r, D S dffuson coeffcent of -component n sold phase; V S the volume of sold phase; ν the stochometrc coeffcent of -component; r reacton rate whch s calculated by the followng correlaton: E A S S S S S cc c R T X r = k 0 e c A c B, K k 0 preexponental factor; E A actvaton energy; R deal gas constant; T S temperature of sold phase; c x S concentraton of actve stes on catalyst; K reacton eqaulbrum constant whch s a functon of the temperature. As t can be seen n the last equaton the effect of temperature on reacton rate s consdered therefore changes of temperature of gas and sold phase are calculated too. Terms n both equatons are the same as those consdered n component balances: d T dt ρ c p B = λ + S + A α ( T T ), ρ densty of gas phase; c heat capacty of gas phase; T temperature of gas phase; λ heat conducton coeffcent n gas phase; α heat transfer coeffcent between the gas and sold phase. a) Temperature n catalyst pellet and n surroundngs b) The concentraton of A component n catalyst pellet and n surroundngs c) Concentraton of B component n catalyst pellet and n surroundngs d) Concentraton of C component n catalyst pellet and n surroundngs Fgure 4: Changes n the value of state-varables along the nvestgated part of reactor n steady-state

5 147 And fnally the heat balance of sold phase: λ S S d T = A α S S ( T T ) + V r ( ΔH ), λ S heat conducton coeffcent n sold phase; H r reacton heat. Ths s just a short descrpton of model equatons to show the structure of pellet model. All physcal propertes are calculated as the functon of temperature. These eqautons were mplemented n COMSOL to develop a pellet model whch replaces the reacton rate of overall catalyst processes of earler developed reactor smulator. Integraton of reactor smulator made n MATLAB and the pellet model mplemented n COMSOL s just a vson yet, stll as t can be seen n next chapter that pellet model gves good results. Results and dscussons To check the applcablty of the developed COMSOL Multphyscs pellet model n our modelng approach, the value of state varables n front of reactor were gven as boundary condtons n the soluton of the pellet model. enerated results are plotted n Fg. 4. In Fg 4a temperature surface can be seen and as t was expected the hghly exothermc reacton takng place n catalyst ncreases the temperature of pellet and t warms up the flowng gas. Due to the dffuson n catalyst pellet the concentraton of reagents decrease n the drecton to the centre of the pellet (check Fg. 4b and Fg. 4c.) whle the concentraton of the product changes n the opposte drecton as shown n Fg. 4d. In ths model all components can be connected to the same actve stes on the catalyst but n realty there s a competton between components and the rate and the equalbrum of the adsorpton determne the concentraton n the catalyst. Snce the temperature profle and propertes of nlet and outlet flow are measured durng the reactor operaton the catalyst pellet model can not be valdated wthout ntegratng t nto the reactor smulator. As t can be seen n Fg. 4d the outlet concentraton of product from the nvestgated part of the reactor s very low and t suggests that the parameters appled to calculate the rate of adsorpton must be modfed. Stll the characterstc of changes n case of all the calculated state varables are the same as we expected. r Conclusons and future work To follow an operaton of a tube reactor usually process operators do not have any more nformaton but some temperature measurements along the reactor and composton of nlet and outle flow. Hence, a reactor smulator can be very useful to follow the operaton and to help process operators, e.g. to avod development of reactor runaway or to optmze reactor operaton. To acheve ths am an adequate reactor model wth correct model parameters s needed. The paper proposed a possble way to mprove a former developed mathematcal model of a heterocatalytc tube reactor appled n the process ndustry to detect reactor runaway. At ths phase of our work applcablty of COMSOL Multphyscs n modelng a catalyst pellet and ts narrow surroundngs s nvestgated. The developed model and the appled software can be appled to generate and smulate state varables n the whole catalyst bed. Integraton of pellet model nto an earler developed reactor smulator s our next step. After the success ntegraton a model valdaton must be performed comparng the calculated temperature profles wth the measured ones. Fnally the accurate model can be bult nto an operator support system to mprove relabllty of runaway detecton. REFERENCES 1. RANADE V. V.: Computatonal flow modellng for chemcal reactor engneerng, Academc Press (00). BEHJAT Y., SHAHHOSSEINI S., HASHEMABADI S. H.: Internatonal Communcatons n Heat and Mass Transfer 5 (008) JUN J., AMWO I. K.: Powder Technology 183 (008) BHOLE M. R., JOSHI J. B., RAMKRISHNA D.: Chemcal Engneerng Scence 63 (008) KLUSENER P. A. A., JONKERS., DURIN F., HOLLANDER E. D., SCHELLEKENS C. J., PLOEMEN I. H. J., OTHMAN A., BOS A. N. R.: Chemcal Engneerng Scence 63 (007) ZHAN D., DEEN N.., KUIPERS J. A. M.: Chemcal Engneerng Scence 61 (006) DARMANA D., DEEN N.., KUIPERS J. A. M.: Chemcal Engneerng Scence 60 (005) CHEN P., SANYAL J., DUDUKOVIC M. P.: Chemcal Engneerng Scence 59 (004) TESCH K., COLLINS M. W., KARAYIANNIS T.., ATHERTON M. A., EDWARDS P.: Appled thermal engneerng, (008) n press 10. VARA T., SZEIFERT F., CHOVÁN T., RÉTI J.: Műszak Kéma Napok 07, Konferenca Kadvány, (007)