Modeling of Transport and Reaction in a Catalytic Bed Using a Catalyst Particle Model.

Transcription

1 Excerpt from the Proceeding of the COMSOL Conference 2010 Boton Modeling of Tranport and Reaction in a Catalytic Bed Uing a Catalyt Particle Model. F. Allain *,1, A.G. Dixon 1 1 Worceter Polytechnic Intitute - Chemical Engineering Department, Worceter, MA, USA *Correponding author: Worceter Polytechnic Intitute, Chemical Engineering Dpt. 100 Intitute Road, Worceter, MA 1609, USA. florent.allain@wpi.edu Abtract: A packed bed reactor coniting of pherical catalyt particle in a tube wa imulated numerically. The teady tate peudoheterogeneou model conited of a peudocontinuum repreentation for the heat and ma tranfer in the reactor tube. The reaction ource term were evaluated by explicitly olving a 1D pherical pellet model at each dicretization point. The ue of coupling variable between two geometrie wa crucial in thi tudy. A tet cae wa firt run againt literature reult for carbon monoxide converion (1). The model wa then run for methane team reforming for comparion to 3D CFD. The tet cae gave atifactory reult when compared to the literature, giving imilar profile but lightly different value for temperature and concentration. Keyword: packed bed, catalyt, particle, reaction engineering. 1. Introduction Tubular packed bed reactor are amongt the mot commonly ued reactor in the indutry, for reaction uch a CO combution, or methane team reforming. Ma and heat tranfer between the fluid phae and the catalytic olid phae repreent the main problem when conidering thee reactor in reaction engineering. Many model have been propoed and tudied throughout the 20th century, improving one after another the coupling between the two phae. From a imple peudo-homogeneou model where both fluid and olid are conidered at the ame temperature, to peudo-heterogeneou model uing effectivene factor to account for diffuion limitation between the two phae, a lot of progre ha been made in the decription of tubular packed bed reactor. Computational power limitation wa a great factor of influence in the implification that had to be made in order to be able to olve thee model. Thee limitation having been greatly overcome, we can now ue more ophiticated model where the reaction ource term are evaluated by explicitly olving a 1D pherical pellet model at every dicretization point of the bed, without the ue of an effectivene factor. One of thee teady-tate peudo-heterogeneou model, with peudo-continuum repreentation for heat and ma tranfer i ued in thi paper to olve 2 cae: the carbon monoxide combution and the methane team reforming (MSR). 2. Reactor model. The peudo-heterogeneou model ued in thi paper i decribed in thi ection. The ytem conit of a bed of catalyt particle and a fluid phae. The fluid phae i decribed by a et of 2D partial differential equation, accounting for the heat and ma balance in the fluid, and the olid phae by the ame number of 1D differential equation, accounting for the balance in the catalyt particle. The catalyt particle are uppoed pherical and urrounded by the uniform concentration and temperature of the fluid at that ame point. The model i pictured in Figure Fluid equation Ma balance: (one for each pecie i) C i z + 1 Pe mr,i Heat balance: T z + 1 Pe r 2 C i r r C i r C i Pe ma,i z 2 = St m,i C i C i, 2 T r T T r r Pe a z 2 = St T T

2 conducted in a reactor with a gradient of temperature along the wall. z = 0 C i z = Pe ma,i C i C i,in T z = Pe a T T in z = L Rt r = 0 r = 1 Convective fluxe for C and T, Axi ymmetry for C and T C i r = 0 inulation T r = Bi T T w 3. Ue of COMSOL Multiphyic Figure 1. 2D bed and 1D particle model. 2.2 Solid equation Ma balance: (one for each pecie i) 2 C,i ξ 2 = 2 C,i + φ 2 rate ξ ξ Heat balance 2 T ξ 2 = 2 T ξ ξ + βφ2 rate 2.3 Boundary condition ξ = 1 Solid phae: C,i ξ = S,i C,i 1, T ξ = Bi T ξ = 0 Axi ymmetry. Fluid phae: The et of boundary condition for the temperature were different in the two tudie. The CO combution (cae 1) wa done at a contant wall temperature, the MSR (cae 2) wa The previouly decribed equation were entered in the chemical engineering module of COMSOL Multiphyic, a teady tate analyi. The fluid equation were entered a convection diffuion equation and the olid one a conduction for the heat balance, and diffuion for the ma balance. The imulation were done with dimenionle parameter. The 2 et of equation had to be coupled. The olid equation had to be olved at every dicretization point of the fluid bed, in order to get the olid urface condition. Thee are then ued to evaluate the tranfer between the two phae at the pellet urface. To do o, a 3D geometry wa created. Two of the coordinate of thi geometry tand for the 2D bed coordinate (the ame a for the fluid equation), and the lat one a the pellet radial coordinate. Therefore, we only ue one of the dimenion of thi 3D model to implement the 1D equation of the olid at every point of the fluid bed. Then, a hown in Figure 2, extruion coupling variable are added to the model, to tranfer the 2D bed condition to the 3D geometry providing the condition urrounding the pellet at every point, and to tranfer the pellet urface condition to the 2D geometry, in order to evaluate the exchange term between fluid and olid urface.

3 D (aniotropic) 1/phiqr R 2/x*cx*1/phiqr-rate ξ=0 Inulation/Symmetry ξ=1 Flux: N 0 =0, c b =1, k c =Sh/phiqr r=0 Inulation/Symmetry r=1 Inulation/Symmetry z=0 Inulation/Symmetry z=1 Inulation/Symmetry Table 3. COMSOL parameter for the ma diffuion model in the olid. Figure 2. Coupling between 2D (Fluid bed) and 3D (Solid particle) geometrie. The following table will give the parameter of the equation a they were entered in COMSOL for the CO converion cae. The MSR cae ued the ame kind of equation, lightly modified becaue of the 3 different reaction and the different wall boundary condition for the heat equation. Alo, the MSR cae wa imulated without axial diperion to implify calculation. The convergence wa et at D (aniotropic) 1/Pemr 0 0 1/Pema R -Stm*(c-cf) u -1/r*1/Pemr v 1 z=0 Flux: N 0 =1 z=l/rt Convective flux r=0 Axial ymmetry r=1 Inulation/Symmetry Table 1. COMSOL parameter for the ma convection and diffuion model in the fluid. k (aniotropic) 1/Pehr 0 0 1/Peha ρ, C p, γ 1, 1, 1 Q -Sth*(T-Tf) u -1/r*1/Pehr 1 z=0 Heat Flux: q 0 =1-T z=l/rt Convective flux r=0 Axial Symmetry r=1 Heat Flux: q 0 =Bi/Peha*(1-T) Table 2. COMSOL parameter for the heat convection and conduction model in the fluid. k (aniotropic) 1/(beta*phiqr) Q 2/x*Tx*1/(beta*phiqr)+rate ξ=0 Inulation/Symmetry ξ=1 Heat Flux: q 0 =0, h=bi/(phiqr*beta), T inf =1, Cont=0, T amb =0 r=0 Inulation/Symmetry r=1 Inulation/Symmetry z=0 Inulation/Symmetry z=1 Inulation/Symmetry Table 4. COMSOL parameter for the heat conduction model in the olid. Our model will be referred to a the ingle pellet model in the ret of the paper. 4. Reult 4.1 CO converion The et of parameter ued for the tudy and imulation of CO converion were found in different ource (1, 2). Amongt other, the inlet concentration i et at 0.5 mol/m 3 for CO. The concentration of O 2 i fixed at 30.6 mol/m 3 and conidered contant. It diffuion in the particle i alo neglected, and we conider that there are no limitation to the tranfer at the urface of the pellet, and therefore the concentration i contant and the ame in the pellet a in the fluid. The inlet temperature, a well a the wall temperature, i et at 385K. The fluid temperature profile i provided in Figure 3. The reult compare with the literature. The profile i imilar, the hot pot appearing at the ame place; however the highet temperature i lower (by 30 K). Thi can be explained by the tranfer between the two phae being repreented more accurately in our cae, with

4 more limitation at the urface of the pellet and therefore a le effective tranfer. Figure 3. Temperature profile in the fluid obtained with the ingle pellet model for the reaction of CO converion (K). Actual tube goe from z =0 to 38. Figure 4 how the difference between olid urface and fluid temperature. When compared to previou work, thi difference i higher in our cae. They howed a maximum difference of approximately 20K, where we get a 45K difference. Thi difference i due to the better evaluation of the olid parameter through the olving of the heat diffuion equation in the entire olid particle. Alo it upport the idea of a bigger limitation for heat tranfer between the two phae. It i alo important to note that thi difference in temperature depend a lot on the diffuivity of CO in the catalyt and thi parameter might need ome adjutment. The profile of temperature in the olid particle i given in Figure 5. We can ee that the profile of temperature in a pellet i relatively flat, and follow the hape of the profile in the fluid, with higher value. Figure 5. Temperature profile in the olid particle obtained with the ingle pellet model. (K) Cae of CO converion. When looking at the CO concentration profile (Figure 6 and 7), we can clearly ee that the reaction occur very fat at the inlet of the tube. Figure 6. CO concentration profile in the fluid, obtained with the ingle pellet model. (mol/m 3 ) Actual tube goe from z =0 to 38. Figure 4. Temperature difference between olid and fluid at r =0.5 obtained with the ingle pellet model. (K) Figure 7. CO concentration in the olid particle, obtained with the ingle pellet model. (mol/m 3 ) Mot of the CO i conumed before z =5. The value for CO concentration in the fluid

5 phae that we obtained in the tudy are cloe to the one from the literature. Thi indicate a good evaluation in the previou tudy of the tranfer between the two phae and a good evaluation of the diffuion in the pellet, which wa completely olved in our cae. The reult we obtained in our cae are globally cloe to the one from the literature. However we have to keep in mind the fact that the concentration of oxygen wa uppoed contant in the fluid, but alo in the olid. The implementation of at leat a diffuion equation for the oxygen in the pellet might improve the reult, for both the concentration and the temperature profile. in the previou cae, that the temperature profile in one pellet i relatively flat. Once again, we will have to reevaluate the parameter for the heat and ma tranfer between the pellet and the fluid, becaue we can ee a temperature difference that goe up to 180K between the two phae, which i clearly not realitic. 4.2 MSR reaction Once the model wa validated with the reaction of CO converion, the cae of methane team reforming wa tudied. Thi cae preent everal challenge, in particular the fact that no concentration can be conidered contant, and that we therefore need to olve a ma balance for each pecie in both the olid and fluid phae. The parameter ued for the reaction rate are from Hou and Hughe (3). The fluid and tube propertie were taken from imulation done by Johnon Matthey. Figure 8 how the temperature profile in the fluid. We can ee that the heating through the wall take place, but the diffuion through the entire fluid i not efficient. Thi probably come from a problem in the evaluation of the effective heat tranfer coefficient at the wall. Figure 9. Temperature profile in the olid particle obtained with the ingle pellet model. (K) MSR Cae. Figure 10. H 2 concentration profile in the fluid, obtained with the ingle pellet model. (mol/m 3 ) Figure 8. Temperature profile in the fluid obtained with the ingle pellet model for the MSR reaction (K). When looking at the temperature profile in the pellet of catalyt in Figure 9, we can ee a Figure 11. H 2 concentration in the olid particle, obtained with the ingle pellet model. (mol/m 3 )

6 Figure 10 and 11 how the H 2 concentration profile in the fluid and in the olid. A the temperature profile how a high gradient near the wall, o doe the concentration profile. Alo the concentration difference between olid and fluid eem to be too high (up to 14 mol/m 3 ) to be realitic, which clearly how that parameter need to be adjuted. The meh need ome refining a well. Calculation were firt conducted on a coare meh, which wa then refined. However, computer power might become a limitation, becaue a better meh i till required. 5. Concluion Thi tudy uccefully imulated the reaction of CO converion uing a ingle pellet model implemented in COMSOL. The temperature and concentration profile where conitent with previou tudie with other reaction engineering model, howing a hot pot near the inlet of the tube, and a reaction occurring at the inlet. The cae of the MSR reaction need adjutment, a it i more complex and involve 3 toechiometrie and 5 pecie, leading to a number of 12 equation. Parameter need to be adjuted and the meh need to be refined in order to get conitent reult. 6. Nomenclature a p Catalyt pecific urface area (m -1 ), Bi i = d p f Biot number for pecie i, 2k C i Fluid concentration of pecie i (mol/ 3 ), C in Total fluid inlet concentration (mol/m 3 ), C i = C i Reduced fluid concentration of C in pecie i, C i Solid urface concentration of pecie i, fluid phae (mol/m 3 ), C,i Solid concentration of pecie i (mol/m 3 ), C i, Solid urface concentration of pecie i, olid phae (mol/m 3 ), C,i = C i, C i Reduced olid concentration of pecie i, C pf d p D a,i D r,i D e,i f k a k r k r,j k g,i k Pe a = urt k a Pe r = urt k r Pe ma,i = urt D a,i Pe mr,i = urt D r,i r Rt r = r Rt rate S i, = d p k g,i 2D e,i St = a p f Rt uρ f C pf St m,i = a p k g Rt u T T in T w T = T T in T w T T = T w T in T = T T u z Specific fluid heat capacity (J/kg/K) Pellet diameter (m), Axial fluid diffuivity for pecie i (m/), Radial fluid diffuivity for pecie i (m/), Diffuivity of pecie i in the catalyt particle (m/), Heat tranfer coefficient W/(m 2 K), Axial fluid thermal conductivity (W/K/m), Radial fluid thermal conductivity (W/K/m), Reaction j rate contant, Ma tranfer coefficient (m/), Catalyt thermal conductivity (W/K/m), Axial heat Peclet number, Radial heat Peclet number, Axial ma Peclet number for pecie i, Radial ma Peclet number for pecie i, Bed radial coordinate (m), Bed radiu (m), Reduced bed radial coordinate, Reaction rate Catalyt Sherwood number for pecie i, Fluid heat Stanton number, Fluid ma Stanton number, Fluid temperature (K), Inlet temperature (K), Wall temperature (K), Reduced fluid temperature, Reduced wall temperature, Temperature in the olid (K), Temperature at the urface of the olid (K), Reduced temperature in the olid, Inlet velocity (m/), Bed length coordinate (m),

7 z = z Rt Reduced bed length coordinate, Greek letter β i = ΔH j C i De,i T k ΔH j Adiabatic temperature rie in the pellet for pecie i, Enthalpy of reaction j (kj/mol) 1/2 φ i,j = d p 2 k r,j ρ 4C i De,i Thiele modulu for pecie i, reaction j, ρ f Fluid denity (kg/m 3 ), ρ Catalyt denity (kg/m 3 ) ξ Pellet radial coordinate (m), ξ = ξ d p /2 Reduced pellet radial coordinate, 7. Reference 1. A. Machac et al., Modeling of heat and ma tranport in a Nonlinear Catalytic Bed Reactor, Excerpt from the Proceeding of the 2006 Nordic COMSOL Conference (2006) 2. G.W. Koning and K.R. Weterterp, Modeling of Heat Tranfer in Wall-Cooled Tubular Reactor, Chem. Eng. Science, 54, (1999) 3. K. Hou and R. Hughe, The kinetic of methane team reforming over a Ni/α-Al 2 O catalyt, Chem. Eng. Journal, 82, (2001) Acknowledgement Acknowledgement i made to the Donor of the American Chemical Society Petroleum Reearch Fund for upport of thi reearch.