From a detailed model of porous catalytic washcoat to the effective model of entire catalytic monolith
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1 Insiue of Chemial ehnology Prague Ceh Republi From a deailed model of porous aalyi washoa o he effeive model of enire aalyi monolih Per Kočí Vladimír Nová Franiše Šěpáne Miloš Mare Milan Kubíče hp://
2 Caalyi monolih reaor monolih hannels d ~1 mm L ~ 10 m wall meal foil or eramis ~ 100 m porous washoa e.g. -Al 2 O 3 ~ m aalyi sies meal rysallies e.g. P ~ 1-10 nm
3 Muliple sales in aalyi monolih reaor maro-sale aalyi monolih ~ 10 m hannel wih aalyi washoa on he wall ~ 1 mm miro-sale porous aalyi washoa ~ 10 m nano-sale meso-porous -Al 2 O 3 wih dispersed P pariles ~ 100 nm Kočí e al. 2006
4 Monolih hannel inle gas oule gas 0 L r 0 flowing gas onveion C H D eff r r mass & hea ransfer porous washoa diffusion ofen no onsidered adsorpion surfae reaions hea aumulaion & onduion wall hea aumulaion & onduion no reaions Gühene e al. 2007
5 flowing gas mass balane C ε a u aalyi surfae mass balane J m m m R 1 ap ν Ψ 1 flowing gas enhalpy balane H p p a u + respeive boundary & iniial ondiions Sandard mahemaial model of a monolih hannel - 1D washoa washoa pores mass balane J C R -ε a ε 1. ν 1 solid phase enhalpy balane 1 1 R 2 2 a R H H J p Gühene e al. 2007
6 flowing gas mass balane C ε a u washoa pores mass balane J R r D r ε eff ν aalyi surfae mass balane J m m m R r 1 ap 1 ν Ψ flowing gas enhalpy balane H p p a u solid phase enhalpy balane 1 d H 1 0 R 2 2 p a r R H a J r Mahemaial model of a monolih hannel - 2D 1D+1D washoa + respeive boundary & iniial ondiions Gühene e al. 2007
7 Porous sruure of he washoa - bimodal pore sie disribuion maropores d ~ 1 m void spae among he supporing maerial miro-pariles mesopores d ~ 10 nm pores inside he supporing maerial miro-pariles maropores bla mesoporous -Al 2 O 3 grey CeO 2 whie noble meals P rysallies several nm 10 m SEM 220 nm EM Complex porous sruure: Overall effeive diffusion oeffiien D eff? m 2 /s Sarý e al. 2006; Kočí e al ; Nová e al. 2009
8 Compuer reonsruion of porous aalys from 2D images 2D SEM or EM image Image proessing hresholding binary image 3D reonsrued medium 30 m Kose e al Generaion of 3D medium: a mehanisi pariles paing and sinering or b sohasi Gaussian fields simulaed annealing R Auoorrelaion Rx Ry funion Ru pore-sie disribuion parile-sie disribuion
9 Charaeriaion of porous sruure Phase funion Z: R 3 {01} Zx = 1 x pore spae Zx = 0 x solid Phase volume fraions = Zx porosiy R Z u Auo-orrelaion funion L R Z u = Zx+u - Zx - / Zx - 2 Minowsi funionals Mean urvaure Gaussian urvaure Cord-lengh disribuion funion e. Kose e al fl l u
10 Dire reonsruion of 3D porous sruure from X-ray miroomography Sanning of he sample from differen angles superposiion of he proeions. Advanage: Non-invasive mehod 3D image of he porous medium obained Disadvanage: lower resoluion han lassial 2D SEM/EM Fig: 3D sanned ordierie subsrae sample. Nová e al μm.
11 wo sales in aalyi monolih washoa: miro and nano aalyi monolih ~ 10 m hannel wih aalyi washoa on he wall ~ 1 mm miro-sale porous aalyi washoa ~ 10 m nano-sale meso-porous -Al 2 O 3 wih dispersed P pariles ~ 100 nm Kočí e al. 2006
12 Reonsruion of porous P/-Al 2 O 3 aalys on nano-sale 1. Defined -Al 2 O 3 nanopariles sie shape. 2. -Al 2 O 3 agglomeraion. se of P nano-pariles 3. Random paing of -Al 2 O 3 nano-pariles and/or lusers. 4. Defined P nano-pariles sie. 5. Random P inserion ono -Al 2 O 3 surfae ino available pores. P/-Al 2 O 3 nano-sysem wih disreised mesopores and P pariles single -Al 2 O 3 nano-parile Kočí e al luser of -Al 2 O 3 nano-pariles sysem of paed -Al 2 O 3 nano-pariles
13 Reonsruion of porous P/-Al 2 O 3 aalys on miro-sale 1. P/-Al 2 O 3 nano-sysem meso-porous sruure disribuion of P nano-pariles. 2. Simplifiaion of he nano-sysem ino he form of defined P/-Al 2 O 3 miro-parile sie shape effeive P onenraion mean inernal meso-pore diameer. 3. Random paing of P/-Al 2 O 3 miropariles wih defined overlap sinering level. P/-Al 2 O 3 nano-sysem Kočí e al P/-Al 2 O 3 miro-parile = simplified represenaion of he nano-sysem P/-Al 2 O 3 miro-sysem = washoa seion wih disreised maro-pores
14 Evaluaion of loal pore sies and loal diffusiviies Loal pore sie deermines loal diffusiviy Knudsen diffusion. How o evaluae effeive loal pore sie in general porous medium? Maximum sphere insripion MSI mehod Map of loal pore sies -> map of loal diffusiviies. Validaion of MSI mehod omparison wih moleular dynamis simulaions. Nová e al. 2009
15 ypial pore-sie disribuions in reonsrued P/-Al 2 O 3 Nano-sale model Miro-sale model Real aalys sample measured by merury porosimery Kočí e al. 2009
16 Mahemaial model of mass & hea ranspor and reaions in spaially 3D reonsrued porous aalys nano- and miro-sale gas mass balanes: surfae mass balanes: enhalpy balane: Kočí e al
17 Mahemaial model es ase reaion ineis: CO oxidaion on P/Al 2 O 3 = aive P sie boundary ondiions: Kočí e al
18 CO onenraion profile in P/-Al 2 O 3 nano-sysem Sysem sie m 3. he delimied ones wih ero CO onenraion orrespond o solid -Al 2 O 3 nano-pariles. he P pariles 4 nm are displayed in dar grey. Aive C P = 184 mol/m 3 = 653 K. Kočí e al. 2009
19 Effes of P pariles sies Sysem sie m 3 onsan oal amoun of P vol. fra. P = Kočí e al C P... onenraion of aive P sies... P dispersion N P... number of aive P sies
20 CO oxidaion in porous P/Al 2 O 3 aalys miro-sale model CO onenraion CO reaion rae Profiles of he CO onenraion and reaion rae. = 240 C 3 and 1 m pariles 1:16 sinering =0.15 M = 18.1 % C P = 50 mol/m 3. Caalys seion sie 10x10x10 m 3. Kočí e al
21 Effe of emperaure on inernal onenraion gradiens = 220 C = 260 C CO onenraion profiles. 3 and 1 m pariles 1:16 sinering =0.15 M = 18.1 % C P = 50 mol/m 3 Kočí e al
22 Dependene of effeiveness faor on emperaure and aalys morphology on miro-sale = 10 m aive C P = 50 mol/m 3 small:large Al 2 O 3 miro-pariles raio = 8 Kočí e al. 2007
23 Dependene of maropores surfae densiy a M hydrauli diameer d h and maroporosiy M on he mixing raio of he 1 and 3 m Al 2 O 3 miro-pariles Kočí e al
24 CO reaion rae profile in P/-Al 2 O 3 miro-sysem Loal represenaion of enire washoa layer = 30 m Sysem sie m 3 miro-sale model. Empy spae = maro-pores. Paed spherial P/-Al 2 O 3 miro-pariles wih diameers 1 m and 3 m small:large pariles raio 32 sinering level =0.15. Inernal meso-pores d=10 nm. Aive C P =50 mol.m 3 uniform disribuion y O2 bnd =2 % y CO bnd =0.5 % bnd =220 C. Kočí e al. 2009
25 Calulaed average reaion raes and effeiveness faors for a model P/-Al 2 O 3 aalyi washoa = 30 m he alulaed able of effeive reaion raes for aual washoa sruure an be used for evaluaion of loal reaion raes in he sandard 1D model of monolih hannel. -> Muli-sale model Sysem sie m 3 miro-sale model. Paed spherial P/-Al 2 O 3 miro-pariles wih diameers 1 m and 3 m small:large pariles raio 32 sinering level =0.15. Inernal meso-pores d=10 nm aive C P =50 mol.m 3 y O2 bnd =2 %. Kočí e al. 2009
26 Muli-sale model simulaed CO ligh-off urve Caalyi monolih 400 psi L = 10 m washoa = 30 m aive C P = 50 mol/m 3. SV = h -1 y CO in = 0.3 % y O2 in = 2 %. Kočí e al. 2009
27 Muli-sale model Simulaed CO ligh-off urve Effe of washoa maropores sinering level Caalyi monolih 400 psi L = 10 m washoa = 30 m aive C P = 50 mol/m 3. SV = h -1 y CO in = 0.3 % y O2 in = 2 %. Kočí e al. 2009
28 Summary Kočí e al Kočí e al. 2009
29 Summary Mehodology and models for deailed simulaions of reaion-ranspor proesses in porous aalys layer washoa were disussed: 3D digial reonsruion of porous aalys based on 2D SEM/EM images and 3D miroomopgraphy. Evaluaion of loal pore sies and diffusiviies. Soluion of reaion-diffusion problem in heerogeneous 3D sysem. Dependene of aalys performane on is sruure -Al 2 O 3 and P parile sies sinering level pore-sie disribuion porosiy. Muli-sale approah he volume-averaged parameers alulaed in he nano- and miro-sysem used as inpu parameers for simulaions a he full sale enire monolih reaor.
30 Referenes P. Kočí V. Nová F. Šěpáne M. Mare M. Kubíče: Muli-sale modelling of reaion and ranspor in porous aalyss Chemial Engineering Siene 2009 in press hp://dx.doi.org/ /.es V. Nová F. Šěpáne P. Kočí M. Mare M. Kubíče: Evaluaion of loal pore sies and ranspor properies in porous aalyss Chemial Engineering Siene 2009 in press hp://dx.doi.org/ /.es P. Kočí F. Šěpáne M. Kubíče M. Mare: Modelling of miro/nano-sale onenraion and emperaure gradiens in porous suppored aalyss Chemial Engineering Siene hp://dx.doi.org/ /.es A. Gühene D. Chaeree M. Weibel B. Krush P. Kočí M. Mare I. Nova E. rononi: Curren saus of modeling lean exhaus gas aferreamen aalyss in "Advanes in Chemial Engineering vol. 33: Auomoive Emission Conrol" pp ed. G. B. Marin ISBN: Elsevier P. Kočí F. Šěpáne M. Kubíče M. Mare: Meso-sale modelling of CO oxidaion in digially reonsrued porous P/ γ-al2o3 aalys Chemial Engineering Siene hp://dx.doi.org/ /.es J. Kose F. Šěpáne M. Mare: Modelling of ranspor and ransformaion proesses in porous and muliphase bodies in Advanes in Chemial Engineering Elsevier More a hp://
31 Insiue of Chemial ehnology Prague Ceh Republi From a deailed model of porous aalyi washoa o he effeive model of enire aalyi monolih Per Kočí Vladimír Nová Franiše Šěpáne Miloš Mare Milan Kubíče hp://
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