10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 20: Reaction and Diffusion in Porous Catalyst
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1 .37 Chemical ad Biological eactio Egieerig, Sprig 7 Prof. K. Dae Wittrup Lecture : eactio ad Diffuio i Porou Catalyt Thi lecture cover: Effective diffuivity, iteral ad overall effectivee factor, Thiele modulu, ad apparet reactio rate eactio & Diffuio -Diffuio i a porou olid phae Ex. Preciou metal o ceramic upport or ug/utriet delivery through tiue -Derive teady tate material balace accoutig for diffuio ad reactio i a pherical geometry -Thiele modulu () r [S] = urface cocetratio of a growth ubtrate (ex. glucoe ad O ) Figure. Sphere of Cell Aume peudo-homogeeou medium ad Fick Law decribe diffuio d[ S] # molecule Flux = D, where Flux [ = ] ad D [ = ] legth time r = kc VmaxC r = K + C area time Cite a: K. Dae Wittrup, coure material for.37 Chemical ad Biological eactio Egieerig, Sprig 7. MIT OpeCoureWare ( Maachuett Ititute of Techology. Dowloaded o
2 -r = = C Figure. ate of reactio veru pecie cocetratio t C K order r VmaxC K C K th order r V max Steady-tate Shell Balace I ome cae, S till ha t peetrated to the ceter t= t Figure 3. Time progreio a pecie, S, eter the phere Thi hell r to (r+δr) S i by diffuio S out by diffuio S co by reactio= 4 4 Flux π r Flux π r k C 4πr Δ r = r+ Δr r Divide through by 4πΔ r ad take the limit a Δr d( Flux r ) kcr = d dc D r kcr = dc dc k + C = d order ODE r D Boudary coditio:.37 Chemical ad Biological eactio Egieerig, Sprig 7 Lecture Prof. K. Dae Wittrup Page of 5 Cite a: K. Dae Wittrup, coure material for.37 Chemical ad Biological eactio Egieerig, Sprig 7. MIT OpeCoureWare ( Maachuett Ititute of Techology. Dowloaded o
3 C = C r=, C i fiite everywhere, or dc = r= Nodimeioalize r C ρ = S = C, ds ds + S = dρ ρ dρ Boudary coditio: ρ= S i fiite everywhere ( D) ( kc, ) kc, characteritic diffuio time = = = D characteritic reactio time If diffuio i low diffuio domiate If reactio i low reactio domiate If << reactio limited regime If >> diffuio limited regime << >> ubtrate throughout ubtrate ca t make it to the ceter Figure 4. eactio ad diffuio limited regime ih( ρ) S = ρ ih( ) e ih( z) = z e z.37 Chemical ad Biological eactio Egieerig, Sprig 7 Lecture Prof. K. Dae Wittrup Page 3 of 5 Cite a: K. Dae Wittrup, coure material for.37 Chemical ad Biological eactio Egieerig, Sprig 7. MIT OpeCoureWare ( Maachuett Ititute of Techology. Dowloaded o
4 =. S = ρ = Figure 5. S veru ρ for variou value of Defie effectivee factor η overall rate of reactio η = rate if C =C everywhere S, overall reactio rate i phere at teady tate = [iward r= (ρ=)]*area dc = D 4π r= ds = 4πDC = 4πDC coth 3 η =,, d ρ ρ = ( coth ) ( ) η.. η.. Figure 6. Log-log plot of effectivee factor veru thiele modulu Higher value of Thiele modulu effectivee goe dow *For a variety of reactio kietic, geometrie ad rate law, plot of η v all look the ame..37 Chemical ad Biological eactio Egieerig, Sprig 7 Lecture Prof. K. Dae Wittrup Page 4 of 5 Cite a: K. Dae Wittrup, coure material for.37 Chemical ad Biological eactio Egieerig, Sprig 7. MIT OpeCoureWare ( Maachuett Ititute of Techology. Dowloaded o
5 Shrikig Core Model I cae with ocatalytic ad irreverible reactio, diffuio limit i decribable by the hrikig core model. Figure 7. Shrikig core model apid, irreverible reactio limited by rate of diffuio of a reactat from the urface The followig mut be writte dow for the hell balace:. ate of reactio. ate of diffuio 3. ate of movemet of the core.37 Chemical ad Biological eactio Egieerig, Sprig 7 Lecture Prof. K. Dae Wittrup Page 5 of 5 Cite a: K. Dae Wittrup, coure material for.37 Chemical ad Biological eactio Egieerig, Sprig 7. MIT OpeCoureWare ( Maachuett Ititute of Techology. Dowloaded o
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