Lecture 22: Combined Internal & External Transport Resistances

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 22: Combined Internal & External Transport Resistances Packed Bed Reactor Æ use PFR equation dFi = Ari eff dz z=0 z=L Figure 1. Packed Bed Reactor ri eff ≠ ri chem ri eff = Ωri chem Æ if Ω ≈ 1 ? if Ω 1 ? ( Ω > 1 ) –weird BL: δ porous catalyst particle dp Figure 2. Porous Catalyst Particle Biot Number: Bi ∼ external heat transfer resistance internal heat transfer resistance Mass transfer Biot Number: Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Bim = kc d p where kc ∼ D fluid eff Dinside D diameter Bim = efffluid Dinside δ δ Mears’ Test: rA′ (observed) ρb R p n if kc C A bulk < 0.15 where n ≡ order of rxn then C Ab ≈ C As (no external diffusion limitation) Æ i.e. no changing concentration across the boundary layer Similarly, if ΔH rxn rA′′ (observed or theory) ρb R p Ea h fluid RT 2 < 0.15 then Tb ≈ Ts (text: Eqn. 12-63) rAno external diff. limit vs. rAobserved [>] Weisz-Prater: if rA′ (observed) ρc R p 2 eff Dinside C A bulk (text: Eqn. 12-61) 1 then you can neglect internal diffusion limitations, i.e. C As ≈ C Ab ≈ C A ( r = 0) 1000 η Ea ∼ 30 RTs β = 0.6 100 ΔH rxn Ea 10 1 .1 1 10 .1 ΔH rxn > 0 100 0⎫ ⎬ temp. dep. & exothermic 0 ⎭ φ1 ΔH rxn = 0 or Ea = 0 Figure 3. (text: Figure 12-7) 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 22 Page 2 of 3 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. β= −ΔH rxn DeC As eff where De ≡ Dinside and kt ≡ heat conductivity ktTs ⎛ ∂Ci ⎞ eff kc ( Ci ,b − Ci , s ) = − Dinside ⎜ ⎟ ⎝ ∂r ⎠ r = R = ∫ ri dV . kc Ci r=R ⎛ ∂Ci ⎞ eff − Dinside = kc Ci , bulk ⎜ ∂r ⎟ ⎝ ⎠ r =R ⎛ ∂Ci ⎞ ⎜ ∂r ⎟ = 0 ⎝ ⎠ r =0 if no significant external diffusion limit: Ci r =R ≈ Ci , bulk rA ≈ −k C A e − Ea RT rAeff ≈ f (k ) C A fit to: Aeff e− Ea eff RT . (text: Table 12-1) 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 22 Page 3 of 3 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].