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 effiidFArdz= z=0 z=L Figure 1. Packed Bed Reactor eff chemiirr≠ Æ eff chemiirr=Ωif ? 1Ω≈if ? 1Ω ( ) –weird 1Ω> porous catalyst particle dpBL: δ Figure 2. Porous Catalyst Particle Biot Number: external heat transfer resistanceinternal heat transfer resistanceiB ∼ 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].mcpieffinsidekdBD= where fluidcDkδ∼ diametermfluidieffinsideDBDδ= Mears’ Test: if ()0.15observedAbpcAbulkrRnkCρ′< where n≡order of rxn then (no external diffusion limitation) Æ i.e. no changing concentration across the boundary layer Ab AsCC≈ Similarly, if 2()0.15observed or theoryrxn A b p afluidHr REhRTρ′′Δ< then bTTs≈ (text: Eqn. 12-63) no externaldiff.limit observedvs.AArr [>] Weisz-Prater: if 2()1observedAcpeffinside A b ulkrRDCρ′ (text: Eqn. 12-61) then you can neglect internal diffusion limitations, i.e. (0As Ab ACCCr)≈≈= 1000 100 10 1 .1 .1 1 10 100 1φ η 0rxnHΔ> 0rxnHΔ = or 0aE = 0.6β= 30asERT∼ 00temp. dep. & exothermicrxnaHEΔ⎫⎬⎭ Figure 3. (text: Figure 12-7)10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 22 Prof. William H. Green 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].rxn e AstsHDCkTβ−Δ= where and effeinsiDD≡detk≡ heat conductivity (),,efficib is insiderRCkC C Dr=∂⎛⎞−=−⎜⎟∂⎝⎠ rd=∫. iV ,effic i inside c i bulkrRrRCkC D kCr==∂⎛⎞−=⎜⎟∂⎝⎠ 00irCr=∂⎛⎞=⎜⎟∂⎝⎠ if no significant external diffusion limit: ,i i bulkrRCC =≈C≈− AArk aERTe− ()effAArfk≈ C fit to: effaERTeffAe−. (text: Table 12-1) 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 22 Prof. William H. Green 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
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