ReviewFundamental Equations:Special Cases:Thiele modulus10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 25: Course Review Review Fundamental Equations: Acc = Flow In – Flow Out + Reaction ,,(,,,)mm o m out mnFF r x y z t dxdydzt∂=− +∂∫∫∫ infinitesimal volume mmmCFrt∂=∇⋅ +∂ rxnGRTeqKe−Δ= (eqK is unitless) 1111NproductsreactantsnjmmeqjjPbarKPbarνν=−=⎛⎞⎜⎟⎝⎠=⎛⎞⎜⎟⎝⎠∏∏ forwardcreversekKk= 22 2 2HO H O→+ nPVRT= 2222111HOeqHOPPbar barKPbar⎛⎞⎛⎜⎟⎜⎝⎠⎝=⎛⎞⎜⎟⎝⎠⎞⎟⎠ [][][]2222cHOKHO= units []cmolKL= Convection dominated: 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].Constant P, constant T, constant reactor V mmFCν≈ 2mmWDCUC∇⋅ ≈ ∇ + ⋅∇m Pressure drop in Packed Bed: Ergun Equation: ()3150 111.75cp pPGGzpgD Dφμφφ⎡⎤−∂−=− +⎢⎥∂⎢⎥⎣⎦ totcv cvjj sUVPFHQtt∂∂+= ++∂∂∑W (U depends on T) totcv ()in out k rxntotalCT T Q r HTtCν⎧⎫−++Δ∂⎪⎪=⎨⎬∂⎪⎪⎩⎭∑ where C is the heat capacity Special Cases: Perfectly Homogeneous (“well stirred”, “perfectly mixed”) Æ no flows, “batch reactor” ()()mmnrCtVt∂=∂ Æ CSTR, no t-dependence ()0in out outFF rC=− + Homogeneous in x,y, not in z (no t-dependence) PFR (typically gives higher productivity than CSTR) ()()mmFArCzz∂=∂ “sort of” PFR ()() ()avgmmFArC z zz∂=∂Ω where ()zΩ is the effectiveness factor bubble • • cat Figure 1. a) mass transfer from gas to liquid b) mass transfer into catalyst particle 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 25 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].10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 25 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 YYYY]. ()222() 0mmmCCDrCrrr∂∂⎛⎞++⎜⎟∂∂⎝⎠ r=- nondimensionalize - some solutions in book - (18.03) plug in to verify guess solution,matlab Thiele modulus φ2rC≡msurface DC2solid m,sR- if small (<1): reaction limited, ignore effectiveness factor Ω (internal diffusion ()fast) - if big: transport matters! () from L interface bulkbubbleFAkC C=− LkA Æ correlations C kc∼ δerential equation into first-order ordinary differential (sphere-packed bed) ()into c bulk sparticleFkAC=−DConverting the second-order diffequations for MatLab solvers: mmCqr∂=∂ 20mmmqDqrrr∂++=∂ mm+r Æ MATLAB: ode15s D 2mqqrr−∂=∂