Ch E 542 - Intermediate Reactor Analysis & Design

Ch E 542 - Intermediate Reactor Analysis & Design Heterogeneous non-catalytic Shrinking Cores

Shrinking Cores • Particles change size during some operations: • drug (pill) dissolution in stomach • ash layer formation around burning coal particle • spent catalyst regeneration • Consider regeneration of a porous catalyst covered (internally and externally) with carbon deposits • Particle is regenerated by hightemperature oxidation • O2 must diffuse into the particlecore, through the outer layer • Carbon deposits are convertedto CO2, which subsequently diffuse out

Model Discrimination General Model with interfacial and intraparticle gradients Heterogeneous Model with shrinking unreacted core General Model of Wen (1968) sharp concentration boundary

Ro r + r r R Differential O2 Mole Balance rate in C + O2 CO2 rate out O2 CO2 Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Differential O2 Mole Balance Total oxygen flux Fick’s Law C + O2 CO2 EMCD Combining with O2 mole balance Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Differential O2 Mole Balance Define Boundary Conditions C + O2 CO2 fast kinetics Integrate this 2nd Order DE Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Differential O2 Mole Balance Define Boundary Conditions C + O2 CO2 fast kinetics Apply the BCs to eliminate Ki Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Differential O2 Mole Balance C + O2 CO2 Substitute C(r) into flux equation Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Differential Carbon Mole Balance rate in or out C + O2 CO2 rate of generation rate of accumulation at r = R combining from O2 mole balance for fast kinetics Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Combined O2/C Mole Balances combined C + O2 CO2 integrated time for complete regeneration Heterogeneous Model with Shrinking Unreacted Core

Ro r + r O2 r R CO2 Heterogeneous Shrinking Core Concentration Profile C + O2 CO2 Carbon Front Profile Complete Regeneration Time Heterogeneous Model with Shrinking Unreacted Core

Mole Balances gas component mole balance CA CS0 CAss solid component mole balance CSs initial conditions boundary conditions fluid film General Model with Interfacial and Intraparticle Gradients

Mole Balances gas component mole balance neglect accumulation term for solid component mole balance porosity = function(conversion) initial conditions effective diffusivity = function() boundary conditions Numerical Solution Required define rate laws General Model with Interfacial and Intraparticle Gradients

Ch E 542 - Intermediate Reactor Analysis & Design