Summary of Chapter 121.The molar flux of A in a binary mixture of A and B is a)For EMCD or for dilute concentration of the solute,a)For diffusion through a stagnant gas,a)For negligible diffusion,1精选课件Summary(contd)2.The rate of mass transfer from the bulk fluid to a boundary at concentration CAs is3.The Sherwood and Schmidt numbers are,respectively,4.If a heat transfer correlation exists for a given system and geometry,the mass transfer correlation may be found by replacing the Nusselt number by the Sherwood number and the Prandtl number by the Schmidt number in the existing heat transfer correlation.2精选课件Summary(contd)5.Increasing the gas-phase velocity and decreasing the particle size will increase the overall rate of reaction for reactions that are externally mass transfer-limited.6.The conversion for externally mass transfer-limited reactions can be found from the equation7.The shrinking core model states that the time to regenerate a coked catalyst panicle is3精选课件Chapter 13Diffusion and ReactionsDepartment of Chemical EngineeringTiefeng Wangwangtftsinghua.edu 4精选课件ObjectiveslDescribe diffusion and reactions in porous catalyst and in Tissue Engineering.lDefine the Thiele modules and the effectiveness factor.lDescribe the regions of reaction limitations and internal diffusion limitations and the conditions that affect them.5精选课件6精选课件12.1 Diffusion and Reaction in Spherical Catalyst Pellets12.1.1 Effective DiffusivitylThe pores in the pellet are not straight and cylindrical;rather,they are a series of tortuous,interconnecting paths of pore bodies and pore throats with varying cross-sectional areas.lIt is fruitful to describe diffusion within each and every one of the tortuous pathways individually.lDefine an effective diffusion coefficient so as to describe the average diffusion taking place at any position r in the pellet.lThe radial flux WAr will be based on the total area(voids and soIid)normal to diffusion transport(i.e.,4r2)rather than void area alone.lThis basis for WAr is made possible by proper definition of the effective diffusivity De.7精选课件Effective DiffusivityThe effective diffusivity accounts for the fact that:lNot all of the area normal to the direction of the flux is available(i.e.,the area occupied by solids)for the molecules to diffuse(p).lThe paths are tortuous().lThe pores are of varying cross-sectional areas(c).8精选课件Effective Diffusivitytortuosity9精选课件Diffusion Mechanism in Pore Channels10精选课件Molecular diffusionSimple diffusion in the gas space of porous structureMolecule mean free path is smaller larger than pore diameterCollisions between molecules dominate over those between molecule and the pore wallValid at high pressures and in large poresMolecular diffusion is described by Ficks law11精选课件Knudsen diffusionCollisions with pore walls dominate over those with other moleculesValid for low pressures and in narrow pores12精选课件Configurational diffusionPores with molecular dimensions(0.3-1 nm)Strong interaction between molecule and the pore wallImportant for microporous catalysts,e.g.ZeolitesHigh resolution TEM picture of ZSM-513精选课件Effect of configurational diffusion on reactionConfigurational diffusion对二甲苯分子直径0.57邻、间二甲苯分子直径0.63精选课件12.1.2 Differential equation describing diffusion and reactionA steady-state mole balance on species AIn Out+Generation =AccumulationShell balance on a catalyst pellet15精选课件For equal molar counter diffusion at constant total concentration:We now need to incorporate the rate law.16精选课件The rate of reaction in different formsRate per unit volume:Rate per unit mass of catalyst:Rate per unit surface area:The surface area at the catalyst per unit mass of catalyst,Typical value of Sa,150m2/grate equation definitions17精选课件The boundary conditions are:18精选课件12.1.3 Dimensionless formThe boundary conditions are:19精选课件The Thiele modulus nWhen the Thiele modulus is large,internal diffusion usually limits the overall rate of reaction;When it is small,the surface reaction is usually rate-limiting;20精选课件For a first-order reaction21精选课件12.1.4 Solution to the different equation for a first-order reaction22精选课件Thiele ModulusSmall n Medium n Large n 精选课件12.2 Internal Effectiveness FactorE.W.Thiele(1939).“Relation between Catalytic Activity and Size of Particle Industrial and Engineering Chemistry,31,916-92024精选课件Actual overall rate of reaction(moles per unit time):Rate of reaction that would results if entire interior surface were exposed to the external pellet surface conditions:External surface25精选课件精选课件Physical Interpretation of Analysis27精选课件?28精选课件Effectiveness factor for different shape of catalyst29精选课件Effectiveness factor for n order reactionFor large values of the Thiele modulus for an n order reaction,For large values of the Thiele modulus for an first order reaction,30精选课件When a reaction is exothermic and non-isothemal,the effectiveness factor can be significantly greater than 1.Multiple stead-states can exist for values of the Thiele modulus less than 1 and when is gre