《反应工程基础(程易)chpt13-internaldiffu》由会员分享，可在线阅读，更多相关《反应工程基础(程易)chpt13-internaldiffu（60页珍藏版）》请在金锄头文库上搜索。
1、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, 1Summary (contd)2. The rate of mass transfer from the bulk fluid to a boundary at concentration C
2、As 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 tra
3、nsfer correlation.2Summary (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.
4、 The shrinking core model states that the time to regenerate a coked catalyst panicle is34Chapter 13Diffusion and ReactionsDepartment of Chemical EngineeringTiefeng W5ObjectiveslDescribe diffusion and reactions in porous catalyst and in Tissue Engineering. lDefine the Thiele modules and the effectiv
5、eness factor. lDescribe the regions of reaction limitations and internal diffusion limitations and the conditions that affect them. 6712.1 Diffusion and Reaction in Spherical Catalyst Pellets12.1.1 Effective DiffusivitylThe pores in the pellet are not straight and cylindrical; rather, they are a ser
6、ies 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 pl
7、ace 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.Effective DiffusivityThe effecti
8、ve 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).8Effective Diffusivity9tortuosityDiffus
9、ion Mechanism in Pore Channels10Molecular diffusion11Simple 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
10、 diffusion is described by Ficks lawKnudsen diffusion12Collisions with pore walls dominate over those with other moleculesValid for low pressures and in narrow poresConfigurational diffusion13Pores with molecular dimensions (0.3-1 nm)Strong interaction between molecule and the pore wallImportant for
11、 microporous catalysts, e.g. ZeolitesHigh resolution TEM picture of ZSM-5Effect 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0.631512.1.2 Differential equation describing diffusion and reactionA steady-state mole balance on species AIn Out + Generation = Acc
12、umulationShell balance on a catalyst pellet16For equal molar counter diffusion at constant total concentration:We now need to incorporate the rate law.The rate of reaction in different forms17Rate per unit volume:Rate per unit mass of catalyst:Rate per unit surface area:The surface area at the catal
13、yst per unit mass of catalyst,Typical value of Sa, 150m2/grate equation definitions18The boundary conditions are:1912.1.3 Dimensionless formThe boundary conditions are:20The Thiele modulus nWhen the Thiele modulus is large, internal diffusion usually limits the overall rate of reaction;When it is sm
14、all, the surface reaction is usually rate-limiting;For a first-order reaction212212.1.4 Solution to the different equation for a first-order reactionThiele ModulusSmall n Medium n Large n 12.2 Internal Effectiveness Factor24E.W. Thiele (1939). “Relation between Catalytic Activity and Size of Particl
15、e” Industrial and Engineering Chemistry, 31, 916-92025Actual 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 surfacePhysical Interpretation of Analysis2728?Effectiveness fact
16、or for different shape of catalyst29Effectiveness factor for n order reaction30For large values of the Thiele modulus for an n order reaction,For large values of the Thiele modulus for an first order reaction,31When a reaction is exothermic and non-isothemal, the effectiveness factor can be signific
17、antly greater than 1.Multiple stead-states can exist for values of the Thiele modulus less than 1 and when is greater than approximately 0.2. There will be no multiple steady stares when the criterion developed by Luss is fulfilled.32Rate without any diffusion effects=1 for no diffusion resistanceTh
18、is sphere expression is a good approximation for all particle shapesCharacteristic length = Effective factor, which accounts for the resistance to pore diffusion1 = Thiele modulus, useful for predicting reactor behavior from known kinetic information, thus known kCWP = Weisz modulus, useful for pred
19、icting experiments since it only includes observationsEffective diffusion coefficient in porous solidswithwhere12.3 Falsified kinetics33A log-log plot of the measured rate of reaction -rA, as a function of the gas-phase concentration CAs, (external mass transfer is eliminated, thus CAs=CAb)Relate th
20、is measured reaction order n to the true reactionorder n.34Using the definition of the effectiveness factor:For large values of the Thiele modulus, is:(external mass transfer is eliminated, thus CAs=CAb)35Overall Effectiveness FactorlWhen both internal AND external diffusion resistances are importan
21、t (i.e., the same order of magnitude), both must be accounted for when quantifying kinetics.lIt is desired to express the kinetics in terms of the bulk conditions, rather than surface conditions:Overall Effectiveness FactorlAccounting for reaction both on and within the pellet, the molar rate become
22、s:lFor most catalyst, internal surface area is significantly higher than the external surface area:ac is the external surface area per unit reactor volumeMolar rate of mass transfer = total rate of reactionOverall Effectiveness Factorreaction rate(internal & external surfaces)mass transport rateinte
23、rnal surfaces not all exposed to CAsRelation between CAs and CA defined by the as:Using Molar rate of mass transfer = total rate of reactionThen, Overall Effectiveness FactorSummary of factor relationships:Rearranging the expression:Overall Effectiveness Factor ()This eq. is for first-order reaction
24、Weisz-Prater Criterion for Internal DiffusionlWeisz-Prater Criterion is a method of determining if a given process is operating in a diffusion- or reaction-limited regime lCWP is the known as the Weisz-Prater parameter. All quantities are known or measured.lCWP 1, severe diffusion limitationsAssume
25、that the external mass transfer is eliminated, thus CAs=CAb.Mears CriterionlMass transfer effects negligible when it is true thatwhere n is the reaction order, and the transfer coefficients kc and h (below) can be estimated from an appropriate correlation (i.e., Thoenes-Kramers for packed bed flow)n
26、 = reaction orderR = catalyst particle radius, mb = bulk density of catalyst bed, (1-)c, kg/m3c = solid density of catalyst pellet, kg/m3CAb= bulk gas concentration of A, mol/m3kc =mass transfer coefficient, m/sMears CriterionlHeat transfer effects negligible when it is true that h = heat transfer c
27、oefficient, kJ/m2sK R = gas constant, kJ/molKHRx = heat of reaction, kJ/mol E = activation energy, kJ/mol12.6 Mass transfer and reaction in a packed bed reactor43Mole flux of AFirst order reactionlAxial dispersion negligible (relative to forced axial convection) whenldp is the particle diameterlU0 i
28、s the superficial velocity of the gaslDa is the effective axial dispersion coefficientcan be simplified as:Which can be rewritten as:B.C.Integrating and applying boundary condition yields:The conversion at the reactors exit, z = L, isDetermination of Limiting Situations from Reaction Data47External
29、mass transfer-limited reactions in packed beds:Limiting conditions48Type of limitationVariation of reaction rate with:VelocityParticle sizeTemperatureExternal diffusionU1/2(dp)-3/2linearInternal diffusionIndependent(dp)-1ExponentialSurface reactionIndependentIndependentExponential4912.7 Experimental
30、 study of the heterogeneous catalytic reactionsIntrinsic reaction kinetics is obtained when both the external mass transfer and internal diffusion are eliminated.5012.7.1 Eliminating the external diffusion51Testing the influence of the external diffusion5212.7.2 Eliminating the internal diffusiondpd
31、p*xAInternal diffusion has no influenceInternal diffusion affects the rateFor kinetics experiments, the size of the catalyst particles should be smaller than dp*12.7.3 Experimental methods for finding ratesExperimental deviceslDifferential (flow) reactorlIntegral (plug flow) reactorlMixed flow react
32、orlBatch reactor for both gas and solidIn principle, any type of reactor with known contacting pattern may be used to explore the kinetics of catalytic reactions.53Comparison of Experimental Reactors: Levenspiel 3rd p400Each run gives directly a value for the rate at the average concentration in the
33、 reactor.A series of runs gives a set of rate-concentration data which can then be analyzed for a rate equation.The small conversions needed in differential reactors require more accurate measurements of composition54Differential ReactorFA0 FA0x=xout-xin is smallThe rate to be constant at all points
34、 within the reactor.This assumption is usually reasonable only for smallconversions or for shallow small reactors.55Integral ReactorThe rate to be constant at all points within the reactor. This assumption is usually reasonable only for smallconversions or for shallow small reactors.lIntegral Analys
35、isA specific mechanism with its corresponding rate equation is put to the test by integrating the basic performance equation to give,lDifferential Analysis.By differentiating the integral Eq., we obtain,See Example 18.3 in Levenspiel 3rd Mixed-Flow Reactor56Sketch of a Carberry basket-type experimen
36、tal mixed flow reactor.Principle of the Berty experimentalmixed flow reactor.Batch Reactor57In this system we follow the changing composition with time and interpret the results with the batch reactor performance equation.Summary1.The concentration profile for a first-order reaction occurring in a s
37、pherical catalyst pellet is where 1 is the Thiele modulus. For a first-order reaction2.The internal effectiveness factor and overall effectiveness factor.58Summary (contd)3.For large values of the Thiele modulus for an n order reaction,4.For internal diffusion control, the me reaction order is related to the measured reaction order by The true and apparent activation energies are related by59Summary (contd)5.The Weisz-Prater Parameter The Weisz-Prater criterion dictates that: If CWP1, internal diffusion limitations present6.Mears Criteria for Neglecting External Diffusion and Heat Transfer60
