反应工程基础程易chpt13-internaldiffu课件(PPT 60页).pptx

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,1VWWACyAA)1ln(AABAycDWAABAycD W)(BAAAABAWWyycDW第1页，共60页。Summary(contd)2.The rate of mass transfer from t

2、he 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 t

3、he Schmidt number in the existing heat transfer correlation.2ABpShDdkcABScDv)(AAAsbcCCkW第2页，共60页。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

4、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 is320A06ccceRtD CLUakXcc11ln2 31 21/21/3AB1 61 2p20.6ReSc20.6cDUkd第3页，共60页。4Chapter 13Diffusion and ReactionsDepartment of Chemical Engineer

5、ingTiefeng W第4页，共60页。5ObjectiveslDescribe 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.第5页，共60页。6第6页，共6

6、0页。712.1 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

7、 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 transpor

8、t(i.e.,4r2)rather than void area alone.lThis basis for WAr is made possible by proper definition of the effective diffusivity De.第7页，共60页。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 occu

9、pied by solids)for the molecules to diffuse(p).lThe paths are tortuous().lThe pores are of varying cross-sectional areas(c).8第8页，共60页。Effective Diffusivity9cwhere Actual distance a molecule travels btw 2 pointstortousityShortest distance btw 2 pointsVolume of void spacepellet porosityTotal volume(vo

10、ids and solids)Constriction factorpABckcppeDDD tortuosity第9页，共60页。Diffusion Mechanism in Pore Channels10第10页，共60页。Molecular diffusion11 Simple diffusion in the gas space of porous structure Molecule mean free path is smaller larger than pore diameter Collisions between molecules dominate over those

11、between molecule and the pore wall Valid at high pressures and in large pores Molecular diffusion is described by Ficks law第11页，共60页。Knudsen diffusion12 Collisions with pore walls dominate over those with other molecules Valid for low pressures and in narrow poresk23aDr u8/uRTMk283arRTDM第12页，共60页。Co

12、nfigurational diffusion13 Pores 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-5第13页，共60页。Effect of configurational diffusion on reactionConfigurational diffusion对二甲苯分子直径0.57邻、

13、间二甲苯分子直径0.63第14页，共60页。1512.1.2 Differential equation describing diffusion and reactionA steady-state mole balance on species AIn Out+Generation =AccumulationrrrWr2A4at in A of raterrrrWrr2A4at out A of rate rrrm2cA4shell heA within t of generation of rate02cA2ArrdrrWdr 04442cA2A2ArrrrWrWmrrrrrShell

14、balance on a catalyst pellet第15页，共60页。16For equal molar counter diffusion at constant total concentration:drdCDdrdycDWAeAeAr02cA2ArrdrrWdr0)/(A2c2errdrrdrdCDdAWe now need to incorporate the rate law.第16页，共60页。The rate of reaction in different forms17Rate per unit volume:Rate per unit mass of catalys

15、t:Rate per unit surface area:)smol/dm(3Ar)scat mol/g(Ar)smol/m(2 ArThe surface area at the catalyst per unit mass of catalyst,)cat/gm(2aSTypical value of Sa,150m2/g222AnAAanAAcanArk CrS k CrS k Crate equation definitions第17页，共60页。180)/(Aca 2e2nknACSkrdrdrdCDrdn02AeA2A2nnCDkdrdCrdrCdThe boundary cond

16、itions are:RrCCrCsat 0at finite is AAA第18页，共60页。1912.1.3 Dimensionless form02AeA2A2nnCDkdrdCrdrCd02222nnddddThe boundary conditions are:1at 10at finite is RrCCs ,AAe1-A22DCRknsnn第19页，共60页。20The Thiele modulus n When the Thiele modulus is large,internal diffusion usually limits the overall rate of re

17、action;When it is small,the surface reaction is usually rate-limiting;212AeeAsurface reaction rate(0)/diffusion ratennnAsnsnsk R Ck RCDDCR第20页，共60页。For a first-order reaction21A 1 ACkr smsmm23 1k221220dddd e1eac 11DkRDSkRs1gmmgsm23ac 11Skksm2eDB.C.1:1 at 1B.C.2:is finite at 0 第21页，共60页。2212.1.4 Solu

18、tion to the different equation for a first-order reaction1111coshsinhyAB 1111coshsinhAB A1A1sinh1sinhsCC y221220dddd 第22页，共60页。Thiele Modulusd 11sinh 1sinh 100.5100.51d 1d 2d 5d 20AsACCSmall n Medium n Large n 第23页，共60页。12.2 Internal Effectiveness Factor24AActual overall rate of reactionRate of reac

19、tion that would result if entire interior surface were exposed to the external pellet surface conditions,ssCTAAAAAAsssrrrrrrspspsMMVrVrrrAAAAAAE.W.Thiele(1939).“Relation between Catalytic Activity and Size of Particle”Industrial and Engineering Chemistry,31,916-920第24页，共60页。251coth31121AAsMM3AA34RkC

20、MssAeA14sdMRD Cd111112111 1coshsinh1(coth1)sinhsinhddActual 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:11sinh1sinh External surface第25页，共60页。第26页，共60页。Physical Interpretation of A

21、nalysis27第27页，共60页。28?第28页，共60页。Effectiveness factor for different shape of catalyst29第29页，共60页。Effectiveness factor for n order reaction30For large values of the Thiele modulus for an n order reaction,)/2-(1Ae2/12/1312312nsnnCkDRnn13For large values of the Thiele modulus for an first order reaction

22、,0.11101000.11 3(coth)/12 3/第30页，共60页。31When 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 greater than approximately 0.2.There will be no multiple stead

23、y stares when the criterion developed by Luss is fulfilled.4(1)Arrhenius numbersERTmaxssTTT第31页，共60页。32Rate without any diffusion effects=1 for no diffusion resistanceThis sphere expression is a good approximation for all particle shapesCharacteristic length=Effective factor,which accounts for the r

24、esistance to pore diffusion1=Thiele modulus,useful for predicting reactor behavior from known kinetic information,thus known kCWP=Weisz modulus,useful for predicting experiments since it only includes observationsEffective diffusion coefficient in porous solidsAA1A()ssrrk C 11213coth111ekRDAse2obsA,

25、21WPCDRrCcwithwhere第32页，共60页。12.3 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 this measured reaction order n to the true reactionorder n.AAnnsrk C第33页，共60页。34Using th

26、e definition of the effectiveness factor:For large values of the Thiele modulus,is:nsnsCkrrAAA)()/2-(1Ae2/12/1312312nsnnCkDRnn2/)1(A2/1eA-1AeAA123 123123nsnnsnnsnnsnnCknDRCkCkDnRCknr(external mass transfer is eliminated,thus CAs=CAb)第34页，共60页。351/2(1)/2AeAA231nnnsnsrD kCk CnR21nnAppT/AppTtruemeasure

27、d ERTERTnnkAekA e AppT2EE 第35页，共60页。Overall Effectiveness FactorlWhen both internal AND external diffusion resistances are important(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 th

28、an surface conditions:A,bulkactual overall reaction raterate if entire surface were exposed to C 第36页，共60页。Overall Effectiveness FactorlAccounting for reaction both on and within the pellet,the molar rate becomes:lFor most catalyst,internal surface area is significantly higher than the external surf

29、ace area:VSarMcc1aAAbArAabccW araS ArAabcW ar S ac is the external surface area per unit reactor volumeMolar rate of mass transfer=total rate of reaction第37页，共60页。Overall Effectiveness FactorbaAASraWcreaction rate(internal&external surfaces)AAArccbscW aVkCCaVmass transport rateinternal surfaces not

30、all exposed to CAsAA1Assrrk C Relation between CAs and CA defined by the as:AA1AabcbscskCCak C SAA1abccbscca k CCa kk SUsing Molar rate of mass transfer=total rate of reactionThen,第38页，共60页。Overall Effectiveness FactorSummary of factor relationships:1AbA1Ab1ab1ab1cccccck k a Crk Ca kk Sk Sk aRearran

31、ging the expression:AbArr1ab1cck Sk a AAAsbrrrA1Assrk CA1Abbrk COverall Effectiveness Factor()This eq.is for first-order reaction第39页，共60页。Weisz-Prater Criterion for Internal DiffusionlWeisz-Prater Criterion is a method of determining if a given process is operating in a diffusion-or reaction-limite

32、d regime lCWP is the known as the Weisz-Prater parameter.All quantities are known or measured.lCWP 1,severe diffusion limitationsAse2obsA,21WPCDRrCcratediffusion A ratereaction Actualratediffusion A at evaluated rateRxn at evaluated rateRxn ratereaction AactualAsAs21WPCCCscsCDRrDRkAe2Ae2121Assume th

33、at the external mass transfer is eliminated,thus CAs=CAb.第40页，共60页。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

34、)15.0AbACknRrcbn =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/s第41页，共60页。Mears CriterionlHeat transfer effects negligible when it is true thatA2 0.

35、15rxnbbHrREhRT h =heat transfer coefficient,kJ/m2sK R =gas constant,kJ/molKHRx =heat of reaction,kJ/mol E =activation energy,kJ/mol第42页，共60页。12.6 Mass transfer and reaction in a packed bed reactor430 ionAccumulat Formation Out In cbAAzcAzczArWAWAzzz0bAAzrdzdW第43页，共60页。0AAAb2Ab2ABrdzdCUdzCdD0bAAzrdzd

36、WUCdzdCDWAbAABAzAba AbACSkrr0Aba bAb2Ab2ABCSkdzdCUdzCdDMole flux of AFirst order reaction第44页，共60页。2AAABaA20bbbbd CdCDUk S CdzdzlAxial dispersion negligible(relative to forced axial convection)whenldp is the particle diameterlU0 is the superficial velocity of the gaslDa is the effective axial disper

37、sion coefficientA00AabppbrdU dU CDcan be simplified as:AaA0bbbdCUkS Cdz第45页，共60页。Which can be rewritten as:AaAbbbdCk SCdzU B.C.AA 00bbzCCIntegrating and applying boundary condition yields:aAA 0expbbbk S zCCUThe conversion at the reactors exit,z=L,isAaA 011 expbbbCk S LXCU 第46页，共60页。Determination of

38、Limiting Situations from Reaction Data471/21/2cpUkdExternal mass transfer-limited reactions in packed beds:AAccrk a C1cpadA3/21prd第47页，共60页。Limiting conditions48Type of limitationVariation of reaction rate with:VelocityParticle sizeTemperatureExternal diffusionU1/2(dp)-3/2linearInternal diffusionInd

39、ependent(dp)-1ExponentialSurface reactionIndependentIndependentExponential第48页，共60页。4912.7 Experimental study of the heterogeneous catalytic reactions()(,)Airf C TintrinsicIntrinsic reaction kinetics is obtained when both the external mass transfer and internal diffusion are eliminated.第49页，共60页。501

40、2.7.1 Eliminating the external diffusion第50页，共60页。51Testing the influence of the external diffusion第51页，共60页。5212.7.2 Eliminating the internal diffusiondpdp*xAInternal diffusion has no influenceInternal diffusion affects the rateFor kinetics experiments,the size of the catalyst particles should be s

41、maller than dp*第52页，共60页。12.7.3 Experimental methods for finding ratesExperimental deviceslDifferential(flow)reactorlIntegral(plug flow)reactorlMixed flow reactorlBatch reactor for both gas and solidIn principle,any type of reactor with known contacting pattern may be used to explore the kinetics of

42、 catalytic reactions.53Comparison of Experimental Reactors:Levenspiel 3rd p400第53页，共60页。Each run gives directly a value for the rate at the average concentration in the reactor.A series of runs gives a set of rate-concentration data which can then be analyzed for a rate equation.The small conversion

43、s needed in differential reactors require more accurate measurements of composition54Differential ReactorFA0 FA0 x=xout-xin is smallThe rate to be constant at all points within the reactor.This assumption is usually reasonable only for smallconversions or for shallow small reactors.第54页，共60页。55Integ

44、ral ReactorThe rate to be constant at all points within the reactor.This assumption is usually reasonable only for smallconversions or for shallow small reactors.DxFA0dwlIntegral AnalysisA specific mechanism with its corresponding rate equation is put to the test by integrating the basic performance

45、 equation to give,lDifferential Analysis.By differentiating the integral Eq.,we obtain,See Example 18.3 in Levenspiel 3rd 第55页，共60页。Mixed-Flow Reactor56Sketch of a Carberry basket-type experimental mixed flow reactor.Principle of the Berty experimentalmixed flow reactor.第56页，共60页。Batch Reactor57In t

46、his system we follow the changing composition with time and interpret the results with the batch reactor performance equation.第57页，共60页。Summary1.The concentration profile for a first-order reaction occurring in a spherical catalyst pellet is where 1 is the Thiele modulus.For a first-order reaction2.

47、The internal effectiveness factor and overall effectiveness factor.5811AAsinhsinh1sCCe2121DRk第58页，共60页。Summary(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 appar

48、ent activation energies are related by59)/2-(1Ae2/12/1312312nsnnCkDRnn12apparenttrue nnapptrue2EE第59页，共60页。Summary(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 Transfer6015.0 2gAbbrxnThRRErH15.0AbACknRrcbAse2obsA,21WPCDRrCc第60页，共60页。