反应工程基础程易chpt13internaldiffusion72640638

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)(baaaabawwyycdwsummary (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

3、by the schmidt number in the existing heat transfer correlation.2abpshddkcabscdv)(aaasbccckwsummary (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 ex

4、ternally 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 2p20.6resc20.6cdukd4chapter 13diffusion and reactionsdepartment of chemical engineeringtiefeng

5、 w5objectivesldescribe 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. 6712.1 diffusion and reaction in

6、 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 ever

7、y 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 voi

8、d area alone. lthis basis for war is made possible by proper definition of the effective diffusivity de.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 molecule

9、s to diffuse (p).lthe paths are tortuous ( ).lthe pores are of varying cross-sectional areas (c).8effective diffusivity9cwhere actual distance a molecule travels btw 2 pointstortousityshortest distance btw 2 pointsvolume of void spacepellet porositytotal volume (voids and solids)constriction factorp

10、abckcppeddd tortuositydiffusion mechanism in pore channels10molecular 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 between molecule and the pore wall valid at high press

11、ures and in large pores molecular diffusion is described by ficks lawknudsen diffusion12 collisions with pore walls dominate over those with other molecules valid for low pressures and in narrow poresk23adr u8/urtmk283arrtdmconfigurational diffusion13 pores with molecular dimensions (0.3-1 nm) stron

12、g interaction between molecule and the pore wall important for 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 s

13、teady-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 balance on a catalyst pellet16for equal molar counter diffusion at constant total conc

14、entration:drdcddrdycdwaeaear02ca2arrdrrwdr0)/(a2c2errdrrdrdcddawe 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:) smol/dm(3ar) scat mol/g(ar) smol/m(2 arthe surface area at the catalyst per

15、 unit mass of catalyst,)cat /gm(2astypical value of sa, 150m2/g222anaaanaacanark crs k crs k crate equation definitions180)/(aca 2e2nknacskrdrdrdcdrdn02aea2a2nncdkdrdcrdrcdthe boundary conditions are:rrccrcsat 0at finite is aaa1912.1.3 dimensionless form02aea2a2nncdkdrdcrdrcd02222nnddddthe boundary

16、conditions are:1at 10at finite is rrccs ,aae1 -a22dcrknsnn20the thiele modulus n when 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;212aeeasurface reaction rate(0)/diffusion ratennnasnsnsk

17、r ck rcddcrfor a first-order reaction21a 1 ackr smsmm23 1k221220dddd e1eac 11dkrdskrs1gmmgsm23ac 11skksm2edb.c. 1: 1 at 1b.c. 2: is finite at 0 2212.1.4 solution to the different equation for a first-order reaction1111coshsinhyab 1111coshsinhab a1a1sinh1sinhscc y221220dddd thiele modulusd 11sinh 1si

18、nh 100.5100.51d 1d 2d 5d 20asaccsmall n medium n large n 12.2 internal effectiveness factor24aactual overall rate of reactionrate of reaction that would result if entire interior surface were exposed to the external pellet surface conditions ,ssctaaaaaasssrrrrrrspspsmmvrvrrraaaaaae.w. thiele (1939).

19、 “relation between catalytic activity and size of particle” industrial and engineering chemistry, 31, 916-920251coth31121aasmm3aa34rkcmssaea14sdmrd cd111112111 1coshsinh1(coth1)sinhsinhddactual overall rate of reaction (moles per unit time):rate of reaction that would results if entire interior surf

20、ace were exposed to the external pellet surface conditions:11sinh1sinh external surfacephysical interpretation of analysis2728?effectiveness factor for different shape of catalyst29effectiveness factor for n order reaction30for large values of the thiele modulus for an n order reaction,)/2-(1ae2/12/

21、1312312nsnnckdrnn13for large values of the thiele modulus for an first order reaction,0.11101000.11 3(coth)/12 3/31when 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

22、1 and when is greater than approximately 0.2. there will be no multiple steady stares when the criterion developed by luss is fulfilled.4(1 ) arrhenius numbersertmaxssttt32rate without any diffusion effects=1 for no diffusion resistancethis sphere expression is a good approximation for all particle

23、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 predicting experiments since it only includes observationseffectiv

24、e diffusion coefficient in porous solidsaa1a()ssrrk c 11213coth111ekrdase2obsa,21wpcdrrccwithwhere12.3 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 r

25、eaction order n to the true reactionorder n.aannsrk c34using the 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)

26、351/2(1)/2aeaa231nnnsnsrd kck cnr21nnappt/appttruemeasured ertertnnkaeka e appt2ee 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

27、kinetics in terms of the bulk conditions, rather than surface conditions:a,bulkactual overall reaction raterate if entire surface were exposed to c overall effectiveness factorlaccounting for reaction both on and within the pellet, the molar rate becomes:lfor most catalyst, internal surface area is

28、significantly higher than the external surface area:vsarmcc1aaabaraabccw aras araabcw ar s ac is the external surface area per unit reactor volumemolar rate of mass transfer = total rate of reactionoverall effectiveness factorbaaasrawcreaction rate(internal & external surfaces)aaarccbscw avkccavmass

29、 transport rateinternal surfaces not 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, overall effectiveness factorsummary of factor relationships:1aba1ab1ab1ab1cccccc

30、k k a crk ca kk sk sk arearranging the expression:abarr1ab1cck sk a aaasbrrra1assrk ca1abbrk coverall effectiveness factor ()this eq. is for first-order reactionweisz-prater criterion for internal diffusionlweisz-prater criterion is a method of determining if a given process is operating in a diffus

31、ion- or reaction-limited 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 aactualasas21wpcccscs

32、cdrrdrkae2ae2121assume 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-kramer

33、s for packed bed flow)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/smears criterionlheat transfer effects negligible wh

34、en it is true thata2 0.15rxnbbhrrehrt h = heat transfer coefficient, 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 reactor430 ionaccumulat formation out in cbaazcazczarwawazzz0baazrdzdw0aaab2ab2abrdzdcudzc

35、dd0baazrdzdwucdzdcdwabaabazaba abacskrr0aba bab2ab2abcskdzdcudzcddmole flux of afirst order reaction2aaabaa20bbbbd 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 dis

36、persion coefficienta00aabppbrdu du cdcan be simplified as:aaa0bbbdcuks cdzwhich 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 determination of limiting situ

37、ations from reaction data471/21/2cpukdexternal mass transfer-limited reactions in packed beds:aaccrk a c1cpada3/21prdlimiting conditions48type of limitationvariation of reaction rate with:velocityparticle sizetemperatureexternal diffusionu1/2(dp)-3/2linearinternal diffusionindependent(dp)-1exponenti

38、alsurface reactionindependentindependentexponential4912.7 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.5012.7.1 eliminating the external diffusion51

39、testing the influence of the external diffusion5212.7.2 eliminating the internal diffusiondpdp*xainternal diffusion has no influenceinternal diffusion affects the ratefor kinetics experiments, the size of the catalyst particles should be smaller than dp*12.7.3 experimental methods for finding ratese

40、xperimental 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 catalytic reactions.53comparison of experimental reactors: levens

41、piel 3rd p400 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 conversions needed in differential reactors require more accurate measurements of

42、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.55integral reactorthe rate to be constant at all points within the reactor. this assumption is usually reasonable only for s