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1、Summary of Chapter 12,1.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,Summary(contd),2.The rate of mass transfer from the bulk fluid to a boundary at concentration CAs is3
2、.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 corr
3、elation.,2,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 shrink
4、ing core model states that the time to regenerate a coked catalyst panicle is,3,4,Chapter 13Diffusion and Reactions,Department of Chemical EngineeringTiefeng Wang,5,Objectives,Describe diffusion and reactions in porous catalyst and in Tissue Engineering.Define the Thiele modules and the effectivenes
5、s factor.Describe the regions of reaction limitations and internal diffusion limitations and the conditions that affect them.,6,7,12.1 Diffusion and Reaction in Spherical Catalyst Pellets,12.1.1 Effective DiffusivityThe pores in the pellet are not straight and cylindrical;rather,they are a series of
6、 tortuous,interconnecting paths of pore bodies and pore throats with varying cross-sectional areas.It is fruitful to describe diffusion within each and every one of the tortuous pathways individually.Define an effective diffusion coefficient so as to describe the average diffusion taking place at an
7、y position r in the pellet.The 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.This basis for WAr is made possible by proper definition of the effective diffusivity De.,Effective Diffusivity,The effective diffusivity
8、accounts for the fact that:Not 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).The paths are tortuous().The pores are of varying cross-sectional areas(c).,8,Effective Diffusivity,9,tortuosity,Diffusion Mechanism in Por
9、e Channels,10,Molecular diffusion,11,Simple 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 de
10、scribed by Ficks law,Knudsen diffusion,12,Collisions with pore walls dominate over those with other moleculesValid for low pressures and in narrow pores,Configurational diffusion,13,Pores with molecular dimensions(0.3-1 nm)Strong interaction between molecule and the pore wallImportant for microporou
11、s catalysts,e.g.Zeolites,High resolution TEM picture of ZSM-5,Effect of configurational diffusion on reaction,Configurational diffusion,对二甲苯分子直径0.57邻、间二甲苯分子直径0.63,15,12.1.2 Differential equation describing diffusion and reaction,A steady-state mole balance on species A,In Out+Generation=Accumulation
12、,Shell balance on a catalyst pellet,16,For equal molar counter diffusion at constant total concentration:,We now need to incorporate the rate law.,The rate of reaction in different forms,17,Rate per unit volume:,Rate per unit mass of catalyst:,Rate per unit surface area:,The surface area at the cata
13、lyst per unit mass of catalyst,Typical value of Sa,150m2/g,rate equation definitions,18,The boundary conditions are:,19,12.1.3 Dimensionless form,The boundary conditions are:,20,The Thiele modulus n,When the Thiele modulus is large,internal diffusion usually limits the overall rate of reaction;When
14、it is small,the surface reaction is usually rate-limiting;,For a first-order reaction,21,22,12.1.4 Solution to the different equation for a first-order reaction,Thiele Modulus,Small n,Medium n,Large n,12.2 Internal Effectiveness Factor,24,E.W.Thiele(1939).“Relation between Catalytic Activity and Siz
15、e of Particle”Industrial and Engineering Chemistry,31,916-920,25,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 surface,Physical Interpretation of Analysis,27,28,?,E
16、ffectiveness factor for different shape of catalyst,29,Effectiveness factor for n order reaction,30,For large values of the Thiele modulus for an n order reaction,For large values of the Thiele modulus for an first order reaction,31,When a reaction is exothermic and non-isothemal,the effectiveness f
17、actor 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 steady stares when the criterion developed by Luss is fulfilled.,32,Rate without any diffusion effects,=1 for no
18、 diffusion resistance,This sphere expression is a good approximation for all particle shapes,Characteristic length,=Effective factor,which accounts for the resistance to pore diffusion,1=Thiele modulus,useful for predicting reactor behavior from known kinetic information,thus known k,CWP=Weisz modul
19、us,useful for predicting experiments since it only includes observations,Effective diffusion coefficient in porous solids,with,where,12.3 Falsified kinetics,33,A log-log plot of the measured rate of reaction-rA,as a function of the gas-phase concentration CAs,(external mass transfer is eliminated,th
20、us CAs=CAb),Relate this measured reaction order n to the true reactionorder n.,34,Using the definition of the effectiveness factor:,For large values of the Thiele modulus,is:,(external mass transfer is eliminated,thus CAs=CAb),35,Overall Effectiveness Factor,When both internal AND external diffusion
21、 resistances are important(i.e.,the same order of magnitude),both must be accounted for when quantifying kinetics.It is desired to express the kinetics in terms of the bulk conditions,rather than surface conditions:,Overall Effectiveness Factor,Accounting for reaction both on and within the pellet,t
22、he molar rate becomes:For most catalyst,internal surface area is significantly higher than the external surface area:,ac is the external surface area per unit reactor volume,Molar rate of mass transfer=total rate of reaction,Overall Effectiveness Factor,reaction rate(internal&external surfaces),mass
23、 transport rate,internal surfaces not all exposed to CAs,Relation between CAs and CA defined by the as:,Using Molar rate of mass transfer=total rate of reaction,Then,Overall Effectiveness Factor,Summary of factor relationships:,Rearranging the expression:,Overall Effectiveness Factor()This eq.is for
24、 first-order reaction,Weisz-Prater Criterion for Internal Diffusion,Weisz-Prater Criterion is a method of determining if a given process is operating in a diffusion-or reaction-limited regime CWP is the known as the Weisz-Prater parameter.All quantities are known or measured.CWP 1,severe diffusion l
25、imitations,Assume that the external mass transfer is eliminated,thus CAs=CAb.,Mears Criterion,Mass 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 pack
26、ed bed flow),n=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,Mears Criterion,Heat transfer effects negligible when it is true that,h=heat transfer coef
27、ficient,kJ/m2sK R=gas constant,kJ/molKHRx=heat of reaction,kJ/mol E=activation energy,kJ/mol,12.6 Mass transfer and reaction in a packed bed reactor,43,Mole flux of A,First order reaction,Axial dispersion negligible(relative to forced axial convection)whendp is the particle diameterU0 is the superfi
28、cial velocity of the gasDa is the effective axial dispersion coefficient,can be simplified as:,Which can be rewritten as:,B.C.,Integrating and applying boundary condition yields:,The conversion at the reactors exit,z=L,is,Determination of Limiting Situations from Reaction Data,47,External mass trans
29、fer-limited reactions in packed beds:,Limiting conditions,48,49,12.7 Experimental study of the heterogeneous catalytic reactions,Intrinsic reaction kinetics is obtained when both the external mass transfer and internal diffusion are eliminated.,50,12.7.1 Eliminating the external diffusion,51,Testing
30、 the influence of the external diffusion,52,12.7.2 Eliminating the internal diffusion,For kinetics experiments,the size of the catalyst particles should be smaller than dp*,12.7.3 Experimental methods for finding rates,Experimental devicesDifferential(flow)reactorIntegral(plug flow)reactorMixed flow
31、 reactorBatch 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.,53,Comparison of Experimental Reactors:Levenspiel 3rd p400,Each run gives directly a value for the rate at the average concentration
32、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 composition,54,Differential Reactor,x=xout-xin is small,The rate to be constant at all poi
33、nts within the reactor.This assumption is usually reasonable only for smallconversions or for shallow small reactors.,55,Integral Reactor,The rate to be constant at all points within the reactor.This assumption is usually reasonable only for smallconversions or for shallow small reactors.,Integral A
34、nalysisA specific mechanism with its corresponding rate equation is put to the test by integrating the basic performance equation to give,Differential Analysis.By differentiating the integral Eq.,we obtain,See Example 18.3 in Levenspiel 3rd,Mixed-Flow Reactor,56,Sketch of a Carberry basket-type expe
35、rimental mixed flow reactor.,Principle of the Berty experimentalmixed flow reactor.,Batch Reactor,57,In this system we follow the changing composition with time and interpret the results with the batch reactor performance equation.,Summary,The concentration profile for a first-order reaction occurri
36、ng in a spherical catalyst pellet is where 1 is the Thiele modulus.For a first-order reactionThe internal effectiveness factor and overall effectiveness factor.,58,Summary(contd),For large values of the Thiele modulus for an n order reaction,For internal diffusion control,the me reaction order is related to the measured reaction order by The true and apparent activation energies are related by,59,Summary(contd),The Weisz-Prater Parameter The Weisz-Prater criterion dictates that:If CWP1,internal diffusion limitations presentMears Criteria for Neglecting External Diffusion and Heat Transfer,60,
