[學(xué)習(xí)]反應(yīng)工程基礎(chǔ)程易chpt12-externaldiffu

1、Summary of Chapter 11,Types of adsorption: (a) Chemisorption (b) Physical adsorption.The Langmuir isotherm relating the concentration of species A on the surface to the partial pressure of A in the gas phase isThe se

2、quence of steps for the solid-catalyzed isomerization: A?B (a) Mass transfer of A from the bulk fluid to the external surface of the pellet (b) Diffusion of A

3、into the interior of the pellet (c) Adsorption of A onto the catalytic surface (d) Surface reaction of A to form B (e) Desorption of B from the surface (f) Diffusion of B from the pellet interior

4、 to the external surface (g) Mass transfer of B away from the solid surface to the bulk fluid,1,Assuming that mass transfer is not rare-limiting, the rate of adsorption isThe rate of surface reaction isThe r

5、ate of desorption isAt steady state,The total concentration of sires is,2,If we assume that the surface reaction is rate-limiting, we setChemical vapor deposition,3,rate-limiting,Catalyst deactivation. Th

6、e catalyst activity is defined as: The rate of reaction at any time t is The rate of catalyst decay is For first-order decay: For second-order decay:8. For slow catalyst decay

7、 the idea of a temperature-time trajectory is to increase the temperature in such a way that the rate of reaction remains constant.,4,5,Chapter 12External Diffusion Effects on Heterogeneous Reactions,Department of Chemi

8、cal EngineeringTiefeng Wangwangtf@tsinghua.edu.cn,Objectives,Discuss Fick's Law and diffusion.Define the mass transfer coefficient, explain what it is function of and how it is measured or calculated. Analyze P

9、BRs in which mass transfer limits the rate of reaction. Discuss how one goes from a region mass transfer limitation to reaction limitation. Apply the shrinking core model to analyze catalyst regeneration.,7,11.1 Diff

10、usion fundamentals11.1.1 Definition,Molar flux: WAz (mol/m2? s)Molar flow rate: FAz=AcWAz (mol/s)Diffusion is the spontaneous intermingling or mixing of molecules by random thermal motion. Concentration gradient r

11、esults in a molar flux of the species in the direction of the concentration gradient.,Molar balance,8,,,,,,z,x,y,,,,,,,,x+?x, y, z+?z,x+?x, y+?y, z+?z,x, y, z+?z,x, y, z,Molar flux WA, with unit of mol/m2?s,In – Out + Ge

12、neration = Accumulation,(In – Out) in z direction,Generation,Accumulation,Molar flux balance of species A,9,Divide by ?x?y?z for rectangular coordinates,,For cylindrical coordinates (rederive),,In vector form,,10,11.1

13、.2 Molar flux,Two contributions to molar flux:(1) Molecular diffusion flux JA(2) Convective flux resulting from the bulk motion BA,yA is the molar fraction of A,Vi is the particle velocity of species i, and V is the mo

14、lar average velocity,Total molar flux of A, WA:,In terms of the molar fraction of A,In terms of the concentration of A,11.1.3 Fick’s first law,Heat flux in one dimension (Fourier’s law)Shear stress (Newton’s law)Ma

15、ss transfer flux (Fick’s law),11,What is the condition for this eq.?,Relationship between flux and gradient,JAz is a scalar,12,Fick’s first law,Talented in mathematics and physicsFick's first contribution as a physi

16、cist was made in 1855 when he was just 26 years old (Fick’s law),The general 3-dimensional constitutive equations for JA:,c the total concentration (mol/dm3)DAB the diffusivity of A in B (m2/s)yA the mole frac

17、tion of A,JA is a vector,Adolph Fick (1829~1901), Germany,Molar flux of A,13,In terms of concentration for constant total concentration:,11.2 Binary diffusion,Evaluating the Molar FluxEquimolar counter diffusion (EMCD)

18、Dilute concentrationsDiffusion through a stagnant GasForced convectionDiffusion and convective transport,14,In equimolar counter diffusion (EMCD), for every mole of A that diffuses in a given direction, one mole of B

19、diffuses in the opposite direction.,Equimolar Counter Diffusion (EMCD),For constant total concentration:,Dilute Concentration,The mole fraction of the diffusing solute is small, BA is neglected compared with JA, thus

20、For porous catalyst with small pore radii, Knudsen diffusion occurs when mean free path of molecules is greater than catalyst pore diameter,,Knudsen diffusivity,,This approximation is almost always used for molecules di

21、ffusing within aqueous systems when the convective motion is small.,WB = 0Involve more than one phase where one species readily diffuse to the other phase (A) while another one cannot (B).,Diffusion through a Stagnant G

22、as,WB = 0,,,Forced Convection,18,JAz is small in comparison with bulk flow contribution:,,JAx,,,JAz,where Ac is the cross-sectional area and v is the volumetric flow rate.,Although JAz is neglected, JAx may not necessari

23、ly be neglected.,,Diffusion and Convective Transport,Diffusion and convective transport :,,For one-dimension at steady state,,1. Specify a concentration at a boundary         &#

24、160;         2. Specify a flux at a boundary a) No mass transfer across a boundary [e.g., at pipe wall]           

25、60;     therefore,Types of Boundary Conditions,Cross-section of a pipe,,b) Reaction at a boundary is equal to the molar flux,Cont’d,3. Planesof Symmetry , [e.g., cylinder],c) Diffusion flux t

26、o a boundary (from z = d to z = 0) is equal to the convective flux away from the boundary (at z = 0).,Modeling Diffusion Without Reaction,Step 1: Perform a differential mole balance on a particular species AStep 2: Subs

27、titute for FAz in terms of WAzStep 3: Replace WAz by the expression for the concentration gradientStep 4: State the boundary conditionsStep 5: Solve for the concentration profileStep 6: Solve for the molar fluxLook

28、 at Example 11-1!,Example 11-1,23,For species A in dilute concentration, concentration profile follows:The molar flux can be determined by using equation:The molar flux can be calculated from concentration profile b

29、y:EMCD also produces same molar flux equation as above.,11.2.4 T and P Dependence of DAB,24,Gas,Bulk,Knudsen,Liquid,Solid,Phase cm2/s m2/s T and P Dependences,Order of Magnitude,11.

30、2.5 Modeling Diffusion with Chemical Reaction,Step 1: Define the problem and state the assumptionsStep 2: Define the system on which the balances are to be madeStep 3: Perform the differential mole balance on a parti

31、cular speciesStep 4: Obtain a differential equation in WA by rearranging your balance equation properly and taking the limit as the volume of the element goes to zeroStep 5: Substitute the appropriate expression in

32、volving the concentration gradient for WA from sec 11.2 to obtain a second-order differential equation for the concentration of A,Step 6: Express the reaction rate rA in terms of concentration and substitute into a dif

33、ferential equationStep 7: State the appropriate boundary and initial conditionsStep 8: Put the differential equations and boundary conditions in dimensionless formStep 9: Solve the resulting differential equation f

34、or the concentration profileStep 10: Differentiate the concentration profile to obtain an expression for the molar flux of AStep 11: Substitute numerical values for symbols,11.2.5. Modeling Diffusion with Chemical

35、Reaction,27,11.3 External resistance to mass transfer11.3.1 Mass transfer boundary layer,The fluid velocity in the vicinity of the spherical pellet will vary with position around the sphere. The hydrodynamic boundary la

36、yer is usually defined as the distance from a solid object to where the fluid velocity is 99% of the bulk velocity U0. Similarly, the mass transfer boundary layer thickness, ?, is defined as the distance from a solid ob

37、ject to where the concentration of the diffusing species reaches 99% of the bulk concentration.,28,11.3.2 Mass transfer coefficient,Concentration profile for EMCD in stagnant film model,In this stagnant film model, all t

38、he resistance to mass transfer is lumped into the thickness ?. The reciprocal of the mass transfer coefficient can be thought of as this resistance:,29,11.3.3 Correlation for the mass transfer coefficient,,The mass trans

39、fer coefficient kc is analogous to the heat transfer coefficient h. For heat transfer:,Heat flux:,For forced convection, the heat transfer coefficient is normally correlated in terms of three dimensionless groups:,is the

40、rmal diffusivity, m2/s,where,For different Re range,30,For high Reynolds number:,For zero or very small Reynolds number:,Analogue of mass transfer to heat transfer,,11.3.4 Mass transfer to a single particle,molar flux to

41、 catalyst surface = reaction rate on surface,,Fast Reaction Kinetics,Fast reaction kinetics,to increase kc,Slow Reaction Kinetics,For slow reaction kinetics,kr is independent offluid velocityparticle size,35,Regions of

42、 mass transfer-limited and reaction-limited reactions,36,11.3.5 Mass Transfer-Limited Reactionsin Packed Beds,In mass transfer-dominated reactions, the surface reaction is so rapid that the rate of transfer of reactant

43、from the bulk gas or liquid phase to the surface limits the overall rate of reaction. Consequently, mass transfer-limited reactions respond quite differently to changes in temperature and flow conditions than do the rat

44、e-limited reactions discussed in previous chapters.,Molar balance in a packed-bed reactor,37,In – Out + Generation = Accumulation,rA"= rate of generation of A per unit catalytic surface area, mol/s?m2ac =

45、 external surface area of catalyst per volume of catalytic bed, m2/m3? = void fractiondp = particle diameter. mAc = cross-sectional area of tube containing the catalyst, m2,38,The molar flow rate of A in the axial di

46、rection is,If dispersion is negligible,,To simplify further the case studies, assume constant U,,U is the superficial molar average velocity through the bed, m/s,Boundary condition (Assuming reaction is at steady state)

47、:,Then,Integrating with boundary condition: at z=0, CA=CA0,,Thus,Analytical solution,Mass transfer limited CA >> CAs,,11.3.6. The effects of temperature and flow rate on conversion,40,The correlation for the mass t

48、ransfer coefficient flow through a packed bed (Thoenes and Kranmers (1958):,For constant fluid properties and particle diameter:,What if the gas velocity is continually increased?,Other mass transfer correlations,41,Most

49、 mass transfer correlations are in terms of Colburn J factor (JD) as a function of the Reynolds number. JD is defined as:,Dwidevi and Upadhyay’s correlation:,11.4 Parameter sensitivity,Example 11-4For a mass transfer-li

50、mited reaction,,42,X=?,,,,,v0,v0,v0,X=0.865,v0,X=?,11.5 Shrinking Core model,The coke (C) deposit into the core of catalyst through pores.O2 diffuse to the catalyst and reaction happens to “clean” the catalyst.The core

51、 is shrinking with time.,Step 1: The mole balance on O2 between r and r+?r,44,In – Out + Generation = Accumulation,Step 2: Molar flux for EMCD,45,where De is an effective diffusivity in the porou

52、s catalyst.,Step 3: Combining the above two equations yields,Step 4: The boundary conditions are:,,Step 5: The radial profile of the concentration of A,46,,47,Step 6: The molar flux of O2 to the gas-carbon interface,Step

53、 7: Overall balance on elemental carbon,In – Out + Generation = Accumulation,48,Step 8: The rate of disappearance of carbon is equal to the flux of O2 to the gas-carbon interface:,I.C., t=0, R=R0,The time neede

54、d to fully regenerate a coked catalyst particle by consuming all carbon, tc, is,Step 9: Integrating with limits R = R0 at r = 0, the time necessary for the carbon solid interface to recede inward to a radius R is,,For a

55、1 cm diameter pellet with a 0.04 volume fraction of carbon, the regeneration time is the order of 10 s.,Fluidized Catalytic Cracker (FCC),,,,12.5.2 Dissolution of Monodispersed Solid Particles,Species A must diffuse to t

56、he surface to react with solid B at the liquid-solid interface. Zero order in B and first order in A. The rate of mass transfer to the surface is equal to the rate of surface reaction.,51,where

57、 is the diameter at which the resistances to mass transfer and reaction rate are equal.,For the case of small particles and negligible shear stress at the fluid boundary:,52,A mole balance on the solid particle yields

58、,53,In – Out + Generation = Accumulation,If 1 mol A dissolves 1 mol B, then,I.C. t=0, dp=dpi,54,The variation of the particle diameter with time:,The time to complete dissolution of the

59、solid particle is,Summary,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

60、diffusion,,55,Summary (cont’d),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 fo

61、r 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.,56,

62、Summary (cont’d),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