1. Reaction Engineering in Heterogeneous Catalysis
Reaction and mass transport in porous catalysts
- Up-Scaling of Reactors
Reinhard Schomäcker
Institut für Chemie
der Technischen Universität Berlin

7. Schematic presentation of a chemical process
Heat
Main product
Reactant-
purification
Reaction
Product-
isolation BP
solvent, reactants, catalyst
Procedure for reactor design
1. Stoichiometry und Thermodynamics
2. Apparatus and Conditions
3. Calculation of Conversion and Reactor Size
4. Calculation of Material Flow

8. Steps of Heterogeneous Reaction
Diffusion of reactant to catalyst
Transport of reactant within catalyst pores
Adsorption of reactant on catalyst surface
Reaction
Desorption of products from catalyst surface
Transport of products out of catalyst pores
Diffusion of products away from catalyst

9. Langmuir Hinshelwood MechanismB

10. Mass Transport and Heterogeneous Catalysis Principles
Surface layer
fluid phase
catalyst
Influence of mass transport on the temperature dependance of het. catalysis
Mass transport
influence
Concentration profile

11. A Dg ~ T1,5 und Dg ~ 1/p Description of pore diffusion 1. Fick`s Law
Average free path length
Average molecular velocity
Dg ~ T1, und Dg ~ 1/p

12. DK ~ T0.5 a) Diffusion in pores dp >> l N2, X N2, X =? N2
Wicke-Kallenbach-Experiment
porous
material
b) Knudsen – Diffusion dp = l
DK ~ T0.5
c) Intermediate range

13. dV Description of simultaneous reaction and pore diffusion
temporal change changes of material changes caused
of materials within = amount by transport by reactions
volume element dV
one dimensional
Spherical geometry

14. Mass balance of sperical particle in steady state
Solution of mass balance and description of average reaction rate
with r= kcn and n=-1
renormalized parameter
= Thiele-Modulus
radial concentration profil
within sperical pellet

15. r = rhet Effectiveness factor
Reaction without mass transport limitation
Effectiveness factor
effectiveness factor

16. Influence of pore diffusion on effective
rate constant

17. Film diffusion und Reaction

18. » c0 cw c0 cw Discussion of a first order reaction with rs=kscw
ß(c0-cw) = kscw
Border cases: c0 cw
ks << ß cw =c ( no layer formation)
ks >> ß cw 0 c0 cw

19. dsphere d Particle surface 6 = a p Particle volume
Calculation of eff. volume related rate constant
dsphere d
Particle volume a 6 3 2 = p
Particle surface

20. Temperature dependance:

21. Three-Phase-Reactors
Gas-Liquid-Reactors
Gas-Solid-Reactors
Three-Phase-Reactors G L G L
Katalysator G L G
Column
Fixed Bed Reactor
Trickle Bed Reactor G L
K+L
K+L G G
Tank Reactor
Packed Bubble Column
Tube Reactor

22. Universal mass balanceVR r jA
Akk.
Reaction
Transp.
Residence time

23. [-] Damköhler Number
reaction
reactor
Solution of general mass balance with boundary conditions for
Different reactions and reactor results in X = f(Da, reactor)

24. . nA q z L . Ideal Tube Reactor (PFTR) steady state (dX/dt=0)L z q nA .
steady state (dX/dt=0)
no back mixing (plug flow)
- Volume of feed is constant
no radial concentration gradient (one dimensional system)
- characteristic time is definied by: t=VR/V .

25. L z q nA .
(4-17)

26. Separation of variables: Integration
Z: L
X: Xe

27. 1. Order reaction: r0=kcA0 F(X)=1-X
0. Order reaction: r0=k F(X)=1
2. Order reaction: r0=kcA0cB0 F(X)=(1-X)2

28. 2. Order reaction: r0=kcA0cB0 F(X)=(1-X)(1-lX)
Conversion as function of Damköhler number

29. F(X); Xe Da Design of a reactor: Produced product Demands: Xe, nP
Residence time:
Reactor capacity : Reactor volume:

30. cA CSTR Fluidized bed reactor (CSTR) VR coordinate zM
CSTR
coordinate z
inlet
outlet cA VR
1. Order reation: F(X)=1-X

31. . LP VR=Vt X 2. Order reaction: F(X)=(1-X)(1-lX) 1 F(X)
Simple procedure for solution of mass balance: X/Da = F(X) X
F(X) 1
X/Da Xe
Reactor design:
F(X) ; Xe Da ; t
LP VR=Vt .

32. Comparison of ideal reactors CSTR and PFTR
Dependence of Conversion on Damköhler number for 1. order raction

33. . [J/m2s] q r VR jA Heat balance of chemical reactors
universal heat balance jA
universal mass balance
universal heat balance
integral heat balance

34. The cooled CSTR d a1 a2 T Tk

35. (4-46)
(4-47)
(4-48)
Coupling Equation

36. . LP VR=Vt Separation for T: Design of cooling follows solution of MB:
Calculation of Ta or Tk from T0

37. Safty Scenario
4.4.3 Stability analysis
a) FW high, T-TK low: right
b) FW low , T-TK high : wrong
Quantitative calculation MB HB

38. Example: 1. Order reactionDa T e
mit k
Mass balance E RT A = + - ( ) 1 n t ( ) 1 + - = St T Da e
Coupling eqn. ad E RT D

39. 4.4.4 Qualitative Description of other reactors
Adiabatic reactors
BR und PFTR
BR:
PFTR:
cooled reactors
BR:
PFTR:

40. r TK
rtube< rcrit.
rtube> rcrit.
Radial temperature profile with tube reactor