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**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

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**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

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**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

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**Langmuir Hinshelwood Mechanism**

B

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**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

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**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

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**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

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**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

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**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

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**r = rhet Effectiveness factor**

Reaction without mass transport limitation Effectiveness factor effectiveness factor

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**Influence of pore diffusion on effective**

rate constant

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**Film diffusion und Reaction**

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**» 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

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**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

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**Temperature dependance:**

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**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

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**Universal mass balance**

VR r jA Akk. Reaction Transp. Residence time

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

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**. 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 .

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L z q nA . (4-17)

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**Separation of variables: Integration**

Z: L X: Xe

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**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

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**2. Order reaction: r0=kcA0cB0 F(X)=(1-X)(1-lX)**

Conversion as function of Damköhler number

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**F(X); Xe Da Design of a reactor: Produced product Demands: Xe, nP**

Residence time: Reactor capacity : Reactor volume:

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**cA CSTR Fluidized bed reactor (CSTR) VR coordinate z**

M CSTR coordinate z inlet outlet cA VR 1. Order reation: F(X)=1-X

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**. 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 .

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**Comparison of ideal reactors CSTR and PFTR**

Dependence of Conversion on Damköhler number for 1. order raction

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**. [J/m2s] q r VR jA Heat balance of chemical reactors**

universal heat balance jA universal mass balance universal heat balance integral heat balance

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The cooled CSTR d a1 a2 T Tk

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

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**. LP VR=Vt Separation for T: Design of cooling follows solution of MB:**

Calculation of Ta or Tk from T0

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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

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**Example: 1. Order reaction**

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

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**4.4.4 Qualitative Description of other reactors**

Adiabatic reactors BR und PFTR BR: PFTR: cooled reactors BR: PFTR:

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

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