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Chemical Reactor Analysis and Design. 3th Edition. G.F. Froment, K.B. Bischoff † , J. De Wilde. Chapter 2. Kinetics of Heterogeneous Catalytic Reactions. Introduction. Principles homogeneous reaction kinetics: valid. But: information at locus of reaction required !.
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Chemical Reactor Analysis and Design 3th Edition G.F. Froment, K.B. Bischoff†, J. De Wilde Chapter 2 Kinetics of Heterogeneous Catalytic Reactions
Introduction Principles homogeneous reaction kinetics: valid But: information at locus of reaction required ! Solid surface of the catalyst (internal) • Formation surface complex: • Essential feature of reactions catalyzed by solids Kinetic equation must account for this ! • Transport processes: • May influence the overall rate
Introduction • Transport of reactants A, B, ... from the main stream to the catalyst pellet surface. • Transport of reactants in the catalyst pores. • Adsorption of reactants on the catalytic site. • Chemical reaction between adsorbed atoms or molecules. • Desorption of products R, S, .... • Transport of the products in the catalyst pores back to the particle surface. • Transport of products from the particle surface back to the main fluid stream. Steps 1, 3, 4, 5, and 7: strictly consecutive processes Steps 2 and 6: cannot be entirely separated ! Chapter 2: considers steps 3, 4, and 5 Chapter 3: other steps
Introduction Ea Ea cat non-cat Principles of catalysis: A╪ • Reaction accelerated • Main reason: decrease Ea • Reverse reaction similarly accelerated • (principle microscopic reversibility) Al Potential energy A ΔH Overall equilibrium not affected ! B Progress of reaction Example: homogeneous versus catalytic ethylene hydrogenation [Boudart, 1958] Homogeneous: At 600 K: 1.44•1011 times faster Catalytic (CuO/MgO):
Introduction Types of catalysts: Acid (silica/alumina, …): • Can act as Lewis (electron acceptor) or Brønsted (proton donor) acids • Form some sort of carbonium /carbenium ion from hydrocarbons Metal (Pt, Pd, …): • Primarily used in hydrogenations and dehydrogenations Classical example: ethanol decomposition: (dehydration) (dehydrogenation) With hydrocarbons: Acid catalyst: cracking or isomerization Metal catalyst: (de)hydrogenations
Introduction Types of catalysts: Dual function or bifunctional: Certain intimacy of the two catalysts required ! single function dual function True intermediate, R, must desorb, move through the fluid phase, and adsorb on the new site if any product S is to be formed !
Introduction Types of catalysts: Dual function or bifunctional: trivial polystep non-trivial polystep • as if steps were successively performed • Rl1 intermediate continuously “bled off” => equilibrium shifted toward higher overall conversion Unique conversion or selectivity can be achieved !
Introduction Types of catalysts: Dual function or bifunctional: Example: Industrially important isomerization of saturated hydrocarbons (encountered in “catalytic reforming”):
Introduction Types of catalysts: Dual function or bifunctional: Example: Cumene cracking: Acidic silica/alumina catalyst: => Intermediate: no role Pt/Al2O3 catalyst: => Metal sites: permit alternative, and then dominant, reaction Presumed sequence:
Adsorption on solid catalysts Surface-catalyzed reaction • Classical Langmuir theory: Hypotheses: • The adsorption sites are energetically uniform • Monolayer coverage • No interaction between adsorbed molecules • Heat of adsorption independent of surface coverage • Usual mass action laws can describe the individual steps Heat of adsorption: with: [kmol/kg cat. s] with: (more than 42 kJ/mol) Unknown surface concentrations [kmol/kg cat.]
Adsorption on solid catalysts Total concentration of sites: If at equilibrium: adsorption isotherm: with: Alternate formulation: fractional coverage: Multi-layer physisorption II with finite porosity solid Langmuir Types of adsorption isotherm. After Brunauer et al. [1940].
Adsorption on solid catalysts Extension of the Langmuir treatment: Two species adsorbing on the same sites: Total concentration of sites: Unknown surface species concentrations [kmol/kg cat.] If at equilibrium: unknown surface concentrations can be eliminated: (i: A, B)
Adsorption on solid catalysts Extension of the Langmuir treatment: Molecule dissociating upon adsorption: If at equilibrium:
Adsorption on solid catalysts More general isotherms for nonuniform surfaces: Integrating over the individual sites: If Qa depends logarithmically on surface coverage: and: dθ Then: Freundlich isotherm As Qam >> RT θ (often used for liquids)
Adsorption on solid catalysts More general isotherms for nonuniform surfaces: If Qa depends linearly on surface coverage: Temkin isotherm (e.g. ammonia synthesis) Application more general isotherms to multicomponent systems: Not yet possible ! Focus on Langmuir treatment
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Rate equation: substitute the concentrations and temperatures at the locus of reaction itself ! Expression required to relate the rate and amount of adsorption to the concentration of the component of the fluid in contact with the surface Langmuir-Hinshelwood or Hougen-Watson rate equations 3. Adsorption of reactants on the catalytic site. 4. Chemical reaction between adsorbed atoms or molecules. 5. Desorption of products R, S, ....
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Single reaction: 3 steps: 1) chemisorption of A: with: 2) reaction: with: 3) desorption of R: with: or: Overall equilibrium constant: Total concentration of sites: May not always be constant !
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Single reaction: Rigorous combination three consecutive rate steps => very complicated expression ! with: W = mass of catalyst V = volume of fluid A) Steady-state approximation on surface species:
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Single reaction: A) Steady-state approximation on surface species (cont.): • Rather complicated expression (single reaction) • 3 rate coefficients to be determined B) Rate-determining step: Intrinsically much slower than the others: B.1) Starting from the steady-state approximation expression: reduces to If: reduces to If: . . . • Much simpler expression • 1 rate coefficient to be determined
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Single reaction: B.2) Direct application: e.g. surface reaction rate controlling: But rA remains finite Not true equilibrium (then rA = 0) or: But rR remains finite Then: or: rA = and: Ct often not measurable => Combine: k = kiCt
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Different step rate-controlling => different rate expression Example: Competitive hydrogenation p-xylene (A) and tetralin (B): (liquid phase) Experimental data [Wauquier and Jungers, 1957]: CA + CB ↑ r = rA + rB ↓ Negative order ?
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Additional data: (zero-order) Hydrogenation rate of A alone: (zero-order) Hydrogenation rate of B alone: B is more strongly adsorbed than A: Consistent rate equation ? => Hougen-Watson description: 1) A → product with surface reaction rate controlling product weakly adsorbed Liquids: KACA >> 1
Rate equations Langmuir-Hinshelwood / Hougen-Watson: 2) B → product = 6.7 Similar as for A: 3) A and B react simultaneously: (product weakly adsorbed) and: Then: Explains experimental data !
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Coupled reactions: e.g. dehydrogenation reactions: Al Assume: Adsorption A rate controlling: r = with: Reaction step: Desorption steps: Total concentration of sites: with:
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Form kinetic equation different according to assumptions ! Kinetic equations for reactions catalyzed by solids: overall rate Summaries groups for various kinetic schemes: Tables 2.3.1-1 [Yang and Hougen, 1950]
Rate equations Langmuir-Hinshelwood / Hougen-Watson: GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations Langmuir-Hinshelwood / Hougen-Watson: GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations Langmuir-Hinshelwood / Hougen-Watson: GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations Langmuir-Hinshelwood / Hougen-Watson: GROUPS IN KINETIC EQUATIONS FOR REACTIONS ON SOLID CATALYSTS
Rate equations Hougen-Watson versus Eley-Rideal: A + B → R Hougen-Watson: A + lAl B + lBl Al + BlRl RlR + l Eley-Rideal: one adsorbed species reacts with another species in the gas phase A + lAl Al + BRl Similar kinetic expressions ! RlR + l
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Coupled reactions: Example: n-pentane isomerization on a dual function Pt/Al2O3 reforming catalyst [Hosten and Froment, 1971] • Three-step sequence: • dehydrogenation, • isomerization, • hydrogenation, • Each step involves: • adsorption • surface reaction • desorption (Pt sites, l) (Al2O3 sites, σ) (Pt sites, l) • Each of the steps can be rate determining ! • Modeling and model discrimination
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Experimental observation: overall rate independent of total pressure Neither of the steps of the dehydrogenation or hydrogenation reactions can be rate determining (involve change of number of moles) One of the steps of the isomerization step is rate determining ! e.g., surface reaction proper in isomerization step rate determining: Three rival models: => Model discrimination using regression and statistical tests
Rate equations Langmuir-Hinshelwood / Hougen-Watson: Complex catalytic reactions: Petroleum refining Petrochemical processes Feedstock very complex ! (Paraffins, olefins, naphthenes, aromatics) e.g. Vacuum Gas Oil (VGO) feedstock hydrocracker: C15 – C40 Conventional kinetic modeling: unrealistic number of rate coefficients ! Different options: A) Consider pseudo-components, « lumps » of species (often based on physical properties, like boiling range) Small number of reactions between pseudo-components Rate coefficients depend upon the feed composition ! Costly experimentation required when feedstock changes
Rate equations B) Structure Oriented Lumping (SOL): Accounts for typical structures of the various types of molecules Lumping not completely eliminated Rate parameters still depend upon feedstock composition C) Single event concept + Evans-Polanyi relationship: • Full detail of the reaction pathways • Expressed in terms of elementary steps • Step involves moieties of the molecule • => Can occur at various positions of the same molecule Number of types of elementary steps <<< Number of molecules in the mixture Reduction of number of rate coefficients to tractable level !
Rate equations Elementary steps of cyclic and acyclic hydrocarbons and carbenium ions
Rate equations Generation of the network of elementary steps: Matrix and vector representation of 2 Me-hexane and its isomer 3-Me-hexane [Froment, 1999].
Rate equations Number of elementary steps of some classes of the hydrocarbon families in hydrocracking: paraffins, P; mononaphthenes, MNAP; dinaphthenes, DNAP; monoaromatics, MARO. From Kumar and Froment [2007].
Rate equations Evans-Polanyi relationship: Relationship between the activation energies of two elementary steps belonging to the same type.