Chemical Reactor Analysis and Design

1. Chemical Reactor Analysis and Design 3th Edition G.F. Froment, K.B. Bischoff†, J. De Wilde Chapter 3 Transport Processes with Reactions Catalyzed by Solids Part one Interfacial Gradient Effects

2. 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

3. Reaction of a component of a fluid at the surface of a solid Define reaction rate based on interfacial surface area: For first-order rate: with: Consumption of A at the interface: to be compensated for by transport from the bulk fluid with: ~ Steady state Eliminate unmeasured surface concentration CAi

4. Reaction of a component of a fluid at the surface of a solid Steady state ~ with k0 « overall » rate coefficient: (for first order rate: add resistances two consecutive linear processes) Two limiting cases: ~ 1) « reaction controlling » ~ 2) « diffusion controlling »

5. Reaction of a component of a fluid at the surface of a solid Same procedure: second order reaction: ~ • Totally different form • Concentration dependence neither first or second order Two limiting cases: ~ 1) (second order) « reaction controlling » ~ 2) (first order) « diffusion controlling » ~ ~ Explicit solution rA not possible ~ For nth order reaction: Iterative

6. Reaction of a component of a fluid at the surface of a solid ~ rA = am∙rA Specific experiments for determining: • Intrinsic reaction kinetics • Conditions such that global rate determined by reaction • Lower T • Increased turbulence • Mass transfer coefficients • Conditions such that global rate determined by mass transfer • Higher T + Isothermal conditions (no heat transfer rate eq.)

7. Mass transfer resistance: Multicomponent diffusion in a fluid General: flux given chemical species driven by: • own concentration gradient • concentration gradients all other species j = 1, 2, …, N-1 depends on system studied (e.g. ideal gas => kinetic theory => Stefan-Maxwell) bulk flow mixture Remark: liquids & thermodynamic nonidealities: no complete theory yet Form too complex for many engineering calculations: Define a mean binary diffusivity for species j diffusing through the mixture: Djm (diagonalize matrix Djk)

8. Mass transfer resistance: Multicomponent diffusion in a fluid Ideal gas Stefan-Maxwell: Alternative (engineering) form: Equate driving force, yj

9. Mass transfer resistance: Multicomponent diffusion in a fluid 1) Classical use (unit operations): « Wilke equation »: Diffusion of species 1 through stagnant 2, 3, … In reacting media: only appropriate for very dilute solutions ! (other species not necessarily stagnant) 2) Steady-state flux ratios of the various components: determined by the reaction stoichiometry constant

10. Mass transfer resistance: Multicomponent diffusion in a fluid 2) cont. Example: Use of mean binary diffusivity: with:

11. Mass transfer resistance: Multicomponent diffusion in a fluid Example: Use of mean binary diffusivity: (cont.) Then: flux expression (1D) becomes: bulk fluid film Consider steady state => NA = const. (1D) L catalyst particle Integrate across the film using an average constant value for DAm

12. Mass transfer resistance: Multicomponent diffusion in a fluid Example: Use of mean binary diffusivity: (cont.) yfA: the “film factor”: with: Written in terms of partial and total pressures: “film pressure factor pfA” Equimolar counterdiffusion => δA = 0, yfA = 1

13. Mass transfer resistance: Mass transfer coefficients Introduce mass transfer coefficient to be modeled: In terms of non-dimensional numbers (equimolar counterdiffusion) • DAm in Sc • L (film thickness) • in terms of jD = f(Re) [kg/(m2s)]

14. Mass transfer resistance: Mass transfer coefficients Introduce mass transfer coefficient to be modeled: In terms of non-dimensional numbers (equimolar counterdiffusion) [kg/(m2s)]

15. Mass transfer resistance: Mass transfer coefficients: Example: packed beds:

16. Mass transfer resistance: Mass transfer coefficients Example: packed beds of spheres with ε = 0.37: for Re = dpG/μ < 190: for Re > 190: kg: Several driving force units are in common use:

17. Heat transfer resistance: Heat transfer coefficients Fluid-to-particle interfacial heat transfer resistances: Heat transfer coefficient: with: jH = f(Re) Heat transfer between a fluid and a bed of particles (spheres; ε = 0.37). Curve 1: Gamson et al. [1943]; Wilke and Hougen [1945]. Curve 2: Baumeister and Bennett (a) for dt/dp > 20, (b) mean correlation [1958]. Curve 3: Glaser and Thodos [1958]. Curve 4: deAcetis and Thodos [1960]. Curve 5: Sen Gupta and Thodos [1963]. Curve 6: Hnadley and Heggs [1968].

18. Concentration or partial pressure and temperature differences between bulk fluid and surface of a catalyst particle One of the most important uses mass and heat transfer relationships: determine external mass & heat transfer resistances for catalyst particles [kmol/(kg cat. s)] [m2p/kg cat.] If kg → ∞ with rA finite Concentration / partial pressure drop over the external film may be neglected Check whether allowed => e.g. experimental kinetic studies

19. Concentration or partial pressure and temperature differences between bulk fluid and surface of a catalyst particle Calculation of ΔpA is not straightforward Calculation of the film pressure factor pfA requires the knowledge of Iterative: 1) Assume L’Hopital’s rule kg (1) (1) 2) ΔpA Better estimate pfA kg (2) etc..

20. External mass and heat transfer resistances in practice • Usually, but not always, ΔpA is rather small • More common: fairly large ΔT • Significant ΔT, or ΔpA: especially likely • in laboratory reactors (low flow rates) • Commercial reactors: commonly small external film • resistance (very high flow rates and Re numbers)

21. External mass and heat transfer resistances in practice Simple estimate ΔTfilm in terms of ΔCfilm [Smith, 1970] Gases in packed beds Maximum possible actual temperature difference: • complete conversion • very rapid reaction and heat release (Quick estimate)

22. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS: (ethanol) (acetaldehyde) • Tubular reactor – fixed catalytic bed • 275°C and 1 bar • Molar feed rate ethanol, FA0 = 0.01 kmol/h • Weight of catalyst, W = 0.01 kg • Inside diameter reactor = 0.035m • Catalyst particles: cylindrical: • diameter = height = d = 0.002 m • Bulk density bed, ρB = 1500 kg/m3 • Void fraction, ε = 0.37, • Conversion = 0.362 (measured) • Reaction rate, rA = 0.193 kmol/(kg cat. h) am = 1.26 m2/kg

23. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS Physicochemical data: estimates through general correlations [Reid, Prausnitz, and Sherwood, 1977]

24. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

25. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS Pa s

26. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

27. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

28. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

29. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

30. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

31. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS

32. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS No further iterations required

33. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM Requires two further properties of the reaction mixture: • The specific heat cp • The thermal conductivity λ • cp values for the pure components: • Literature • Accurate estimation: correlation [Rihani & Doraiswamy, 1965]

34. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM Thermal conductivities pure components: estimated by Bromley’s method

35. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM

36. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM

37. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM

38. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM CH3CHO (cont.)

39. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM

40. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM THERMAL CONDUCTIVITY OF THE GAS MIXTURE Estimation factors Aij: Lindsay-Bromley equation

41. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM THERMAL CONDUCTIVITY OF THE GAS MIXTURE 50 % higher than the more correct estimate

42. Example: INTERFACIAL GRADIENTS IN ETHANOL DEHYDROGENATION EXPERIMENTS ESTIMATION OF THE TEMPERATURE DROP OVER THE FILM Then, the Prandtl number is: