Ch E 542 – Intermediate Reactor Analysis & Design

1. Ch E 542 – Intermediate Reactor Analysis & Design Catalysis

2. Catalysts The photo above shows a variety of different solid catalysts used in industry. Those on the front row consist of porous substrate material coated or impregnated with catalyst; The two samples on the back row are fine powders with large surface areas

3. Silica-Alumina Cat-Cracking Catalyst (100X) fresh spent

4. Silica-Alumina Cat-Cracking Catalyst (400X) fresh spent

5. Silica-Alumina Cat-Cracking Catalyst (800X) fresh spent

6. Fresh Silica-Alumina Cat-Cracking Catalyst (1700 & 3000X)

7. Silica-Alumina Cat-Cracking Catalyst (5000X) fresh spent

8. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A bulk gas phase hydrodynamic boundary layer porous catalyst particle

9. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A internal diffusion of A bulk gas phase hydrodynamic boundary layer porous catalyst particle

10. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A internal diffusion of A adsorption of A bulk gas phase A + SA•S hydrodynamic boundary layer porous catalyst particle S catalyst adsorption site

11. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A reaction of A to B internal diffusion of A A•S B•S adsorption of A bulk gas phase A + SA•S hydrodynamic boundary layer porous catalyst particle

12. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A reaction of A to B internal diffusion of A A•S B•S adsorption of A desorption of B bulk gas phase B•S B + S A + SA•S hydrodynamic boundary layer porous catalyst particle

13. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A reaction of A to B internal diffusion of A internal diffusion of B A•S B•S adsorption of A desorption of B bulk gas phase B•S B + S A + SA•S hydrodynamic boundary layer porous catalyst particle

14. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A external diffusion of B reaction of A to B internal diffusion of A internal diffusion of B A•S B•S adsorption of A desorption of B bulk gas phase B•S B + S A + SA•S hydrodynamic boundary layer porous catalyst particle

15. Transport & Kinetic Processes in Catalytic Reactions external diffusion of A external diffusion of B reaction of A to B internal diffusion of A internal diffusion of B A•S B•S adsorption of A desorption of B B•S B + S A + S A•S • One of these seven transport and kinetic processes occurs the slowest. We say that step is “rate-limiting” • It is necessary to determine the “rate-limiting” step to analyze the kinetics. • Start by restricting ourselves to these steps…

16. Molecular Adsorption adsorption of A A + SA•S Treat as an elementary reaction site balance: pressure is a measureof collision frequency(from the moleculartheory of gases) rate of adsorption: rate of desorption: = 0 net rate of sorption: at equilibrium KA  equilibrium constant (kA/k-A) Ct  total concentration of sites per mass catalyst Cv  concentration of vacant sites per mass catalyst

17. Molecular Adsorption WOW! Langmuir Adsorption Isotherm

18. Langmuir Adsorption Isotherm note that we’ve treatedboth adsorption anddesorption in this analysis A + SA•S adsorption of A • Assumes • monolayer coverage of surface • uniform surface • Interaction between gas/site only Langmuir Isotherm describesthe equilibrium partitionof gas between sorbedand desorbed states. Langmuir Adsorption Isotherm

19. Atomic (Dissociative) Adsorption A2 + 2S 2A•S adsorption of A2 site balance: rate of adsorption: rate of desorption: net rate of sorption (at equilibrium)

20. Multicomponent Adsorption A + SA•S B + SB•S adsorption of A and B site balance: rate of adsorption: rate of desorption: net rate of sorption (at equilibrium)

21. Surface Reaction A•S  B•S single site mechanism Langmuir-Hinshelwood adjacent-siteinteraction A•S + S  B•S + S dual site mechanisms A•S + B•S  C•S + D•S adjacent-speciesinteraction A•S + B•S'  C•S' + D•S differentsite types A•S + B(g)  C•S + D(g) Eley-Rideal Kinetics gas phase interaction

22. Rate Limiting Step • Steady state, heterogeneous reactions; • Solution Algorithm: • Select a mechanism • Assume a rate limiting step • Find the expression for Ci•S using the steps that are not rate limiting (occur at equilibrium) • Write the site balance • Derive the rate law • Compare with experimental data

23. Example 1 A + S A•S Select a mechanism A•S B•S Assume a rate limiting step  B•S B + S Find Ci•S (steps not rate-limiting occur at equilibrium)

24. Example 1 A + S A•S Select a mechanism A•S B•S Assume a rate limiting step  B•S B + S Find Ci•S (steps not rate-limiting occur at equilibrium) Write the site balance Derive the rate law

25. Example 1 A + S A•S A•S B•S rate limiting  B•S B + S

26. Example 2 A + S A•S Same mechanism A•S B•S B•S B + S different rate limiting step  Find Ci•S (steps not rate-limiting occur at equilibrium)

27. Example 2 A + S A•S Same mechanism A•S B•S B•S B + S different rate limiting step  Find Ci•S (steps not rate-limiting occur at equilibrium) Write the site balance Derive the rate law

28. Example 2 A + S A•S A•S B•S B•S B + S rate limiting 

29. Example 3 A + S A•S another rate limiting step  A•S B•S Same mechanism (again) B•S B + S Find Ci•S (steps not rate-limiting occur at equilibrium)

30. Example 3 A + S A•S another rate limiting step  A•S B•S Same mechanism (again) B•S B + S Find Ci•S (steps not rate-limiting occur at equilibrium) Write the site balance Derive the rate law

31. Example 3 rate limiting  A + S A•S A•S B•S B•S B + S

32. Summary rate limiting step rate equation A + S A•S A•S B•S B•S B + S

33. Example 4 Another mechanism reactant adsorption C + S C•S inhibitor adsorption I + S I•S surface reaction (one product to gas phase) C•S  B•S + P(g) co-product desorption B•S B + S

34. Example 4 rate limiting step reactant adsorption C + S C•S inhibitor adsorption I + S I•S surface reaction (one product to gas phase) C•S  B•S + P(g) co-product desorption B•S B + S

35. Example 4 Write the site balance

36. Example 4 site balance becomes rate law becomes combining

37. Example 4 catalytic decomposition of cumene follows this mechanism C + S  C•S I + S  I•S C•S  B•S + P(g) B•S B + S using method of initial rates to analyzewith (PB=PP=0) highpressure lowpressure

38. L-H Analysis Protocol • Protocol for developing rate laws for heterogeneous catalytic reactions using Langmuir-Hinshelwood kinetic models: • Propose a mechanism • Write net rate laws for each step in mechanism • Identify (select) a rate-limiting step • Apply pseudo-steady state hypothesis • Eliminate adsorbed species concentrations • Write total site balance, solve for vacant sites • Substitute Cv and group constants

39. Propose Mechanism/Rate Laws A + S A•S W + S W•S W•S +A•S B•S + S B•S B + S

40. Rate-Limiting Step & PSSH A + S A•S W + S W•S W•S +A•S B•S + S B•S B + S

41. Eliminate X•S Concentrations

42. Eliminate X•S Concentrations

43. Perform Site Balance recall:

44. Perform Site Balance Rate law for mechanism with surface reaction as limiting kinetics

45. Propose Mechanism/Rate Laws A + S A•S W + S W•S W•S +A•S B•S + S B•S B + S

46. Rate-Limiting Step & PSSH A + S A•S W + S W•S W•S +A•S B•S + S B•S B + S

47. CX•S, Site Balance, Substitute A + S A•S W + S W•S site balance unchanged W•S +A•S B•S + S B•S B + S

48. Analysis of Catalytic Rate Data • Data for the gas-phase catalytic reaction A + B  C, are given. The limiting step in the reaction is known to be irreversible, so the overall reaction is also. The reaction was carried out in a differential reactor to which A, B, and C were all fed. • For an entering partial pressure of A of 2 atm in a PBR, what is the ratio of sites of A to C sites at 80% conversion of A? • At what conversion are the number of A and C sites equal?

49. Analysis of Catalytic Rate Data • As PA increases (at fixed PB and PC) the rate increases then levels off. Thus, PA must be in both numerator & denominator

50. Analysis of Catalytic Rate Data • Because the reaction is irreversible, PC must be in the demoninator.