1. EKC 337/3 REACTOR DESIGN AND ANALYSIS ( Semester II 2009/2010 ) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS Assoc Prof Dr Ahmad Zuhairi Abdullah

2. Course contents 1) Classification of heterogeneous reactions/reactors 2) Gas-solid catalytic reactions 3) Steps in catalytic reactions 4) Identification of rate limiting step 7) Catalyst preparation methods 8) Catalyst characterization methods 6) Experimental method for finding rate law (Duration : 7 weeks) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

3. Course Learning Objectives 1) List and discuss different types of heterogeneous catalytic processes in a gas-solid catalytic reaction 2) Describe and formulate rate expressions for main steps involved in a solid-catalyzed reaction and to analyze the catalytic system for rate-limiting steps 3) Describe and apply different types of laboratory scale reactor to determine the rate equations and model parameters 4) Describe catalysts preparation methods and their characterization methods SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

4. Catalyst ~ Substances added to a chemical process ~ Do not enter into the stoichiometry ~ Accelerate the reaction by a factor of a million or more ~ Provide alternative path for the reaction to occur ~ Negative catalyst may slow down a reaction ~ Cannot alter the equilibrium composition in a reactor because that would violate the Second Law of Thermodynamics which says that equilibrium in a reaction is uniquely defined for any system SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

5. A graphical representation of the role of a catalyst SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

6. General observations ~The selection of a catalyst to promote a reaction is not well understood => Extensive trial and error is needed ~Duplication of the chemical constitution of a good catalyst is no guarantee that the solid produces will have the catalytic activity ~Reactant molecules are somehow changed, energized of affected to form intermediates in the regions close to the catalyst surface ~Catalyst never determine the equilibrium or end point of a reaction ~A large readily accessible surface in easily handled material is desirable SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

7. Homogeneous and heterogeneous catalysts ~Homogeneous catalyst => molecules in the same phase as the reactants (usually a liquid solution) ~Acids, bases and organometallic complexes are example of homogeneous catalysts ~Heterogeneous catalysts are in another phase (usually solid whose surfaces catalyze the desired reaction ~Solid powders, pellets and reactor walls are examples of heterogeneous catalysts SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

8. Catalyst properties ~A large interfacial area ~Porous structure-supplies the surface area needed ~Typical silica-alumina cracking catalysts Pore volume = 0.6 cm 3 /g Pore radius (average) = 4 nm Surface area = 300 m 3 /g ~Small pore preventing large molecules but allowing small molecules => molecular sieves e.g. clays, zeolites or crystalline aluminosilicate. They allow the desired molecule to react + 6 H 2 ~The configuration of the reacting molecules may be able to be controlled by placement of the catalyst atoms at specific sites in the zeolite catalyst ~Sufficiently active catalyst-no need porous catalyst->monolithic SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

9. ~Monolithic catalysts are normally encountered in processes where pressure drop and heat removal are major considerations ~Typical monolithic catalysts-Pt gauze reactor in NH 3 oxidation step of nitric acid manufacture and catalytic converters used to oxidize pollutants in automobile exhaust ~A catalyst could consist of minute particles of an active material dispersed over a less active substance called a support. The active material is frequently a pure metal of metal alloy. Such catalysts are called supported catalyst. ~Unsupported catalysts-active ingredients are of major amounts. Other substances are called promoters which increase the activity. Catalyst properties (cont’d) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

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11. Catalyst pellets SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

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14. Monolithic substrates SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

15. Catalyst deactivation ~Catalysts do not maintain their activities at the same level for indefinite period ~Deactivation = The decline in a catalyst’s activity as time progresses ~Aging phenomenon = A gradual change in surface crystal structure ~Deposition of a foreign material on active portions of the surface =>poisoning or fouling of the catalyst ~Deposition of carbonaceous materials=>coking (fast deactivation) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

16. Gas phase reaction catalyzed by solid surface ~One or all reactants become attached to the surface-adsorption ~Physical and chemisorption Physical adsorption ~Similar to condensation ~Heat of adsorption is relatively small (1-15 kcal/g-mol). ~The forces of attraction between the gas molecules and the solid surface are weak ~van der Waals forces consists of interaction between permanent dipoles, between a permanent dipole and an induced dipole and/or between neutral atoms and molecules ~Amount adsorbed decrease with increasing temperature SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

17. Chemisorption ~Affects the rate of a chemical reaction ~Adsorbed atoms/molecules are held to the surface by valence forces of the same types as those that occur between bonded atoms in molecules ~Electronic structure of the chemisorbed molecule is perturbed significantly => extremely reactive ~Exothermic process. Heats of adsorption are of the same magnitude as the heat of a chemical reaction (10-100 kcal/g-mol) ~If a catalytic reaction involved chemisorption, it must be carried out within the temperature range where chemisorption of the reactants is appreciable SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

18. ~Reaction is not catalyzed over the entire solid surface but only at specific active sites or centers ~Active sites – sites where highly reactive intermediates (i.e. chemisorbed species) are stabilized long enough to react ~Active sites – defined as a point on the catalyst surface that can form strong chemical bonds with an adsorbed atom/molecules ~Turn over frequency (N) – the number of molecules reacting per active site per second at the condition of the experiment ~When a metal catalyst e.g. Pt is deposited on a support, the metal atoms are considered active sites ~The dispersion (D) of the catalyst is the fraction of the metal atoms deposited that are on the surface Adsorption of ethylene on Pt to form chemisorbed ethylidyne SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

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21. Porous catalysts ~Rate is usually proportional to the surface area =>Catalysts need to have the highest possible surface area to minimize the total reactor volume ~Powder catalyst-pressed into porous pellets and packed into the reactor ~e.g. amorphous silica can be prepared with high surface area by precipitating silica from an aqueous silicate solution (gel) and drying the precipitate (SA ~ 500 m 2 /g) ~Alumina can be prepared can be prepared by precipitating Al 2 O 3 from aqueous solution, followed by drying and heating (SA~200 m 2 /g) ~Alumina forms a porous network as the water is removed SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

22. Reactant Porous catalyst SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

23. Diffusion of reactants in a porous catalyst SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

24. Measures of reaction rate for porous catalysts Based on void volume in the reactor -r A = - 1V1V dN A dt = kC A Mol reacted M 3 voids  S Based on weight of catalyst pellet -r’ A = - 1W1W dN A dt = k’C A Mol reacted kg cat  S Based on catalyst surface -r” A = - 1S1S dN A dt = k”C A Mol reacted M 2 cat. surface  S Based on volume of catalyst pellet -r’” A = - 1Vp1Vp dN A dt = k’”C A Mol reacted M 3 solid  S Based on total reactor volume -r”” A = - 1Vr1Vr dN A dt = k””C A Mol reacted M 3 reactor  S SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

25. Reaction rate for porous catalysts -r’ A = k’C A n where, k’ = ~For porous catalyst particles, rate based on unit mass and on unit volume of particles, r’ and r’” are the useful measures ~For n’th order reaction (m 3 gas) n (mol A) n-1 (kg cat )  S Mol A kg cat  S -r’” A = k”’C A n where, k”’ = (m 3 gas) n (mol A) n-1 (m 3 cat )  S Mol A (M 3 cat )  S SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

26. Classification of catalysts 1) Alkylation and dealklylation reactions ~ Addition of alkyl group to an inorganic compound ~ Commonly use the Friedel-Crafts catalysts (AlCl 3 ) ~ Cracking of petroleum products is the most common dealkylation reaction (catalyst: silica-alumina, silica magnesia) C 4 H 8 + i-C 4 H 10  i-C 8 H 18 C 6 H 6 + C 2 H 4  C 6 H 5 -C 2 H 5 SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

27. Classification of catalysts (cont’d) 2) Isomerization reactions ~ Conversion of normal chain HC to branched chains leading to higher octane number ~ Catalysts : usually acid-promoted Al 2 O 3 ~ Conversion to isoparaffins is easiest when both acid sites and hydrogenation sites are present such as in Pt/Al 2 O 3 3) Hydrogenation and dehydrogenation reactions ~ The bonding strength between H and metal surface increases with an increase in vacant d-orbitals ~ The bonding strength between H and metal surface increases with an increase in vacant d-orbitals ~ Lower catalytic activity if the bonding is too strong as the products are not readily released ~ Active metals: Co, Ni, Rh, Ru, Os, Pd, Ir and Pt SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

28. 4) Hydrogenation and dehydrogenation reactions (cont’d) ~ V, Cr, Cb, Mo, Ta and W, each of which has a large number of vacant d-orbitals are inactive as a result of the strong adsorption for the reactants or the products or both ~ Dehydrogenation reactions are favored at high T (< 600 o C) and hydrogenation reactions are favored at lower T CH 3 CH=CHCH 3 Catalyst CH 2 =CHCH=CH 2 + H 2 (possible catalysts: calcium nickel phosphate, Cr 2 O 3 ) ~ The same catalyst could be used in the dehydrogenation of ethyl benzene to form styrene  -CH 2 CH 3 Catalyst  CH=CH 2 + H 2 SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

29. 5) Oxidation reactions ~ Mostly transition group elements (d-block) and Subgroup 1 ~ Ag, Cu, Pt, Fe, Ni and their oxides. V 2 O 5 and MnO 2 are frequently used for oxidation reactions ~ Principal types of oxidation reaction are: i) Oxygen addition ii) Oxygenolysis of C-H bonds iii) Oxygenation of N-H bonds iv) Complete combustion 2 CO + O 2 2 CO 2 Cu 2 CH 3 OH + O 2 2 HCHO + 2 H 2 O 4 NH 3 + 5 O 2 4 NO + 6 H 2 O Pt 2 C 2 H 6 + 7 O 2 4 CO 2 + 6 H 2 O Ni SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

30. 6) Hydration and dehydration reactions ~ Catalysts have a strong affinity for water CH 2 =CH 2 + H 2 O CH 3 CH 2 OH ~ Al 2 O 3 is used in the dehydration of alcohols to olefin ~ Silica-alumina gels, clay, phosphoric acid, phosphoric acid salts on inert carriers ~e.g. synthesis of ethanol from ethylene 7) Halogenation and dehalogenation reactions ~ Reaction can take place without catalyst ~ Catalyst is used when selectivity to the desired product is low or it is necessary to run the reaction at a lower temperature ~ Supported Cu and Ag halides can be used for halogenation of HC ~ Hydrochlorination can be carried out with Hg-Cu or Zn halides as catalysts SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

31. Catalytic reactors for heterogeneous catalysts 1) Batch reactor ~The catalytic particles are suspended in a mechanically stirred liquid ~The catalyst may be filtered or centrifuged off after the reaction ~Simple, flexible and easily e.g oligomerization of isobutene with ion-exchanged catalyst at 100 o C, 20 bar (Bayer process) ~Excessive heat of reaction is absorbed through liquid medium and exchanged by external cooling jacket ~Excessive heat of reaction can be controlled by partial vaporization of liquid medium SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

32. Catalytic reactors for heterogeneous catalysts 2) Packed bed reactor ~Most commonly used industrial reactor for a large scale continuous process and a slow rate of reaction ~Typically a tank or tube filled with catalyst pellets with reactant entering at one end and the products leaving at the other ~Large particles => less pressure drop but more diffusion resistance SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

33. 2) Packed bed reactor (cont’d) ~Multitube reactors allow efficient heat transfer for exothermic and endothermic reactions ~Assuming no mixing, the mass balance on the fluid will be a PFR UdC j dz = j r ~For multiple reactions UdC j dz =  ij r i i ~Where, U is an average velocity of the fluid around the catalyst. The total volume is V R and this is a sum of the volume occupied by the fluid and catalyst V R = V fluid + V catalyst SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

34. 2) Packed bed reactor (cont’d) ~These can be related by the relations V fluid =  V R V catalyst = (1-  )V R Where,V R = volume of the reactor  V R = volume occupied by fluid  = void fraction Calculation of pressure drop (Ergun Equation) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

35. ~If the fluid is gas => difficult to stir solid particles and gas mechanically ~Can be accomplished by using very small particles and flowing the gas such that the particles are lifted and the gas and particles swirl around the reactor => fluidized bed reactor ~The moving fluid in the reactor is well mixed within the reactor so that the mass balance on reactant species A is that of a CSTR V fluid =  V R 3) Slurry reactor ~The fluid and the catalyst are stirred instead of having the catalyst fixed in the bed ~If the fluid is liquid=>slurry reactor in which catalyst pellets or powders are held in a tank through which catalyst flows ~Fast enough stirring to mix the fluid and the particles ~Catalyst must be sufficiently small to avoid settling SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

36. 3) Slurry reactor (cont’d) ~The reaction often involves complex mass transfer from the gas bubbles to liquid medium and finally to the catalytic particles Slurry bubble column reactor ~Excessive heat of reaction is absorbed through liquid medium and exchanged by external cooling jacket ~e.g. hydrogenation of benzene to cyclobenzene with Raney-Nickel catalyst at 200 o C and 20-30 bar. ~The particles are suspended in a mechanically stirred liquid and also by the uprising gas bubbles SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

37. 4) Fluidized bed reactor ~The catalyst particles are supported by an upflow of gas ~Easy loading and removing of catalysts => good when the catalysts must be removed and replaced frequently ~Less expensive to construct but hydrodynamics are very complex ~A high conversion with a large throughput SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

38. 4) Fluidized bed reactor (cont’d) ~Catalyst particle should be attrition resistant and not agglomerate ~Cyclones are usually needed to return the fines to the bed ~20-100 micron average particle size with a narrow size distribution is generally recommended ~Excessive heat of reaction can be easily controlled with good temperature uniformity ~Minimum fluidization velocity for a spherical catalyst: SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

39. 4) Fluidized bed reactor (cont’d) ~e.g. the manufacture of acrylonitrile by the ammoxidation of propylene over complex metal oxide catalysts at 400-500 o C and 1.5 bar ~Advantages : Uniform particle mixing, uniform temperature gradient and ability to operate in continuous mode ~Disadvantages : Increased reactor size, pumping requirement, pressure drop, particle entrainment, erosion and wear of external components SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

40. 5) Trickle column reactor ~The catalytic particles are fixed in their positions and liquid/gas reaction medium flow downward concurrently through the bed ~Distributor design may be needed for even distribution of gas/liquid ~Continuous mode ~No specific requirement for particle size and shape. Larger particles will produce less pressure drop and more diffusion limitations ~Excessive heat of reaction can be controlled by partial vaporization of liquid medium SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

41. 5) Trickle column reactor (cont’d) ~Ergun Equation for calculating pressure drop ~e.g. production of isopropanol by the addition of water to propylene over a solid sulfonic acid ion exchanger at 130-160 o C with a pressure of 80-100 bar SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

42. Steps in a catalytic reaction Transport of reactant and reaction SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

43. Steps in a catalytic reaction (cont’d) 1) External mass transfer (diffusion) of reactant from the bulk fluid 2) Internal mass transfer (diffusion) of reactant to the surface 3) Adsorption of reactant onto the catalyst surface 4) Reaction on the surface 5) Desorption of the products from the surface 6) Internal diffusion of the products to the pore mouth 7) External diffusion of the products to the bulk fluid External diffusion Internal diffusion Desorption Adsorption Surface Reaction SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

44. Steps in a catalytic reaction (cont’d) ~The overall rate of reaction is equal to the rate of the slowest step ~When the diffusion steps (1,2,6,7) are very fast compared with the reaction steps (3,4,5), the concentrations in the vacinity of the active sites are indistinguishable from those in the bulk fluid ~If the reaction steps are very fast, mass transport does affect the rate ~If the external diffusion affect the rate, changing the flow conditions past the catalyst should change the overall reaction rate ~In porous catalysts, diffusion within the catalyst pores may limit the reaction rate. The overall rate will be unaffected by external flow conditions SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

45. Steps in a catalytic reaction (cont’d) Reactant concentration profiles around and within a porous catalyst pellet SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

46. Mathematical expressions – Adsorption isotherms ~Active site (S), alone it will denote a vacant site with no atom, molecule of complex adsorbed on it ~The combination of S with another letter (e.g. A  S) means that one unit of A will be adsorbed on the site S ~Species A can be atom, molecule or some other atomic combination ~The adsorption of A on a site S A + S A  S ~The total molar concentration of active sites per unit mass of catalyst is equal to the number of active sites per unit mass divided by Avogadro’s number. (C t, mol/g cat ) ~The molar concentration of vacant sites, C v, is the number of vacant sites per unit mass of catalyst divided by Avogadro’s number ~Assuming no deactivation => total concentration of active sites remains constant SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

47. Mathematical expressions – Adsorption isotherms (cont’d) ~Further definition P i = partial pressure of species i in the gas phase (atm) C i  s = surface concentration of sites occupied by species i (gmol/g cat ) A B A, B = adsorbed species ~Total concentration of sites (site balance) is; C t =C V + C A  S + C B  S (1) ~Two models are postulated for adsorption of CO on metals: CO adsorbed as molecules (CO) and as individual atoms ( O and C) CO + SCO  S (molecular/non-dissociative) CO + 2SC  S + O  S (dissociative) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

48. Mathematical expressions – Adsorption isotherms (cont’d) ~e.g. CO + -M-M-M--Fe-Fe-Fe- -Ni-Ni-Ni- CO CO CASE I:Consider adsorption as molecule (non-dissociative) CO + SCO  S (2) ~The rate of attachment usually directly proportional to the CO partial pressure (P co ) and the concentration of vacant sites (C v ) Rate of attachment=k A P co C v ~The rate of detachment usually directly proportional to the concentration of occupied sites (C co  s ) Rate of detachment=k  A C co  s SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

49. Mathematical expressions – Adsorption isotherms (cont’d) ~The net rate of adsorption r AD =k A P co C v - k  A C co  s ~Rearrangement, r AD =k A P co C v - C co  s KAKA (4) Where K A = k A /k  A ~k A for molecular adsorption is virtually independent of T while k  A increases exponentially with increasing T. Thus, K A decrease exponentially with increasing T ~Since CO is the only adsorbed molecule, the site balance gives C t =C v + C co  s (5) ~At equilibrium, r AD = 0 P co C v =C co  s /K A or C co  s =K A C v P co (6) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

50. Mathematical expressions – Adsorption isotherms (cont’d) ~From (5), to give C v in terms of C co  s and C t, replace into (6) C co  s =K A P co C t 1 + K A P co ~ C co  s as a function of P co => Langmuir isotherms C co  s (mol/g cat ) P co (kPa) (7) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

51. Mathematical expressions – Adsorption isotherms (cont’d) ~Eq. (7) can be linearized to check for molecular adsorption (8) ~The linearity of a plot P co /C co  s as a function of P co will determine if the data conform to a Langmuir single site isotherm P co C co  s P co Slope = 1/C t Intercept = 1/K A C t Molecular adsorption (Non-dissociative) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

52. Mathematical expressions – Adsorption isotherms (cont’d) CASE II:Consider adsorption as atoms (dissociative) Rate of adsorption=k A P co C v 2 ~Rate of adsorption is proportional to P co as it governs the number of gaseous collisions with the surface ~Two adjacent vacant sites are required when CO adsorbed in its molecular form ~The probability of two vacant sites occurring adjacent to one another is proportional to the square of the concentration of the vacant sites ~The rate of desorption is proportional to the product of the occupied site concentration i.e. (C  S) x (O  S) ~The net rate of adsorption r AD =k A P co C v 2 - k  A C o  s C c  s (9) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

53. Mathematical expressions – Adsorption isotherms (cont’d) ~Factoring out k A r AD =k A P co C v 2 - C c  s C o  s KAKA Where K A = k A /k  A ~For dissociative adsorption, both k A and k -A increase exponentially with increasing temperature while KA decreases with increasing temperature ~At equilibrium (r AD = 0), from Eq. (9) k A P co C v 2 =k  A C o  s C c  s ~For C o  s = C c  s (k A P co ) 1/2 C v =C o  s (10) ~From (1) C v =C t - C o  s - C c  s =C t - 2C o  s SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

54. Mathematical expressions – Adsorption isotherms (cont’d) ~This value can be substituted into (10) C o  s = (K A P co ) 1/2 C t 1 + 2(K A P co ) 1/2 (11) ~Taking the inverse of both sides then multiplying through (P co ) 1/2 (12) ~If the model is correct, a plot of (P co ) 1/2 /C o  s versus P co 1/2 should be linear P co 1/2 C o  s P co 1/2 Slope = 2/C t Intercept = 1/(K A ) 1/2 C t (Dissociative adsorption) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

55. Mathematical expressions – Adsorption isotherms (cont’d) ~When more than one substance is present (A and B) C A  s = K A P A C t 1 + K A P A + K B P B (13) ~When the adsorption of both A and B are first-order, the desorptions are also first-order SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

56. Mathematical expressions – Surface reaction (cont’d) ~The rate of adsorption of species A onto a solid surface A + S A  S is given as r AD =k A P A C v - C A  s KAKA ~Once the reactant has been adsorbed, it is capable of reacting in a number of ways to form products a) Single site mechanism A  S B  S r s =k s C A  S - C B  s KsKs Elementary reaction Where K s = k s /k  s = surface reaction equilibrium constant SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

57. Mathematical expressions – Surface reaction (cont’d) b) Dual site mechanism A  S + S B  S + S ~Adsorbed reactant interacts with another site (either occupied or unoccupied) to form the product r s =k s C A  S C v - C B  s C v KsKs (16) AB ~Another example of a dual site mechanism is the reaction between two adsorbed species A  S + B  S C  S + D  S AD BC SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

58. Mathematical expressions – Surface reaction (cont’d) ~With the rate law r s =k s C A  S C B  S - C C  s C D  S KsKs (17) ~The third dual site mechanism is the reaction of two species adsorbed on different types of sites, S and S’ A  S + B  S’ C  S’ + D  S AD B C r s =k s C A  S C B  S’ - C C  s’ C D  S KsKs (18) ~Reaction involving either single or dual site mechanisms are sometimes referred to as following Langmuir-Hinshelwood kinetics SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

59. Mathematical expressions – Surface reaction (cont’d) ~The fourth dual site mechanism is the reaction between an adsorbed molecule and a molecule in the gas phase A  S + B (g) C  S + D (g) r s =k s C A  S P B - C C  s P D KsKs (19) ACBD ~This type of mechanism is referred to as an Eley-Rideal mechanism SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

60. Mathematical expressions – Desorption ~Products of the surface reaction adsorbed on the surface are subsequently desorbed into the gas phase C  S C + S C = adsorbed species ~The desorption rate law is r D =k D C C  S - P C C v K DC (20) Where K DC is the desorption equilibrium constant ~The desorption step for C is the reverse of the adsorption step for C r D =-r ADC ~The desorption equilibrium constant (K DC ) is just the reciprocal of the adsorption equilibrium constant for C (K C ) K DC =1/K C SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

61. The rate-limiting step ~At steady state -r A ’ = -r AD = r S = r D ~One particular step in the series is usually found to be rate-limiting or rate controlling ~If we could make this particular step to go faster, the entire reaction would proceed at an accelerated rate ~Algorithm to determine the rate-limiting step Molecular or atomic adsorption Single or dual site reaction Write rate laws for each step Postulate a rate-limiting step SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

62. Synthesis a rate law, mechanism and rate-limiting step ~To develop rate laws for catalytic reactions that are not external diffusion limited ~Consider the decomposition of cumene to form benzene and propylene C 6 H 5 CH(CH 3 ) 2 C 6 H 6 + C 3 H 6 ~Nomenclatures to be used: C = cumene, B = benzene, P = propylene and I = inhibitor C + S C  S Adsorption of cumene kAkAkAkA C  S B  S + P Surface reaction to form adsorbed benzene and propylene in the gas phase ksksksks B  S B + S Desorption of benzene from the surface kDkDkDkD SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

63. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~Treat each step as an elementary reaction, concentrations are replaced by partial pressure (C c  P c ) ~The rate of expression for the adsorption of cumene is -r AD = k A P c C v - k -A C C  S (1) -r AD = k A (P c C v - C C  S /K c )(2) ~The rate law for surface reaction C  S B  S + P(g) kAkAkAkA r S = k S C C  S - k -S P P C B  S (3) r S = k S (C C  S - P P C B  S /K S )(4) ~With the surface reaction equilibrium constant being K s = k s /k -s (5) ~Typical units for k a and K s are s -1 and atm, respectively SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

64. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~Propylene is not adsorbed on the surface C P  S = 0 ~The rate of benzene desorption is r D = k D C B  S - k -D P B C v (6) r D = k D (C B  S - P B C v /K DB )(7) ~Typical units of k D and K DB are s -1 and kPa, respectively. ~Desorption is just the reverse of the adsorption of benzene, thus, benzene adsorption equilibrium constant K B is just the reciprocal of the benzene desorption constant K DB K B = 1/K DB (8) ~Equation (7) can be rewritten as r D = k D C B  S - k -B P B C v (9) ~As no accumulation of reacting species, the rates of each steps in sequence are all equal -r C ’ = r AD = r S = r D (10) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

65. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~In order to determine which step is rate-limiting, first assume one of the steps to be rate-limiting and then formulate the reaction rate law in terms of the partial pressures of the species present CASE I : Is the adsorption of cumene is rate–limiting? -r c ’ = r AD = k A (P c C v - C C  S /K c )(11) ~Cannot measure C v or C C  S  replace these variables with measurable quantity. Under steady state; -r C ’ = r AD = r S = r D (12) ~For adsorption limited reactions, k A is small, k s and k D are large r S = k S (C C  S - C B  S P P /K s )(13) If, C C  S = C B  S P P /K s ) (14) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

66. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~To express C C  S solely in terms of partial pressures  evaluate C B  S r D = k D (C B  S - K B P B C v )(15) ~For adsorption limited reaction C B  S = K B P B C v (16) ~Combining equation (14) and (16) C C  S = K B P B P P C v (17) KsKs ~Replacing C C  S in (17) into (11) and then factoring C v (18) ~Where K P =K s K c /K B is overall partial pressure equilibrium constant K s K c /K B =K p C B + P ~K P can be determined from thermodynamic data RT ln K = -  G SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

67. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~The concentration of vacant sites (C v ) can be eliminated from (18) Total sites = vacant sites + occupied sites C t = C v + C C  S + C B  S (19) ~Substituting (16) and (17) into (19) C t = C v + (K B /K s )P B P P C v + K B P B C v (20) ~Solving for C v (21) ~Initially, no products are present, P Po =P Bo =0, initial rate is -r co ’ = C t K A P CO = kP co Initial partial pressure, P co Initial rate -r’ co Uninhibited adsorption limited reaction SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

68. Synthesis a rate law, mechanism and rate-limiting step (cont’d) CASE II : Is the surface reaction rate–limiting? r s = k s (C C  S - P P C B  S /K s ) ~The rate of surface reaction is ~Utilize adsorption and desorption steps to eliminate C C  S and C B  S ~From (11) (adsorption rate). Surface reaction controlling (r AD /k A =0) C C  S = K c P c C v ~The surface concentration of adsorbed benzene can be evaluated from the desorption rate expression (equation 15) when r D /k D = 0) C B  S = K B P B C v ~Substituting C B  S and C C  S in the rate of surface reaction SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

69. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~Site balance C t = C v + C C  S + C B  S ~Substituting for concentrations of the adsorbed species C B  S and C C  S ~Initial rate is k ~Low partial pressure ~High partial pressure as 1>>K C P Co SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

70. Initial partial pressure, P co Initial rate -r’ co Surface reaction limited Synthesis a rate law, mechanism and rate-limiting step (cont’d) CASE III : Is the desorption of benzene rate–limiting? ~The rate for desorption of benzene is r D = k D (C B  S - K B P B C v )(1) ~From r s /k s = 0 (k AD and k s are very large compared to k D ) C B  S = K s C C  S (2) P ~From r AD /k AD = 0 C C  S = K C P C C v (3) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

71. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~Substitute C C  S in (2) C B  S = K C K s P C C v (4) P ~Combining (1) and (4) (5) ~Where,K C is the cumene adsorption constant K s is the surface reaction equilibrium constant K P is the gas-phase equilibrium constant C t = C v + C C  S + C B  S ~Substituting for concentrations of the adsorbed species C B  S and C C  S ~Replacing C v in (5) and by multiplying the numerator and denominator by P P SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

72. Synthesis a rate law, mechanism and rate-limiting step (cont’d) ~To determine the dependence of the initial rate on partial pressure of cumene, set P Po =P Bo =0 to give; Initial partial pressure, P co Initial rate -r’ co Desorption limited reaction SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

73. Irreversible surface-reaction-limited rate laws ~Single sitesRate law A  S B  S ~Dual sites i) A  S+ S B  S + S ii) A  S+ B  S C  S + S ~Eley-Rideal A  S + B (g) C  S SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

74. Algorithm for determination of reaction mechanism & rate-limiting step ~Isomerization of n-pentene (N) to i-pentene (I) over alumina catalyst NINI Al 2 O 3 1) Select a mechanism (e.g. dual site) N + S N  S Adsorption N  S + S I  S + S Surface reaction I  S + S I + S Desorption (Treat each reaction step as an elementary reaction when writing rate laws) 2) Assume a rate-limiting step. Choose the surface reaction first since >75% of heterogeneous reactions that are not diffusion-limited are surface reaction-limited 3) Find the expression for concentration of the adsorbed species C I  S. Use the other steps that are not limiting to solve for C I  S (e.g. C N  S and C I  S ) SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

75. Algorithm for determination of reaction mechanism & rate-limiting step From r AD /k AD =0C N  S = P N K N C v From r D /k D =0C I  S = P I C v /K D = K I P I C v Al 2 O 3 4) Write a site balance C t = C v + C N  S + C I  S 5) Determine the rate law (combine steps 2,3 & 4) 6) Compare with data. If they agree, we have found the correct mechanism & rate-limiting step. It the rate law does not agree; a) Assume a different rate-limiting step, repeat 2  6 b) If none of the derived rate laws agree with the data, select a different mechanism (e.g. a single-site mechanism) N + S N  S N  S I  S I  S I + S SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

76. Algorithm for determination of reaction mechanism & rate-limiting step ~Proceed through step 2  6 ~The single-site mechanism turns out to be the correct one. For this mechanism, SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

77. Deriving a rate law using Pseudo Steady State Hypothesis (PSSH) ~Consider isomerization of n-pentene (N) to iso-pentene (I) N + S N  S N  S I  S I  S I + S k N k -N ksks k I k -I ~The rate law for the irreversible surface reaction is -r’ N = r s = k s C N  S ~The net rates of generation of N  S sites and I  S sites are r* N  S = k N P N C v – k -N C N  S – k s C N  S = 0 r* I  S = k s C N  S – k I C I  S + k -I P I C v = 0 ~Solving for C N  S and C I  S gives SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

78. Deriving a rate law using Pseudo Steady State Hypothesis (PSSH) ~Substituting for C N  S in the surface reaction rate law gives ~From a site balance, we obtain C t = C v + C N  S + C I  S ~After substituting for C N  S and C I  S, solving for C v, which we then substitute in the rate law SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

79. Deriving a rate law using Pseudo Steady State Hypothesis (PSSH) ~The adsorption constants are just the ratio of their respective rate constants K I =k I /k -I andK N =k N /k -N ~For surface reaction step as rate-limiting 1>>k s /k -N ~The rate law becomes k SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 337/3 REACTOR DESIGN AND ANALYSIS

80. SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS