1. SABIC Chair in Catalysis at KAU Chemical Reaction Engineering Dr. Yahia Alhamed

2. SABIC Chair in Catalysis at KAU What is reaction rate? It is the rate at which a species looses its chemical identity per unit volume. The rate of a reaction can be expressed as:- - The rate of disappearance of a reactant or - The rate of appearance of a product. Kinetics and Reaction Rate

3. SABIC Chair in Catalysis at KAU Reaction Rate Consider species A: -r A = the rate of formation of species A per unit volume r B = the rate of formation of species B per unit volume EXAMPLE: If B is being formed at 0.2 moles per decimeter cubed per second, ie, r B = 0.2 mole/dm 3 /s Then A is disappearing at the same rate: -r A = 0.2 mole/dm 3 /s The rate of formation (generation of A) is rA= -0.2 mole/dm3/s

4. SABIC Chair in Catalysis at KAU Reaction Rate Consider species j: r j is the rate of formation of species j per unit volume [e.g. mol/dm 3 *s] r j is a function of concentration, temperature, pressure, and the type of catalyst (if any) r j is independent of the type of reaction system (batch, plug flow, etc.) r j is an algebraic equation, not a differential equation

5. SABIC Chair in Catalysis at KAU Rate Law Basics A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration.

6. SABIC Chair in Catalysis at KAU Reaction Rate for solid catalytic reactions For a catalytic reaction, we refer to -r A ', which is the rate of disappearance of species A on a per mass of catalyst basis. -r ' A = r A /bulk density of the catalyst (ρb)

7. SABIC Chair in Catalysis at KAU Rate Law Basics A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration. Power Law Model k is the specific reaction rate (constant) k is given by the Arrhenius Equation: Where:E = activation energy (cal/mol) –R = gas constant (cal/mol*K) –T = temperature (K) –A = frequency factor (units of A, and k, depend on overall reaction order)

8. SABIC Chair in Catalysis at KAU General Mole Balance

9. SABIC Chair in Catalysis at KAU Batch Reactor Mole Balance

10. SABIC Chair in Catalysis at KAU Constantly Stirred Tank Reactor Mole Balance CSTR or MFR

11. SABIC Chair in Catalysis at KAU Plug Flow Reactor (PFR) Mole Balance The integral form is : This is the volume necessary to reduce the entering molar flow rate (mol/s) from F A0 to the exit molar flow rate of F A.

12. SABIC Chair in Catalysis at KAU Packed Bed Reactor Mole Balance PBR The integral form to find the catalyst weight is:

13. SABIC Chair in Catalysis at KAU Space time and space velocity  F A0 = C Ao v o  θ = is called space time (s) = V/v o  Space velocity = 1/θ, where;  F A0 = Molar feed rate of key reactant A (mol/s)  C Ao = Concentration of key reactant A in the feed (mol/m 3 )  v o =Volumetric flow rate of feed to the reactor (m 3 /s)  V = volume of the reactor  For constant volume systems v = v o where v is volumetric flow rate leaving the reactor

14. SABIC Chair in Catalysis at KAU Reactor Mole Balance Summary

15. SABIC Chair in Catalysis at KAU Reactor Mole Balance Summary

16. SABIC Chair in Catalysis at KAU Reactor Mole Balance Summary

17. SABIC Chair in Catalysis at KAU Reactor Mole Balance Summary

18. SABIC Chair in Catalysis at KAU Reactor Mole Balance Summary

19. SABIC Chair in Catalysis at KAU Conversion Consider the general reaction: aA + bB -  cC + dD We will choose A as bases of calculation (i.e. Key reactant) The limiting reactant is usually taken as the key reactant Then: A + (b/a)B  (c/a)C + (d/a)D X A = moles reacted/moles fed

20. SABIC Chair in Catalysis at KAU Batch Reactor Conversion

21. SABIC Chair in Catalysis at KAU CSTR Conversion Algebraic Form: There is no differential or integral form for a CSTR.

22. SABIC Chair in Catalysis at KAU PFR Conversion PFR Differential Form : Integral Form:

23. SABIC Chair in Catalysis at KAU Design Equations V

24. SABIC Chair in Catalysis at KAU Reactor Sizing (CSTR) Given -r A as a function of conversion, -r A =f(X), one can size any type of reactor. We do this by constructing a Levenspiel plot. Here we plot either as a function of X. volume of a CSTR is:

25. SABIC Chair in Catalysis at KAU Reactor Sizing (PFR) For PFR th evolume of the reactor needed is given by the area under the curve =area

26. SABIC Chair in Catalysis at KAU Summary

27. Rate Law Basics A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration. Power Law Model k is the specific reaction rate (constant)

28. SABIC Chair in Catalysis at KAU Examples of Rate Laws First Order Reactions (1) Homogeneous irreversible elementary gas phase reaction with

29. SABIC Chair in Catalysis at KAU First Order Reactions (1) Homogeneous irreversible elementary gas phase reaction with (2) Homogeneous reversible elementary reaction with and Examples of Rate Laws

30. SABIC Chair in Catalysis at KAU First Order Reactions (1) Homogeneous irreversible elementary gas phase reaction with (2) Homogeneous reversible elementary reaction with and Second Order Reactions (1) Homogeneous irreversible non-elementary reaction with and This is first order in ONCB, first order in ammonia and overall second order. Examples of Rate Laws At 188˚C

31. SABIC Chair in Catalysis at KAU Examples of Rate Laws with Second Order Reactions (2) Homogeneous irreversible elementary reaction

32. SABIC Chair in Catalysis at KAU Examples of Rate Laws with Second Order Reactions (2) Homogeneous irreversible elementary reaction This reaction is first order in CNBr, first order in CH 3 NH 2 and overall second order. (3) Heterogeneous catalytic reaction: The following reaction takes place over a solid catalyst: