Reaction Kinetics Mechanical Engineer ing.pptx

Reaction Kinetics1P1

1. Fundamentals of Reaction Kinetics Part One

2. 1. Overview T hermodynamics provides steady state i nformation of the combustion process, chemical kinetics describes the transient states of the system . Chemical kinetics is the science of chemical reaction rates. It describes the rate at which species are consumed and produced, and the rate at which the heat of reaction is released.

3. 1. Overview (cont.) Combustion chemistry has two important characteristics; reaction rates are highly sensitive to temperature , and a large amount of heat is released during a reaction . Heat transfer from products to reactants raises the reactant temperature so that the chemical reaction proceeds at a high rate. The rate at which fuel and oxidizer are consumed is of great importance to combustion engineering, as one needs to ensure sufficient time for chemical reactions when designing a combustion system.

4. 1. Overview (cont.) Reaction kinetics is the study of reaction rates How fast does a reaction proceed and what factors affecting it; A measure of the change of the concentration of a reactant (or a product) as a function of time. The study of rate yields information on the mechanism by which a reaction occurs at molecular level. K inetics also sheds light on the reaction mechanism (exactly how the reaction occurs).

5. 1. Overview (cont.) Reaction Rates may be: Initial Rates Rates measured at the beginning of the reaction, which is dependent on the initial concentrations of reactants. Instantaneous Rates Rates measured at any point during the reaction. Average Rates An overall rate measured over a period or time interval.

6. Reaction speed is measured by the change in concentration with time. Important factors which affect rates of reactions: reactant concentration temperature action of catalysts surface area pressure of gaseous reactants or products 1. Overview (cont.)

7. In many combustion processes, chemical reaction rates control the rate of combustion, In essentially all combustion processes, chemical rates determine pollutant formation and destruction. The study of the elementary reactions and their rates (chemical kinetics), is a specialized field of physical chemistry 1. Overview (cont.)

8. 1. Overview (cont.) When chemical kinetics is coupled with fluid dynamics and heat transfer , a combustion system can be characterized Another important area related to combustion chemistry is emissions, the formation of pollutants is controlled primarily by chemical kinetics. Pollutants are present in small amounts in the products, yet their impact on the environment and human health can be significant.

9. 2. Global Versus Elementary Reactions A chemical reaction may occur when two or more molecules or atoms approach one another. A reaction that takes place by such a collisional process is called an elementary reaction , which occurs due to collisions between specific molecules in the gas phase An overall or global reaction , is the end result of many elementary reactions The overall reaction of one mole of fuel with a moles of an oxidizer to form b moles of combustion products can be expressed by the global reaction mechanism

10. 2. Global Versus Elementary Reactions (cont.) Global reactions may be viewed as a result of many of these elementary processes. The assumption of a single rate for a one-step global reaction, to describe the structure of ignition and flame phenomena , can therefore not be justified on the basis of chemical kinetics . From a careful point of view, a reaction rate may only be attributed to elementary reactions .

11. 2. Global Versus Elementary Reactions (cont.) Global reaction represents a useful approximation in order to simplify the mathematical analysis . From experimental measurements , the rate at which the fuel is consumed can be expressed as: Where the notation [X i ] is used to denote the molar concentration ( kmol /s) of the ith species in the mixture

12. 2. Global Versus Elementary Reactions (cont.) The constant of proportionality, is called the global rate coefficient , and, in general, is not constant, but rather is a strong function of temperature. The minus sign indicates that the fuel concentration decreases with time. The exponent n and m relate to the reaction order .

13. 2. Global Versus Elementary Reactions (Cont.) The equation says that the reaction is n th order with respect to the fuel, m th order with respect to the oxidizer, and ( n+m ) th order overall For global reactions, n and m are not necessarily integers and arise from curve fitting of experimental data. The use of global reactions to express the chemistry in a specific problem is frequently a " black box" approach. Although this approach may be useful in solving some problems, it does not provide a basis for understanding what is actually happening chemically in a system.

14. 2. Global Versus Elementary Reactions (Cont.) The collection of elementary reactions that describe the overall, global reaction is referred to as a reaction or combustion mechanism. Depending on the amount of detail , a combustion mechanism can consist of only a couple of steps , or thousands of elementary reactions. For instance, a detailed hydrogen-oxygen combustion mechanism contains about 9 species and 21 elementary reaction steps. For hydrocarbon fuels, due to the large number of isomers and many possible intermediate species , the number of species and steps in a detailed mechanism can grow substantially with the size of the fuel molecule.

15. 2. Global Versus Elementary Reactions (Cont.) For CH4/air combustion, the chemical kinetics can be reasonably described by 53 species and 400 steps A recent detailed mechanism for isooctane contains 860 species and 3,606 steps . Computing of chemical kinetics with such a large mechanism requires a significant amount of computer resources even for one-dimensional flames . In general, there are four main types of elementary reactions that are important in combustion : chain initiation , chain branching , chain terminating or recombination , and chain propagating .

16. 2. Global Versus Elementary Reactions (Cont.) Chain Initiation : the initiation of the combustion reaction is through reactions such as where M is a third body with enough energy to break the H2 or O2 bonds. Chain Branching : chain branching reactions, such as

17. 2. Global Versus Elementary Reactions (Cont.) The equations produce two radicals on the product side (OH and O in the first equation , H and OH in second equation, and consume one on the reactant side (H in first equation and O in the second equation ). The net gain of one radical is significant because these reactions increase the pool of radicals rapidly, leading to the explosive nature of combustion. For instance, ten collisions would increase the radical population by about 1,000 times. Because the number of collisions among molecules at standard conditions is of the order of 10 to the power 9/s , the number of radicals can grow enormously in a short period of time.

18. 2. Global Versus Elementary Reactions (Cont.) Chain Propagating : Chain propagating steps are reactions involving radicals where the total number of radicals remains unchanged. Different radicals can appear on both the reactant and product sides, but the total number of radicals in the reactant and product sides stays the same. For instance, the reaction step consumes 1 mol of OH radicals and produces 1 mol of H radicals so that the net change in the number of radicals is zero. This reaction is still very important, as it produces most of the H 2 O formed in hydrogen-oxygen combustion .

19. 2. Global Versus Elementary Reactions (Cont.) Chain Terminating, or Recombination When sufficient radicals or third bodies are present, radicals can react among themselves to recombine or react to form stable species . Recombination steps (also called termination steps) are depicted by and they decrease the radical pool by half.

20. 2. Global Versus Elementary Reactions (Cont’d) In reality, many sequential processes can occur involving many intermediate species . For example, consider the global reaction. To represent this global conversion, the following elementary reactions , are important ( more than 20 elementary reactions can be considered). .

21. 3. Reaction Rate Law of mass action “ The rate of a chemical reaction is proportional to the concentration of reacting species .” For the reaction a A +b B . ----- l L + m M The rate of reaction will be :- -d [A]/d t = -(a/b)*(d [B]/d t) = (a /l)*(d[L]/d t) =(a /m )*(d [M]/d t) The elementary (one step) reaction may be: uni -molecular, bimolecular, or tri-molecular

22. 3.1. Unimolecular Elementary Reactions As the name suggests, unimolecular reactions involve a single species undergoing a rearrangement (isomerization or decomposition) to form one or two product species), i.e., or Examples of unimolecular reactions include the typical dissociation reactions important to combustion:

23. 3.1. Unimolecular Reactions (Cont.) Unimolecular reactions are first order at high pressures: while at low pressures , the reaction rate also depends on the concentration of any molecules, M , with which the reacting species may collide , in this case:

24. 3.2. Bimolecular Reactions and Collision Theory Most elementary reactions of interest in combustion are bimolecular ; that is, two molecules collide and react to form two different molecules. For an arbitrary bimolecular reaction, this is expressed as The rate at which the reaction proceeds is directly proportional to the concentrations of the two reactant species, i.e.,

25. 3.2. Bimolecular Reactions and Collision Theory (Cont.) All elementary bimolecular reactions are overall second order , being first order with respect to each of the reacting species. The rate coefficient, again is a function of temperature, but unlike the global rate coefficient, this rate coefficient has a theoretical basis. If the temperature range of interest is not too great, the bimolecular rate coefficient can be expressed by the empirical Arrhenius form , A is a constant ( pre-exponential factor or frequency factor)

26. 3,3. Trimolocular Reactions Trimolecular reactions involve three reacting species The general form of a trimolecular reaction is Recombination reactions such as and are important examples of trimolecular reactions in combustion.

27. 3.3. Trimolocular Reactions (Cont.) Trimolecular reactions are third order , and their rates can be expressed as where , again, M may be any molecule and is frequently referred to as a third body . When A and B are the same species , as in H + H + M , a factor of two must multiply the right-hand-side of equation since two of species A molecules disappear to form C.

28. 4. Net Production Rates In the previous sections, we introduced the idea of a sequence of elementary reactions that leads from reactants to products, which we termed the reaction mechanism. Knowing how to express the rates of elementary reactions, we can now mathematically express the net rates of production or destruction for any species participating in a series of elementary steps. For example, let us return to the H2-O2 reaction mechanism, which is incompletely given by the previous 4 equations and include both forward and reverse reactions as indicated by the symbol :

29. 4. Net Production Rates (cont’d) are the elementary forward and reverse rate coefficients, respectively, for the i th reaction.

30. 4. Net Production Rates (cont’d) The net rate of production of O2 , for example, is the sum of all of the individual elementary rates producing O2 minus the sum of all of the rates destroying O2 ; i.e.,

31. 4. Net Production Rates (cont’d) And for H atoms ,

32. 4. Net Production Rates (cont’d) We can write similar expressions for each species participating in the mechanism, which yields a system of first-order ordinary differential equations that describes the evolution of the chemical system starting from given initial conditions. This set of equations couples with any necessary statements of conservation of mass, momentum, or energy, and state equations , which can be integrated numerically using a computer.

33. 4. Net Production Rates (Cont.) Packaged routines, efficiently integrate the stiff system of equations that arise in chemical systems. A set of equations is considered stiff when one or more variables change very rapidly, while others change very slowly. This disparity in time scales is common in chemical systems where radical reactions are very fast compared with reactions involving stable species.

34. . Any Questions ?? Prof. Dr. Mahmoud Elkady