Reaction Kinetics Mechanical Engineer ing.pptx

Fundamentals
of
Reaction Kinetics
Part One

1. Overview
 Thermodynamics provides steady state information 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.

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.

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.
 Kinetics also sheds light on the reaction mechanism
(exactly how the reaction occurs).

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.

 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.)

 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.)

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.

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

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.

 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 [Xi] is used to denote the molar
concentration (kmol/s) of the ith species in the mixture

 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.

2. Global Versus Elementary Reactions (Cont.)
 The equation says that the reaction is nth order with respect to
the fuel, mth 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.

 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.

 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.

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

 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.

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 H2O
formed in hydrogen-oxygen combustion.

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.

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).
.

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

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:

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:

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.,

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)

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.

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.

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:

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

 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.,

•
And for H atoms,

 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.

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.

.
Any Questions ??
Prof. Dr. Mahmoud Elkady

Reaction Kinetics Mechanical Engineer ing.pptx

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