Spark Ignition Engine Combustion
MAK652E
Chemical Kinetics of HC Combustion
Prof.Dr. Cem Soruşbay
Istanbul Technical University
Chemical Kinetics of HC Combustion





Introduction
Elementary reactions
Multi-step Mechanisms
Oxidation of Hydrocarbons
Oxidation of Carbon Monoxide
1
Introduction
The study of the elementary reactions and their rates is a
specialized field of physical chemistry called chemical kinetics
Overall reaction of a mole of fuel with a mole of an oxidizer to form b
moles of products can be expressed by global (overall) reaction
mechanism – has no physical relevance
F + a Oxidizer → b Products
From experimental measurements the rate at which fuel is consumed can
be expressed as,
d[ X F ]
n
m
 kG (T ) X Fuel  X Oxidizer 
dt
where [Xi] is the molar concentration [kmol/m3] in SI, [gmol/cm3] in CGS
kG is global rate coefficient – strong function of temperature
n and m are related to reaction order
Introduction
In real applications many sequential processes can occur involving
many intermediate species
example
consider global reaction 2 H2 + O2 → 2 H2O
elementary reactions, show what happens in a molecular
level
H2 and O2 collide and react
H2 + O2 → HO2 + H
-do not yield water
H + O2 → OH + O
but form intermediate species
OH + H2 → H2O + H
HO2 , hydroperoxy radical
H + O2 + M → HO2 + M and a hydogen atom
Radicals (or free radicals) are reactive molecules or atoms that
have unpaired electrons
Collection of elementary reactions to describe overall reaction is
called a reaction mechanism
2
Elementary Reactions
Unimolecular reaction – single species undergoing a
rearrangement (isomerization or decomposition)
A → B or
A→B+C
d [ A]
 kunimolec A
dt
For example, O2 → O + O
First order at high pressures,
at low pressures reaction rate also depends on concentration of
any molecule with which the reacting species may collide
d [ A]
 k A M 
dt
Elementary Reactions
Bimolecular reaction
A+B→C+D
d [ A]
 kbimolec A B
dt
3
Elementary Reactions
Trimolecular reaction – involve three reactant species and
correspond to reverse of unimolecular reaction at low pressures
A+B+M→C+M
example, recombination reactions such as H + H + M → H2 + M
Third order reactions
d [ A]
 kter A B M 
dt
M is called “third body” representing any molecule present in the
system and it removes some energy released by formation of new
chemical bond, preventing the product from immediate
dissociation
Elementary Reaction Rates
reaction rate,

d [ A]  no of collisions A and B molecules  probability that
kmol of A


.a collision leads to reaction . no of molecules of A 
dt
unit volume . unit time




Second term on rhs, can be expressed as a product of two factors
energy factor , exp[-EA / RuT] – which expresses fraction of
collisions that occur with an energy above the treshold level
necessary for reaction EA (activation energy)
a geometrical (steric) factor, p, that takes into account the
geometry of collisions between A and B
4
Elementary Reaction Rates
If the temperature range of interest is not too large, bimolecular rate
coefficient can be expressed by empirical Arrhenius form,
 E 
k (T )  A exp   A 
 RuT 
Here
A is a constant called pre-exponential factor or
frequency factor, giving collision probability without
effect of concentrations (depends on T1/2 )
E is activation energy , energy that the molecule
must acquire before it can take part in the reaction
three-parameter functional form,
 E 
k (T )  AT b exp   A 
 RuT 
Multi-step Mechanisms
The reaction mechanism - sequence of elementary reactions that
lead from reactants to products
For example H2 – O2 reaction mechanism
H2 + O2  HO2 + H
H + O2  OH + O
OH + H2  H2O + H
H + O2 + M  HO2 + M
kf , forward and kb , backward (reverse) rate coefficients
5
Multi-step Mechanisms
For example the net rate of production of O2 is the sum of all
individual elementary rates producing and destroying O 2
d [O2 ]
 kr1[ HO2 ][ H ]  kr 2 [OH ][O ]  kr 4 [ HO2 ][ M ] 
dt
 k f 1[ H 2 ][O2 ]  k f 2 [ H ][O2 ]  k f 4 [ H ][O2 ][ M ]
and for H atoms,
d[ H ]
 k f 1[ H 2 ][O2 ]  k r 2 [OH ][O]  k f 3[OH ][ H 2 ] 
dt
 k r 4 [ HO2 ][ M ]  k r1[ HO2 ][ H ]  k f 2 [ H ][O2 ]
 k r 3[ H 2O][ H ]  k f 4 [ H ][O2 ][ M ]
H2 + O2  HO2 + H
H + O2  OH + O
OH + H2  H2O + H
H + O2 + M  HO2 + M
Multi-step Mechanisms
Similar expressions can be written for each species in the
mechanism which yields a system of first-order O.D.E.
describing evolution of the chemical system starting from
initial conditions,
with
d [ X i ](t )
 fi  [ X 1 ](t )  [ X 2 ](t )  ....  [ X n ](t )
dt

[ X i ](0)  [ X i ]0
The above set of eqns (together with conservation eqns for mass,
momentum, energy and state eqns) can be integrated numerically
using a computer.
6
Multi-step Mechanisms
Stiff system equations – one or more variables change rapidly while
others change very slowly
time scales of radical reactions (very fast) are much
different than reactions involving stable species
Reduction of chemical reactions
assumed steady state reactions expressed in form of
algebraic equations instead of time dependent
Steady-State Approximations
Highly reactive intermediate species (radicals) are formed in
many chemical systems of interest to combustion
These can be simplified by appliying steady-state
approximation to reactive intermediate species, radicals
After rapid initial buildup in concentration, radicals are destroyed as
rapid as they are formed – then forming the intermediate species is
slow, destroying them is with fast reactions
- as a result their concentrations are small
Zeldovich mechanism is a good example
7
Steady-State Approximations
Consider Zeldovich mechanism,
O + N2
N + O2
(k1)
(k2)
→ NO + N slow, hence rate limiting
→ NO + O extremely fast
hence net production of N atoms,
d[ N ]
 k1 [O][ N 2 ]  k2 ] [N][O2 ]
dt
This approaches zero, and
[ N ]StedyState 
0  k1[O][ N 2 ]  k2 [ N ]StedyState[O2 ]
k1[O][ N 2 ]
k2 [O2 ]
Steady-State Approximations
Time rate of change of [N]ss can be obtained by differentiating the
above eqn (as it rapidly adjusts),
d [ N ]StedyState
dt

d  k1[O][ N 2 ] 


dt  k2 [O2 ] 
8
Temperature Dependence of Rate Coefficients
Rate coefficients depend strongly on temperature
in a nonlineer way
Arrhenius law
 E 
k (T )  AT b exp   A 
 RuT 
Pressure Dependence of Rate Coefficients
Consider a three-step mechanism,
A + M ka → A* + M
A* + M –ka → A + M
A* ku → P
Products
activation
deactivation
unimolecular reaction
Energy is added to the molecule by collision with other molecules M
for the excitation of molecular vibrations.
Then excited molecule may decompose into Products or it can
deactivate through a collision
Lindemann mechanism
9
Lindemann Mechanism
d[P]/dt = ku[A*]
d[A*]/dt = ka[A][M] - k-a[A*][M] - ku[A*]
where A* is high internal energy (energised) molecule
assuming concentration of A* is in steady state, d[A*]/dt = 0
[A*] = ka[A][M] / k-a[M] + ku
d[P]/dt = ku ka[A][M] / k-a[M] + ku
Lindemann Mechanism
In low pressure range concentration of collision partner M is small,
ka[M] << ku
d[P]/dt = ka[A] [M]
reaction is proportional to concentration of A and M
because activation is slow at low pressures (rate limiting)
In high pressure range M has large concentration,
k-a[M] >> ku
d[P]/dt = ku ka[A] / k-a = k [A]
Reaction rate does not depend on concentration of M (high
collision), decomposition of activated molecule A* is rate-limiting
10
Reaction Mechanisms
Chain Reactions
involve production of a radical species that subsequently
react to produce another radical.
This radical in turn reacts to produce another radical
It continues until formation of a stable species from two
radicals break the chain
example
A2 + B2  2 AB global reaction
chain initiating reaction
chain propagating reactions
chain terminating reaction
A2 + M (k1)  A + A + M
A + B2 (k2)  AB + B
B + A2 (k3)  AB + A
A + B + M (k4)  AB + M
Reaction Mechanisms
In early stages conc of product AB is small, A and B are also small
thus reverse reaction can be neglected
d[A2]/dt = -k1[A2][M] – k3[A2][B]
d[B2]/dt = -k2[B2][A]
d[AB]/dt = k2[A] [B2] + k3[B][A2] + k4[A][B][M]
A2 + M (k1)  A + A + M
A + B2 (k2)  AB + B
B + A2 (k3)  AB + A
A + B + M (k4)  AB + M
For radicals A and B , steady state approximation
2k1[A2][M] – k2[A][B2] + k3[B][A2] - k4[A][B][M] = 0
k2[A] [B2] - k3[B][A2] - k4[A][B][M] = 0
[A] and [B] obtained from ss
d[A2]/dt , d[B2]/dt , d[AB]/dt calculated from initial concentrations
11
Reaction Mechanisms
Chain-branching Reactions
involve formation of two radical species from a reaction
that consumes only one reaction.
Example
O + H2O → OH + OH
Concentration of radical species build up rapidly – rapid formation
of products
The rate of chain initiation step does not control overall reaction
rate – rates of radical reactions dominate.
Chain branching reactions are responsible for a flame being
self-propagating
H + O2 → O + OH a very important reaction – laminar
flame speeds are critically dependent on the rate of this reaction
Reaction Mechanisms
Chain-propagating Reactions
have same number of radicals on both the reactant side
and the product side
OH + H2 → H + H2O
Chain-termination (Chain-breaking) Reactions
consume radicals
H + OH + M → H2O
have normally no temperature dependence, which is
reflected in zero value of activation energy
12
Hydrocarbons
Low temperature mechanism
There is clear distinction between types of reactions that
dominate overall combustion process as temperature rise from 850
K to beyond 1200 K
Much of low temp chemistry of HCs is governed by size and
structure of carbon backbone.
It is generally accepted that initial attack on saturated HCs involve
abstraction of hydrogen atom to give alkyl radical and
hydroperoxy radical
CnH2n+2 + O2 → CnH2n+1 + HO2
Hydrocarbons
In methane,
CH4 + O2 → CH3 + HO2
HO2 radical may attack methane
CH4 + HO2 → CH3 + H2O2
or undergo a radical recombination reaction such as
HO2 + HO2 → H2O2 + O2
or
CH3O2 + HO2 → CH3OOH + O2
The methyl radical CH3 plays important role in overall process
CH3 + O2 + M ↔ CH3O2 + M
13
Hydrocarbons
High temperature mechanism
Free radical chain initiation processes are not normally
predominant in control of events
Consider the possibilities,
CnH2n+2 + O2 → CnH2n+1 + HO2 , kI = 1014 exp{-2500/T}
oxidation of fuel by hydrogen abstraction may yield a hydroperoxy
radical (HO2) and an alkyl radical (CnH2n+1) in which carbon backbone
of the alkane remains intact
CnH2n+2 → CjH2j+1 + CmH2m+1 ,
kII = 5x1016 exp{-4200/T}
By contrast unimolecular decomposition of fuel may yield two new alkyl
radicals as a result carbon backbone of the alkyl is severed
Hydrocarbons
Temperature has greatest effect on which reaction will dominate, but
oxygen concentration is also important
oxidation route predominate at temperatures below 1000 K
and carbon backbone structure of fuel remain intact
14
Engine Fuels - Classification
Liquid hydrocarbons
Cn H m
Engine fuels are mainly mixtures of hydrocarbons, with bonds between
carbon atoms and between hydrogen and carbon atoms.
During combustion these bonds are broken and new bonds are
formed with oxygen atoms, accompanied by the release of chemical
energy. Principal products are carbon dioxide and water vapour.
Fuels also contain small amounts of
O2 , N 2 , S , H 2O
Alkanes
Alkanes or Paraffins can in general be represented by Cn H 2 n  2
all the carbon bonds are single bonds – they are “saturated”
high number of H atoms, high heat content and low density
(620 – 770 kg/m3)
The carbon atoms can be arranged as a straight chain or as branched
chain compounds.
15
Alkanes
Straight chain group (normal paraffins)
shorter the chain, stronger the bond
not suitable for SI engines – high tendancy for autoignition
according to the value of “n” in the formula, they are in gaseous
(1 to 4), liquid (5 to 15) or solid (>16) state.
Branched chain compounds (isoparaffins)
when four or more C atoms are in a chain molecule it is possible to form
isomers – they have the same chemical formula but different
structures, which often leads to very different chemical properties.
example : iso-octane
C8 H18
2. 2 .4 trimethyl pentane
Naphthenes
Also called cycloparaffins
Cn H 2 n
saturated hydrocarbons which are arranged in a circle
have stable structure and low tendancy to autoignite compared to
alkanes (normal paraffins)
can be used both in SI-engines and CI-engines
low heat content and high density (740 – 790 kg / m3)
16
Alkenes
Also called olefins
mono-olefins
Cn H 2 n
or dio-olefins Cn H 2 n 2
have the same C-to-H ratio and the same general formula as
naphthenes, their behavior and characteristics are entirely different
they are straight or branch chain compounds with one or more
double bond. The position of the double bond is indicated by the
number of first C atom to which it is attached, ie,
CH2=CH.CH2.CH2.CH3
called pentene-1
CH3.CH=CH3
called butene-2
olefinic compounds are easily oxidized, have poor oxidation stability
can be used in SI-engines, obtained by cracking of large molecules
low heat content and density in the range 620 – 820 kg / m3
Aromatics
Aromatic hydrocarbons are so called because of their “aromatic” odor
Cn H 2 n6
they are based on a six-membered ring having three conjugated
double bonds
aromatic rings can be fused together to give polynuclear aromatics,
PAN, also called polycyclic aromatic hydrocarbons, PAH
simplest member is benzene
C6 H 6
can be used in SI-engines, to increase the resistance to knock
not suitable for CI-engines due to low cetene number
low heat content and high density in the range 800 – 850 kg / m3
17
Aliphatic Hydrocarbons
Alicyclic and Aromatic Hydrocarbons
18
Oxygenic Hydrocarbons
Composition of Engine Fuels
19
Typical Boiling Curves for Gasoline and Diesel
Octane Numbers
Properties of Engine Fuels
20
Hydrocarbon Oxidation Process
Diagram of Hydrocarbon Oxidation Process
21
Diagram of Hydrocarbon Oxidation Process
Reaction diagram of alkanes both at low and high T :
h abstraction from HC molecule
Low Temp :
R’OOH formed
will break down to smaller HC by oxidation and
dehydration
important in engine combustion
Diagram of Hydrocarbon Oxidation Process
High Temp :
one alkane and alkyl radical formed
from larger alkyl radical
- produced by H abstraction
22
Hydrocarbon Oxidation Process
To estimate T and
concentration at flame
front - partial
equilibrium assumption
due to high T
Mechanism of Alkane Oxidation
High temperature combustion of methane and ethane
main propagating free radicals are H, O, OH, HO2, CH3
Key features are,
*Mechanism of two step primary fuels are linked at interplay
between CH3 and C2H5 or C2H4
*Formaldehyde, CH2O and formyl radicals, CHO are the main partially
oxygenated products of C1 and C2 hydrocarbon fragments
Decomposition of CHO can be source of H by
CHO + M → CO + H + M
But competitive oxidation also a major source of HO2 at all temps
CHO + O2 → CO + HO2
*Carbon monoxide, CO is end product of virtually all chain
sequences
23
Oxidation of Carbon Monoxide
From practical point of view it is difficult to free CO from all traces of
hydrogenous material
there are often traces of CH4 in CO (in ppm)
Oxidation of hydrogen or methane involve OH and HO 2 radicals, thus if
small quantities of H2 or CH4 present, chain propagation and branching
in CO oxidation is promoted by,
CO + HO2 → CO2 + OH
propagation
CO + OH → CO2 + H
propagation
followed by
H + O2 → OH + O
branching
or
H + O2 + M → HO2 + M
propagation
followed by
CO + O + M → CO2 + M
termination
Also supplementary branching step,
O + CH4 → CH3 + OH
Oxidation of Higher Paraffins
CnH2n+2 , higher paraffins n > 2
Oxidation of paraffins can be characterized by three sequential processes
*Fuel molecule attacked by O and H atoms, breaks down primarily
forming olefins and hydrogen
hydrogen oxidizes to water, if oxygen is available
*Unsturated olefins further oxidize to CO and H2
essentially all of H2 is converted to water
*CO burns out by
CO + OH → CO2 + H
nearly all heat release associated with overall combustion process occurs
in this step
24
Reaction Kinetics in Engine Simulation
Reaction Rate Parameters
Westbrook and Dryer
25
Consumption Times for an iso-octane/air System
Constant global
consumption times
for iso-octane/air
system as a function
of pressure and
temperature constant pressure
and temperature
calculations
Normalized Fuel and Total HC Mass Profiles
1450 K, atmospheric pressure in an iso-octane/air system; 1000 ppm isooctane, 9% CO2, 14% H2O, 4.5% CO, 2% H2, 1% O2
26