chemical kinetics - what chemical reactions occurs in a chemical process, i.e. reaction mechanisms...
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X.S. Bai Chemical Kinetics
Lecture 3
Chemical Kinetics
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X.S. Bai Chemical Kinetics
• A swirling stabilized flame
Chemical kinetics plays important role in flame zone
Fuel
air
air
Flame zone: chemistry rules
Post flame zone: close to chemical
equilibrium
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X.S. Bai Chemical Kinetics
What does chemical kinetics do?
• Chemical kinetics deals with – how fast chemical reactions proceed, i.e. reaction
rates – what chemical reactions occurs in a chemical
process, i.e. reaction mechanisms
• Chemical kinetics is the key to understand – how does a flame propagate – why a flame can be quenched ...
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X.S. Bai Chemical Kinetics
• Elementary reactions – law of mass action – Arrhenius expression
• Reaction mechanisms – detailed mechanism – reduced mechanism – global mechanism
• H2-O2 explosion, NOX formation
Outline
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X.S. Bai Chemical Kinetics
Elementary reactions
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X.S. Bai Chemical Kinetics
Detailed reaction mechanisms (1)
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X.S. Bai Chemical Kinetics
Detailed reaction mechanisms (2) H2+O2 mechanism
Chain initiating
Chain branching
Chain propagating
Chain terminating
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X.S. Bai Chemical Kinetics
Elementary reaction (1)
• Definition – the actual reaction among individual atoms and/or
molecules • Types of elementary reactions
– uni-molecular reaction (thermal dissociation) – bi-molecular reaction (most of reactions of this
type) – ter-molecular reaction (recombination reactions)
• Physical interpretation of elementary reaction – Collision theory – Activated complex theory – ...
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X.S. Bai Chemical Kinetics
Elementary reaction (2) Physical interpretation of bimolecular and termolecular reactions (collision theory)
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X.S. Bai Chemical Kinetics
Elementary reaction (3)
• Physical interpretation of unimolecular reaction (activated complex theory)
A+M A*+M
A+M A*+M
A* Products
M = third body = any molecules
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X.S. Bai Chemical Kinetics
Elementary reaction (4)
• Physical interpretation of effect of temperature on elementary reactions (collision theory)
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X.S. Bai Chemical Kinetics
Elementary reaction (5)
• Physical interpretation of effect of catalysis on elementary reactions (collision theory)
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reactions (1)
• Law of mass action
H+O2 OH+O
2
2 )(3 OHfO CCTkdtdC
−=
Rate coef. Change rate of molar concen.
Reaction order
• Overall order: 2 • radicals: molecules/atoms
with unpaired electrons • how reaction really proceed?
Radicals O, OH Radical H
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reaction (2)
• Bimolecular reaction
H+O2 OH+O
)/exp()(,)( 33 2
2 TREATTkCCTkdtdC
uAb
fOHfO
−=−=
Frequency factor
Activation energy • Arrhenius form often used;
experimental data is used to find model constants A, EA, b • collision theory for rate coef. • Second overall order
Arrhenius expression
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reaction (3)
• Unimolecular reaction
• Termolecular reaction
O2 O + O
Recombination of radical H
Third body
• third body M carry away energy formed
Oxygen dissociation
at high p
2
2 )( OuniO CTkdtdC
−=
M + H2 H + H + M 2( )H
ter M HdC k T C Cdt
= -‐
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reaction (5)
• Effect of pressure on reactions rate
– at high pressures termolecular reactions become more important than bimolecular reactions and unimolecular reactions
nnnnnn ppkYkYkCdtdC
∝∝∝∝ ρ
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reaction (6)
• How to obtain rate coefficients? – Theoretical calculations (difficult) – experiments (mostly used approach) – if the forward reaction rate is known, one can use equilibrium
constants to calculate the backward reaction, and vice versa.
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reaction (7)
• Units used in reaction rate calculation
nkCdtdC
∝
scmmole 1
3n
cmmole
⎟⎟⎠
⎞⎜⎜⎝
⎛3
scmmole n 11
3
−
⎟⎟⎠
⎞⎜⎜⎝
⎛
?
Kinetic data are often given in engineering unit - cm, mole, s, etc. (Turns book Table 5.3). If you change C to SI unit, do not forget to change k to SI unit as well. Remember k’s unit is different for different reactions. Recommendation: use cm, mole, s … unit first to calculate the rate, then translate to SI unit
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X.S. Bai Chemical Kinetics
Reaction Mechanisms
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X.S. Bai Chemical Kinetics
Reaction mechanisms
• Global reaction mechanism models – a combustion process using one, two or a few steps, for
example one step reaction
• Detailed reaction mechanism consists of – hundreds elementary reactions, for example methane
oxidation mechanism listed in Turns book
• Reduced mechanism simplifies detailed reaction mechanism by reducing the number of elementary reactions
2H2O 2H2+O2
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X.S. Bai Chemical Kinetics
Detailed reaction mechanisms (2) H2+O2 mechanism
Chain initiating
Chain branching
Chain propagating
Chain terminating
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X.S. Bai Chemical Kinetics
Detailed reaction mechanism (3) - H2+O2
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X.S. Bai Chemical Kinetics
Reaction rate for Elementary reaction (4)
• For a detailed reaction mechanism
• reaction rates for species i
Backward rate
LjMM i
N
iiji
N
iij ,...,1
1
''
1
' =⇔∑∑==
νν
( )
∏ ∏
∑
= =
=
−=
−=≡
N
i
N
iijbijfj
j
L
jijij
ii
ijij CkCkq
qdtdC
1 1
1
'''
''' νν
ννω
forward rate
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X.S. Bai Chemical Kinetics
An example: H2-O2 explosion a chemical explanation
• heterogeneous reaction: – Radicals + Wall products (I)
• chain initiating – H2 + M H+H+M (II)
• chain branching and propagating – H+O2 O+OH (III)
• chain terminating – H+O2+M HO2+M (IV)
• chain branching – HO2 + H OH+OH (V)
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X.S. Bai Chemical Kinetics
H2-O2 explosion diagram (a sketch)
pressure
Tu 500 C 550 C 400 C
1 atm
No explosion
explosion
I dominant
III dominant
IV dominant
V dominant
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X.S. Bai Chemical Kinetics
Example 2: CO-O2 reaction effect of humidity
• CO + O2 CO2 + O (I) • O + H2O OH + OH (II) • CO + OH CO2 + H (III) • H + O2 OH + O (IV)
– (I) slow – (III) much faster – (IV) key reaction even for moisture CO combustion!!!
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X.S. Bai Chemical Kinetics
CH4-O2 reaction path
CH4 O2
CH3 + H H
OH + O CH2O + H
H2 + CH3 O
H2 + CH2O
OH
CHO + H2
H
OH + H
O
CO + H2 H
CO2 + H
H2O + H
OH
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X.S. Bai Chemical Kinetics
CH4-O2 reaction mechanism
• CH4 + M CH3 + H + M • CH4 + H CH3 + H2 • CH3 + O CH2O + H • CH3 + OH CH2O + H2 • CH2O + H HCO + H2 • HCO + H CO + H2 • CO + OH CO2 + H2 (CO mechanism) • H2 mechanism
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X.S. Bai Chemical Kinetics
CnH2n-O2 reaction mechanism (n>1)
• H abstract • beta-scission rule • high C break down • to HCO • to CO • to CO2
C-C bond weaker than C-H bond: C-C 85 kcal/bond; C-H 98 kcal/bond
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X.S. Bai Chemical Kinetics
Thermal NO mechanism
O2 N2
NO + N
NO
OH NO + O
O
T (K) NO formation rate 500 3.50e-45 1000 2.00e-15 1500 1.50e-5 2000 1.34 2050 3.06 2100 6.74 2150 14.35 2200 29.45
28
1/ 2 16 1/ 226
690902 6 10 expNOk k K TT
− ⎛ ⎞≡ = × −⎜ ⎟
⎝ ⎠
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X.S. Bai Chemical Kinetics
Fuel NOx formation mechanism
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X.S. Bai Chemical Kinetics
Reduced reaction mechanism
• How to simplify a detailed reaction mechanism? – Some reactions proceed faster than others. If both the forward and
backward reactions are fast, one can assume this reaction is in partial equilibrium
– Some species are in lower concentrations than others. If the net formation and destruction rate of this species are small, one may assume this species is in steady states.
– ILDM (intrinsic low dimensional manifold) – Experimental approach
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X.S. Bai Chemical Kinetics
Reaction rate for Global reaction mechanism (1)
• hydrogen and oxygen reaction
2H2+O2 2H2O
nO
mH
O CCTkdtdC
222 )(−=
Rate coef. Change rate of mole concen.
Reaction order
• Overall order: m+n • m, n can be non-integers • how reaction really proceed?
[ ] [ ] iii XXiC ρ=≡≡
Mole concen. of i
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X.S. Bai Chemical Kinetics
Reaction rate for Global reaction mechanism (2)
• How to determine rate coefficients and m, n? – rate coefficients, m, n are obtained from curve-
fitting with experimental data • Advantages
– simple to use • disadvantages
– not directly related to the fundamental reaction process
– rate coefficients, m, n only valid for short range of temperature and equivalence ratio
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X.S. Bai Chemical Kinetics
Thermal explosion (thermal runaway)
One step global reaction
First order reaction
K. Seshadri, UCSD
http://nccrd.in/iciwsindia2015
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X.S. Bai Chemical Kinetics
Thermal explosion (thermal runaway)
Heat loss to wall
Change of fuel mass Chemical reaction rate
Change of Sensible energy
Heat release rate
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X.S. Bai Chemical Kinetics
Thermal explosion (thermal runaway)
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X.S. Bai Chemical Kinetics
Thermal explosion (thermal runaway)
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X.S. Bai Chemical Kinetics
Thermal explosion (thermal runaway)
• Critical condition for thermal runaway
= 0
! !1 ! ! 0
! exp(" ) ="
0
1
2
3
4
5
6
7
8
0 0.5 1 1.5 2 2.5 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5
! =1/ eexp(! )
! !
! =" / exp(" )
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X.S. Bai Chemical Kinetics
Thermal explosion (thermal runaway)
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X.S. Bai Chemical Kinetics
Hydrogen/air auto-ignition
Initial temperature
Ignition delay time H2 + M = H + H + M
Low T0
High T0
thermal runaway and radical runaway
Induction period
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X.S. Bai Chemical Kinetics
Hydrogen/air auto-ignition
Ignition delay time of H2/air mixture
rpm CAD time 1000 30 5 ms 2000 30 2.5 ms 3000 30 1.25 ms
Combustion duration
From Fan Zhang, Yajing Wu
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X.S. Bai Chemical Kinetics
n-heptane-air auto-igntion
From N. Peters, 15 lectures, 1992