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Terms and concepts
CO and CH4 oxidation kinetics
Elementary and global reactions
Modelling of kinetics – rate law, kinetic parameters
Irreversible, reversible, consecutive, competitive rxns
Chain reactions: Initiating, branching, propagating,
terminating
Equilibrium vs. kinetics
Example: CO oxidation
CO + ½O2 = CO2
T=1000 °C, p=1 bar
0
0.05
0.1
0.15
0.2
0 50 100 150 200
Mole
fra
ction (
-)
Time (s)
O2
CO2
CO
CO oxidation
CO + ½O2 = CO2
T=1000 °C, p=1 bar
0
0.05
0.1
0.15
0.2
0 50 100 150 200
Mole
fra
ction (
-)
Time (s)
O2
CO2
CO
Global reaction
CO + ½O2 = CO2
Elementary reactions
CO+O+M=CO2+M
CO+O2=CO2+O
O2 = 2 O
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03
Mole
fra
ction (
-)
Time (s)
O2
CO
CO2
O
CO oxidation
Global reaction
CO + ½O2 = CO2
Elementary reactions
CO+O+M=CO2+M
CO+O2=CO2+O
O2 = 2 O
Rate coefficient(classical definition)
The rate coefficient (k) of any reaction can be written in the Arrhenius
form, but the constants in such form have physical meaning only for
elementary reactions!
k = A· exp(-Ea/RT)
collision frequencye.g., A + B D + E
activation energy
Tn
Experiments with known concentrations and at different
temperatures
Plot concentration versus time at different temperatures
⇒ slope = k
Plot Arrhenius equation ( ln(k) versus 1/T):
⇒ Slope = -Ea/R
⇒ intercept = ln(A)
Experimental determination of rate coefficient
Rate coefficient
Ea also theoretically
Molecular orbital calculations
Transition state – Activated complex
Chemical Kinetics – Rate Law
CO + O2 → CO2 + O
Rate =k·[CO]1·[O2]1
k = A· exp(-Ea/RT)
A = 2.5·1012
n = 0
Ea = 4.77·104 (cal/mol)
Tn
-6.0E-08
-5.0E-08
-4.0E-08
-3.0E-08
-2.0E-08
-1.0E-08
-1.0E-23
1.0E-08
0 50 100 150 200
CO
Rate
Of
Pro
duction (
mole
/cm
3-s
)
Time (s)
GasRxn Total
CO+O+M=CO2+M
CO+O2=CO2+ORXN Total
r1 :CO+O+M=CO2+M
r2: CO+O2=CO2+O
CO oxidation
d[CO]/dt = 1·r1 + 1·r2.
Chemical Kinetics – Rate Law
CO + O2 → CO2 + O
Rate =k·[CO]1·[O2]1
k = A· exp(-Ea/RT)
A = 2.5·1012
n = 0
Ea = 4.77·104 (cal/mol)
TnTemperature
dependence
0
0.05
0.1
0.15
0.2
0 50 100 150 200
Mole
fra
ction (
-)
Time (s)
Example: CO oxidation
0
0.05
0.1
0.15
0.2
0 50 100 150 200
Mole
fra
ction (
-)
Time (s)
O2
CO2
CO
O2
CO2
COH2O
1 vol-% H2O added
CO + ½O2 = CO2
T=1000 °C, p=1 bar
0
0.05
0.1
0.15
0.2
0 0.002 0.004 0.006 0.008 0.01
Mole
fra
ction (
-)
Time (s)
Example: CO oxidation
0
0.05
0.1
0.15
0.2
0 50 100 150 200
Mole
fra
ction (
-)
Time (s)
O2
CO2
CO
O2
CO2
CO
1 vol-% H2O added
CO + ½O2 = CO2
T=1000 °C, p=1 bar
H2O
With H2O
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01
Mole
fra
ction (
-)
Time (s)
O2
CO
CO2
H2O
H
O
OH
H2
HO2
CO reactions involved
CO+O+M=CO2+M
CO+O2=CO2+O
CO+OH=CO2+H
CO+HO2=CO2+OH
HCO+M=H+CO+M
HCO+H=CO+H2
HCO+O=CO+OH
HCO+OH=CO+H2O
HCO+O2=CO+HO2
-0.0016
-0.0014
-0.0012
-0.0010
-0.0008
-0.0006
-0.0004
-0.0002
0.0000
0.0002
0 0.002 0.004 0.006 0.008 0.01
CO
Rate
Of
Pro
duction (
mole
/cm
3-s
)
Time (s)
GasRxn Total_
CO+O+M=CO2+M
CO+OH=CO2+H
CO+HO2=CO2+OH
HCO+M=H+CO+M
HCO+H=CO+H2
HCO+O=CO+OH
HCO+OH=CO+H2O
HCO+O2=CO+HO2
With H2O
RXN Total
CO+OH=CO2+H
CO+O+M=CO2+M
-0.0015
-0.0010
-0.0005
0.0000
0.0005
0.0010
0 0.002 0.004 0.006 0.008 0.01 0.012
OH
Ra
to-O
f-P
rod
uc
tio
n (
RO
P)
(mo
le/c
m3
/s)
Time (s)
OH_ROP_GasRxn_Total(mole/cm3-sec)O + OH = H + O2
O + H2 = OH + H
2 OH = H2O + O
H + OH + M = H2O + M
H + O + M = OH + M
HO2 + H = 2 OH
HO2 + O = OH + O2
HO2 + OH = H2O + O2
H2O2 + M = 2 OH + M
CO + OH = CO2 + H
With H2O
CO+OH=CO2+H
10 vol-% CO, 20 vol-% O2
CO mole fraction contour
Top view
CO oxidation
10 vol-% CO, 20 vol-% O2
1 vol-% H2O
CO mole fraction contour
Top view
10%
CO
0%
CO
10%
CO
0%
CO
Summary (1/2)
Global reaction (e.g CO + ½ O2 = CO)
An “overall/net” reaction
Elementary reactions (actual molecular reactions), e.g
CO + O2 = CO2 + O
CO + OH = CO2 + H
Reaction rate – rate law
Global RXN:
r = k·[A]c·[B]d·[ ]…, c and d no physical meaning, can
even be negative
Elementary RXN:
r = k·[A]1·[B]1·[M]1, usually two reactants
k = A·Tn· exp(-Ae/RT), important parameters for kinetics
modeling!
CO oxidation kinetics; importance of H2O
Chemical Kinetics – reaction types Chain reactions (in combustion CH4+2O2 → CO2 + 2H2O):
Many chemical reactions can be
summarized into a global reaction
(e.g. combustion)
In reality the reactions are a chain of
elementary reactions consisting of:
O2 + M → O* + O* + M
CH4 + M → CH3* + H* + M
CH4 + O* → OH* + CH3*
CH3* + O2 → O* + CH3O*
CH3* + O2 → OH* + CH2O
CH4 + H* → CH3* + H2
CH2O + H* → CHO* + H2
CH3* + CH3* + M → C2H6 + M
CH2O + OH* → CH3* + O2
... →....
... →... + CO2
... →... + H2O
Consecutive reactions: Products from one
reaction undergoes further reactions to give
other products
Competitive reactions: two or more
sets of products are produced from
same set of reactants
Opposing reactions: the products and reactants
of a reaction are switched in another reaction
Chemical Kinetics – reaction types
Chain reactions:
Free radicals
Active species in gas combustion, characterized by unpaired
electrons.
Free radicals are electrically neutral (compared with ions that
are electrically charged)
H
..
H : C : H..
H
+ . O .
CH4 + O* → OH* + CH3*
→
H
..
. C : H..
H
. O : H
Chemical Kinetics – reaction types Chain reactions:
Chain-reactions can be defined as following:O2 + M → O* + O* + M
CH4 + M → CH3* + H* + M
CH4 + O* → OH* + CH3*
CH3* + O2 → O* + CH3O*
CH3* + O2 → OH* + CH2O
CH4 + H* → CH3* + H2
CH2O + H* → CHO* + H2
CH3* + CH3* + M → C2H6 + M
CH2O + OH* → CH3* + O2
... →....
... →... + CO2
... →... + H2O
Chain-initiating:
Radicals are produced from none radicals
Chain-branching:
More radicals are produced than destroyed
Chain-propagating:
Radicals are produced from as many radicals
Chain-terminating:
Radicals react to none radical species
CO oxidation with H2O
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01
Mole
fra
ction (
-)
Time (s)
O2
CO
CO2
H2O
H
O
OH
H2
HO2
CO reactions involved
CO+O+M=CO2+M
CO+O2=CO2+O
CO+OH=CO2+H
CO+HO2=CO2+OH
HCO+M=H+CO+M
HCO+H=CO+H2
HCO+O=CO+OH
HCO+OH=CO+H2O
HCO+O2=CO+HO2
Chain-initiating
Chain-branching
Chain-propagating
Chain-terminating
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01
Mo
le f
racti
on
(-)
Time (s)
O2
CO
CO2
H2O
NO
NO2
N2O
H
O
OH
H2
HO2
H2O2
HCO
CO kinetics 1000 °C
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01
Mo
le f
racti
on
(-)
Time (s)
O2
CO
CO2
H2O
Equilibrium CO
1000 °CCO kinetics and equilibrium
• Time to equilibrium ?
• Equilibrium CO concentration ?
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01
Mo
le f
racti
on
(-)
Time (s)
O2
CO
CO2
H2O
Equilibrium CO
1500 °CCO kinetics and equilibrium
• Time to equilibrium ?
• Equilibrium CO concentration ?
1.E-22
1.E-20
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01
Mo
le f
racti
on
(-)
Time (s)
O2
CO
CO2
H2O
Equilibrium CO
2000 °CCO kinetics and equilibrium
• Time to equilibrium ?
• Equilibrium CO concentration ?
Summary (2/2)
Irreversible, reversible, consecutive, competitive rxns
Chain reactions: Initiating, branching, propagating,
terminating
CO oxidation - Equilibrium vs. kinetics
Time to equilibrium
~1 s at 1000°C
~0.1 s at 1500 °C
Typical residence times in steam boilers ~ few seconds
Equilibrium concentration
Increases with temperature