Gaseous Combustion Kinetics - users.abo.fiusers.abo.fi/maengblo/CombChem_2018/Gaseous_Combustion_Kinetics... · Terms and concepts CO and CH 4 oxidation kinetics Elementary and global

Gaseous Combustion Kinetics

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 + ½ O2 → CO2

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

Chemical Kinetics – Rate Law

”How fast is the reaction?”

CO + O2 → CO2 + O

Rate =k·[CO]1·[O2]1

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

Input 10 vol-% CO, 20 vol-% O2

CO mole fraction contourTop view

CO oxidation

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

Chemical kinetics and chemical equilibrium

Example: CO oxidation

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

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