Fundamentals of Chemical Kinetics. Application to Combustible Systems and especially to the rate of formation and destruction of nitrogen oxides

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Fundamentals of Chemical Kinetics.

Application to Combustible Systems and especially to the rate of formation

and destruction of nitrogen oxides

Gabrielle DUPRÉ

Institute of Combustion, Aerodynamics, Reactivity and Environment (I.C.A.R.E.), National Center of Scientific Research (C.N.R.S.)

and

University of Orléans, ORLÉANS, France

Università del Sannio, Benevento, Italy, May 16-17, 2011

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Fundamentals of chemical kinetics

1. Fundamentals of chemical kinetics 2. Elementary reactions

3. Characteristics of combustible mixtures

4. Reaction mechanisms in flames or in combustion processes

5. Formation of nitrogen oxides in combustion

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1. Fundamentals of chemical kinetics

1.0 - Introduction 1.1 - Reaction rate

1.2 - Reaction order, rate constant, activation energy, half-life time 1.3 - Main types of reactions of a defined order

2. Elementary reactions

3. Characteristics of combustible mixtures 4. Reaction mechanisms in flames

5. Formation of nitrogen oxides in combustion

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1

1. Fundamentals of chemical kinetics

1.0 - Introduction

Definition:

• Study the rate of chemical reactions and of chemical mechanisms Aim:

• Determine the time-evolution laws of chemical species (reactants, products, intermediate species)

• Interpret the time-dependent laws

Necessary condition: For the reaction: Reactants  Products

• Reaction must be thermodynamically possible: ΔAT,V ≤ 0 or ΔGT,P ≤ 0 with A: utilizable energy (A = U – TS) ; G: free enthalpy (G = H – TS) Non sufficient condition: Example: 2 H₂(g) + O₂(g)  2 H₂O (l)

• at T = 273 K, P = 101.3 kPa: extremely slow reaction

• at T > 873 K, for any P: explosive reaction

An important factor: TIME

Two important parameters: TEMPERATURE, PRESSURE

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1. Fundamentals of chemical kinetics

1.1 – Reaction rate

1.1.1 - General expression of the rate (v) of reaction:

^ν₁^A₁ ^{+ ν}₂^A₂ + ...  ν₁’A’₁ + ν₂’A’₂ + ...

For species Ai: νi: stoichiometric coefficient ; [Ai]: species concentration [Ai] = ni /V with: ni: mole number ; V: reaction volume ; t: time

Reaction rate: v ₌ - 1 d [A_i]

ν_i dt = + 1 d [A’ⁱ]

ν_i^’ dt ν_iV dt ν_iV² dt

if V is time-dependent 1 dn_{i +} n_i dV - =

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1. Fundamentals of chemical kinetics

1.1 – Reaction rate

1.1.2 - Expression of reaction rate at constant V

ν

A

+ ν

A

+ ...  ν

’A’

+ ν

’A’

+ ...

With constant reaction volume V: n_i . dV ν_iV² dt 1

d [A_i] ν_i dt

1 d [A’_i] ν^’_i dt

v = ^-

v = +

= 0

(v expressed in mol m^-3 s^-1)

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1. Fundamentals of chemical kinetics

1.2

–

For the reaction: ^ν_A^{A + ν}_BB  Products

v = k [A]

[B]

v

with k: rate constant ; m_A and m_B: partial orders m_A + m_B = m: overall order If: m_A = ν_A and m_B = ν_B

↔

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1. Fundamentals of chemical kinetics

1.2

–

For the reaction: ν_AA + ν_BB  Products

v = k [A]^mA [B]^mB

with: k = k₀ exp (- E_a / RT) Arrhenius law

v: reaction rate (mol m^-3 s^-1)

k: rate constant ; k₀: pre-exponential factor ; k and k₀: same units Ea: activation energy (J mol^-1)

R: perfect gas constant (J mol^-1 K^-1) ; T: temperature (K)

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1. Fundamentals of chemical kinetics

1.2

–

E

For the reaction:

k = k

exp (- E

/ RT)

Determination of E_a from:

- the linear representation: ln k = f (1 / T)  k₀, E_a

- the measurements of v or k at two temperatures T₁ and T2

if T₁ ≠ T₂ : v₁/v₂ = k₁/k₂ = (k₀)₁/(k₀)₂ exp[-E_a/R (1/T₁ – 1/T₂)]

if T1 # T2 : (k₀)₁ # (k₀)₂ ; (k₀)₁/(k₀)₂ # 1  E_a

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1. Fundamentals of chemical kinetics

1.2

–

1.2.4 – Half-life time: t

A + B  Products at t = 0 a b

at t a – x b – x

The half-life t_½ is the time corresponding to the half of reactant initial concentration:

at t = t_½ a – x = a / 2 ↔ x = a / 2 or b – x = b / 2 ↔ x = b / 2

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1. Fundamentals of chemical kinetics

1.3 – Main types of reactions of a defined order

1.3.0 - Order 0: (m = 0) with a unique reactant (ν = 1):

this case is rather rare !

A  Products

at t = 0 a 0 at t a – x

Reaction rate: v = ?

Concentration: [A] = f (t)?

Units for k: ?

Half-life: t_½ = ?

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1. Fundamentals of chemical kinetics

1.3 – Main types of reactions of a defined order

1.3.1 – Order 1: (m = 1) with a unique reactant (ν = 1):

this case appears mostly for disintegration of radioactive atoms.

A  Products

at t = 0 a 0

at t a – x

Reaction rate: v = ?

Concentration:[A] = f (t)?

Units for k: ?

Half-life: t_½ = ?

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1. Fundamentals of chemical kinetics

1.3 – Main types of reactions of a defined order

1.3.2 – Order 1: (m = 1) with 2 reactants (ν_A = ν_B = 1) with one reactant in excess

A + B  Products

at t = 0 a b 0 at t a – x b – x

If b >> a avec a > x  b >> x  b – x # b

Reaction rate: v = ?

Concentration: [A] = f (t)?

Units for k: ?

Half-life: t_½ = ?

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1. Fundamentals of chemical kinetics

1.3 – Main types of reactions of a defined order

Most chemical reactions are bimolecular

1.3.3 – Order 2: (m = 2) with a unique reactant (ν = 1) A  Products

at t = 0 a 0 at t a – x

Reaction rate: v = ?

Concentration: [A] = f (t)?

Units for k: ?

Half-life: t_½ = ?

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1. Fundamentals of chemical kinetics

1.3 – Main types of reactions of a defined order

1.3.4 – Order 2: (m = 2) with 2 reactants (ν_A = ν_B = 1)

A + B  Products

at t = 0 a b 0 at t a – x b – x

1) for a ≠ b Reaction rate: v = ?

Concentration: [A] = f (t)?

Units for k: ?

Half-life: t_½ = ?

2) for a = b See the case of m = 2, ν = 1 for a unique reactant

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1. Fundamentals of chemical kinetics

1.3 – Main types of reactions of a defined order

We could treat also reactions of order 3: these reactions do exist but are rare because of a low probability of three species colliding

simultaneously

1.3.5 – Order 3: (m = 3) with a 1 reactant (ν_A = 1)

1.3.6 – Order 3: (m = 3) with a 2 reactants (ν_A = 2 ; ν_B = 1 for example)

We could also treat reactions of any order m (whole or fractional) 1.3.7 – Order m: (m ≠ 1 or m = 1) with 1 reactant (ν = 1)

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Fundamentals of chemical kinetics Application to combustible mixtures

1. Fundamentals of chemical kinetics 2. Elementary reactions

2.1 – Bimolecular reactions at constant volume 2.2 – Collision Theory of gas reactions

2.3 – Activated-Complex Theory

3. Characteristics of combustible mixtures 4. Reaction mechanisms in flames

5. Formation of nitrogen oxides in combustion

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2. Elementary reactions

2.1 – Bimolecular reactions at constant volume

A + B  P

with ν_A = m_A = 1 et ν_B = m_B = 1 (≡ elementary reaction of order 2)

• v = - d[A]/dt = - d[B]/dt = + d[P]/dt

• v = k [A]¹ [B]¹

• Generally:

k = k

exp[-E

/RT]

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• Any chemical reaction results more likely of a collision between two chemical species, through an elementary act

(except for the disintegration process of a radioactive atom: m=1 and for the collision - rare - between three species)

•The collision frequency is evaluated on the basis of the kinetic theory of gases

2. Elementary reactions

2.2 – Collision Theory for gaseous reactions

• Any chemical reaction results of a collision between two chemical species through an elementary act

• The collision frequency Z_AB can be evaluated on the basis of the kinetic theory of gases (assuming that species are like hard spheres) :

Z_AB = σ_AB c_AB [N_A/V ] [N_B/V ] [expressed in coll. m^-3 s^-1] with: d_AB = ½ (d_A+d_B) σ_AB = π (d_AB)² c_AB = (8 k_BT/π µ_AB)^1/2

B

B

A c_AB

σ_AB B

B

2. Elementary reactions

2.2 - Collision Theory for gaseous reactions

where 1/µ_AB = 1/m_A+1/m_B N_A/V = n_A

N_B/V = n_B

Z_AB = [N_A/V ] [N_B/V ] (8 k_BT/π µ_AB)^1/2 π (d_AB)²

with N_A/V = n_A and N_B/V = n_B

n_A, n_B: numbers of molecules A and B per volume unit

Z_AB = n_A n_B (8k_BT/π µ_AB)^1/2 π (d_AB)²

• Each collision is not a reactive process: v << Z_AB

• Two limiting factors :

- Energetic factor: f = exp (-Eexp (-E_AA/RT) /RT) - Steric factor: p

v v = - dn= - dn_AA/dt = Z/dt = Z_{AB AB} p exp(-Ep exp(-E_AA/RT) = k n/RT) = k n_AA n n_BB

k = (8 k_BT/π µ_AB)^1/2 π (d_AB)² p exp(-Eexp(-E_AA/RT) = k/RT) ₀ exp(-E_A/RT)

with k₀ = (8 k_BT/π µ_AB)^1/2 π (d_AB)² p

2.2 - Collision Theory for gaseous reactions

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Finally :

- d[n_A]/dt = n_A n_B σ_AB c_AB p exp (-E_A/RT)

2. Elementary reactions

2.2 - Collision Theory for gaseous reactions

Rate constant : Rate constant :

k k = = σ σ

c c

p p

exp (-E exp (-E

/RT) /RT)

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Validity of the collision theory for gaseous reactions ?

How to evaluate E_A ? How to estimate p ?

2. Elementary reactions

2.2 - Collision Theory for gaseous reactions

Existence of a transition state and activated complex: (AB^‡)

A + B  AB^‡  Products

with K^‡ : pseudo-equilibrium constant:

K^‡ = [AB^‡] c°/ [A] [B]

v = + d[P]/dt = ν^‡ [AB^‡] = ν^‡ K^‡ [A] [B] / c°

v = k_II [A] [B] k_II : bimolecular rate constant

where:

ν^‡ : vibration frequency of the bond in AB^‡ that breaks to give products c° : concentration in the reference state (= P°/RT° for a gaseous reaction) = 1 mol m^-3

2.

2.3 – Activated-Complex Theory

kk_IIII = = νν^{‡ ‡} KK^‡‡ / c° / c°

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Expression de K^‡ ? ???

2. Elementary reactions

2.3 – Activated-Complex Theory

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Calculation of K^‡ from the partition functions of energy Q_i

K^‡ = (Q_AB ^‡ / Q_A Q_B) exp (-E^‡₀ /RT)

with: Q_i = (q_e q_n q_tr³ q_rot^a q_vib^3N-b)_i for each species i N: number of atoms in the species i

a = 2 ; b = 5 for a linear molecule

a = 3 ; b = 6 for a non-linear molecule

E^‡₀: difference of potential energy between (AB^‡) and reactants

2. Elementary reactions

2.3 – Activated-Complex Theory

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K^‡ = (Q_AB ^‡ / Q_A Q_B) exp (-E^‡₀ /RT)

If: h ν^‡ << k_B T

Q_AB^‡ = Q’_AB^‡ / [1 – exp (- hν^‡/k_BT)] # Q’_AB^‡ k_BT / hν^‡

where Q’_AB‡ is the product of all terms not dealing with bond scission

ν‡ : vibration frequency of the bond in AB‡ that breaks to give products h : Planck constant ; k_B: Boltzmann constant ; T: temperature

2. Elementary reactions

2.3 – Activated-Complex Theory

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2. Elementary reactions

2.3 – Activated-Complex Theory

Determination of surfaces of potential energy

S

 U

P Q

S

E^‡₀

Reaction coordinate 

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Calculation of K^‡ from the partition functions of energy Q_i

2. Elementary reactions

2.3 – Activated-Complex Theory

k_II = (Q’_AB^‡ / Q_A Q_B) (k_BT/h) (1/c°) exp(-E^‡₀ /RT) Calculation of k_II: k_II = ν‡ K‡ / c° becomes:

(from A.G. GAYDON and H.G. WOLFHARD, Chapman and Hall, 4^th Edition, 1979) Concentrations : in mol cm^-3 Time : in seconds

Reaction Rate constant

CH₄ + OH = CH₃ + H₂O 3 x 10¹³ exp (-2500/T) CH₄ + H = CH₃ + H₂ 2 x 10¹⁴ exp (-5950/T) CH₄ + O = CH₃ + OH 2 x 10¹³ exp (-3450/T) CH₃ + O = CH₂O + H 3.5 x 10¹³ exp (-1650/T) CH₃ + O₂ = CH₂O + OH 1 x 10¹² exp (-7500/T) CH₂O + M = CO + H₂ + M 2 x 10¹⁶ exp (-17500/T)

CH₂O + OH = CHO + H₂O 2.5 x 10¹³ exp (-500/T) CH₂O + O = CHO + OH 3 x 10¹³

CHO + O₂ = CO + HO₂ 1 x 10¹⁴

CHO + OH = CO + H₂O 5.5 x 10¹¹ exp (-540/RT)

Reaction Rate constant

HO₂ + OH = O₂ + H₂O 2.5 x 10¹³

HO₂ + H = OH + OH 2 x 10¹⁴ exp (-1000/RT) HO₂ + H = O₂ + H₂ 6 x 10¹³ exp (-1000/RT) H + O₂ + M = HO₂ + M 1.4 x 10¹⁶ exp (-500/RT)

H + O₂ = OH + O 1.4 x 10¹⁶ exp (-500/RT) O + H₂ = OH + H 2.2 x 10¹⁴ exp (-8400/RT) OH + H₂ = H₂O + H 2.2 x 10¹³ exp (-2600/RT) H + OH + M = H₂O + M 7 x 10¹⁹ T^-1

H + H + M = H₂ + M 2 x 10¹⁹ T^-1

CO + OH = CO₂ + H 5.5 x 10¹¹ exp (-540/RT)

RATE CONSTANTS for the combustion of methane

(simplified mechanism for a laminar flame)

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2. Elementary reactions

2.3 – Activated-Complex Theory

• Difficulties encountered with ab initio methods:

- Calculation of E_‡0

– Determination of surfaces of potential energy

- Calculation of partition functions of energy for the activated complex

– Structure of activated complex

• GAUSSIAN software: a good help for the selection of reaction steps

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Fundamentals of chemical kinetics Application to combustible mixtures

1. Fundamentals of chemical kinetics 2. Elementary reactions

3. Characteristics of combustible mixtures 4. Reaction mechanisms in flames

5. Formation of nitrogen oxides in combustion

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3. Characteristics of combustible mixtures

• The chemical reaction occurs in gaseous phase (except for rare cases)

• Complex reaction mechanisms are made of a large number of elementary steps

• The elementary steps mostly imply neutral species (molecules, radicals, atoms, but rarely ions)

• The elementary steps are mostly bimolecular, but can be also uni- or trimolecular (as in next table)

(from A.G. GAYDON and H.G. WOLFHARD, Chapman and Hall, 4^rd Edition, 1979) Concentrations : mol cm^-3 Time : second

Reaction Rate constant

CH₄ + OH = CH₃ + H₂O 3 x 10¹³ exp (-2500/T) CH₄ + H = CH₃ + H₂ 2 x 10¹⁴ exp (-5950/T) CH₄ + O = CH₃ + OH 2 x 10¹³ exp (-3450/T) CH₃ + O = CH₂O + H 3.5 x 10¹³ exp (-1650/T) CH₃ + O₂ = CH₂O + OH 1 x 10¹² exp (-7500/T) CH₂O + M = CO + H₂ + M 2 x 10¹⁶ exp (-17500/T)

CH₂O + OH = CHO + H₂O 2.5 x 10¹³ exp (-500/T) CH₂O + O = CHO + OH 3 x 10¹³

CHO + O₂ = CO + HO₂ 1 x 10¹⁴

CHO + OH = CO + H₂O 5.5 x 10¹¹ exp (-540/RT)

Reaction Rate constant

HO₂ + OH = O₂ + H₂O 2.5 x 10¹³

HO₂ + H = OH + OH 2 x 10¹⁴ exp (-1000/RT) HO₂ + H = O₂ + H₂ 6 x 10¹³ exp (-1000/RT) H + O₂ + M = HO₂ + M 1.4 x 10¹⁶ exp (-500/RT)

H + O₂ = OH + O 1.4 x 10¹⁶ exp (-500/RT) O + H₂ = OH + H 2.2 x 10¹⁴ exp (-8400/RT) OH + H₂ = H₂O + H 2.2 x 10¹³ exp (-2600/RT) H + OH + M = H₂O + M 7 x 10¹⁹ T^-1

H + H + M = H₂ + M 2 x 10¹⁹ T^-1

CO + OH = CO₂ + H 5.5 x 10¹¹ exp (-540/RT)

ELEMENTARY REACTIONS in the combustion of methane (Simplified mechanism for a laminar flame)

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3. Characteristics of combustible mixtures

How to evaluate the kinetic parameters at high temperature ?

• Experimentally

– Flow reactor – Shock tube

– Fast compression machine …

• On a theoretical basis

• By coupling the experimental study and a simulation (with a sensitivity study)

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4 . Reaction mechanisms in flames or in combustion processes

1. Basic chemical kinetics 2. Elementary reactions

3. Characteristics of combustible mixtures

4. Reaction mechanisms in flames or in combustion processes

4.1 – Linear-chains reactions

4.2 – Branching-chains reactions

4.3 – Conclusion on reaction mechanisms

4.4 - Numerical resolution of the system of equations

5. Formation and destruction of nitrogen oxides

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4 . Reaction mechanisms in flames or in combustion processes

4.1 – Linear-chains reactions

Discovery of complex mechanisms

• Bodenstein 1906 :

½ H₂ (g) + ½ Br₂ (g)  HBr (g) Δ_rH°₂₉₈ = -30,4 kJ mol^-1

• Reaction with non-defined order :

v = d[HBr]/dt = k [H2] [Br2]^1/2 /(1 + k’ [HBr]/[Br2])

• Strictly a gas-phase reaction: not a catalytic reaction, no heterogeneous effect, no effect of the reactor wall

• HBr added to reactants makes the reaction rate decrease (HBr is an inhibitor for the reaction)

• Linear-chains mechanism: Polanyi et al., 1919

Steady-state approximation applied to atoms, radicals, intermediate species:

d[R]/dt = 0 Since they appear and disappear, [R] = constant

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4 . Reaction mechanisms in flames or in combustion processes

4.1 – Linear-chains reactions

Overall reaction: H₂ + Br₂  2 HBr Detailed mechanism:

Br₂ + M  2 Br + M initiation

H2 + Br  HBr + H propagation Kinetic

Br2 + H  HBr + Br propagation chain

H + HBr  H2 + Br inhibition

2 Br + M  Br2 + M termination/rupture

• Calculated overall reaction rate v corresponds to the experimental results of Bodenstein

• It is a linear-chains mechanism: discovered by Polanyi et al., 1919

• Chains carriers: H et Br: for them, apply the steady-state approximation

Steady-state approximation applied to atoms, radicals, intermediate species:

Since H and Br appear and disappear during the reaction,

[H] = constant ; [Br] = constant d[H]/dt = 0 and d[Br]/dt = 0

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4 . Reaction mechanisms in flames or in combustion processes

4.2 - Branching chains reactions

H

(g) + ½ O

(g)  H

O (g)

• The experiments show that, for this stoichiometric reaction, the curve of P = f (T) :

– is an inversed S-curve with three « explosion limits » between autoignition (slow oxidation) and explosion (very rapid reaction)

– shows regions of autoignition and regions of explosion

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4 . Reaction mechanisms in flames or in combustion processes

4.2 - Branching chains reactions

H₂ (g) + ½ O₂ (g)  H₂O (g)

• Simplified mechanism:

H2 + O2  2 OH Initiation

H2 + M  2 H + M Initiation

H₂ + OH  H2O + H Propagation (pr) H + O2  OH+ O Chain branching O + H2  OH + H Chain branching

H + O2 + M  HO2 + M Homogeneous rupture H2 + HO2  H2O + OH Propagation (less efficient) H + wall  recombination Heterogeneous rupture (or O, OH, HO2) at the wall

• Detailed mechanism: 37 steps, 9 species (including H,O,OH,HO2,H2O2,O3)

• Reaction rate v_r: v_r = d[H₂O]/dt = k_pr [H₂][OH]

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4 . Reaction mechanisms in flames or in combustion processes

4.2- Branching chain reactions

A  R^• (Initiation) v_i = {d[R^•]/dt}_i

R^• + A  R^• + P (Propagation) v_p = k_p [R^•] ; {d[R^•]/dt}_p = 0 R^• + A  αR^• (Branching) v_b = k_b [R^•] = (d[R^•]/dt)/(1-α) R^• + A  B (Termination) v_t = k_t [R^•] = {-d[R^•]/dt)}_t

A: reactant P: product [R^•] : intermediate species

Rate of the variation of the intermediate species concentration R^• : (d[R^•]/dt) = v_i + (α-1)v_b – v_t = v_i + {k_b(α-1) - k_t }[R•] = v_i + Φ[R•]

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4 . Reaction mechanisms in flames or in combustion processes

4.2- Branching chain reactions Conditions of explosion

• d[R^•]/dt = v_i + Φ [R^•] Φ = k_b(α-1) - k_t

* Stationary state possible if Φ < 0 = transmission factor [R^•]_steady = - v_i /Φ

• Integration of d[R^•]/dt = v_i + Φ [R^•]

[R^•] = (v_i /Φ) [exp(Φt) - 1)] with t: time

• Overall rate : V_r = + d[P]/dt

V_r = k_P [R^•] = k_P (v_i /Φ) [exp(Φt) - 1)]

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4 . Reaction mechanisms in flames or in combustion processes

4.2- Branching chain reactions Conditions of explosion

v_r = k_P [R^•] = k_P (v_i /Φ) [exp(Φt) - 1)]

Φ = 0 Φ>0

Explosion

Φ<0

Slow reaction v

t

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4 . Reaction mechanisms in flames or in combustion processes

4.3 - Conclusion on reaction mechanisms

• Complex mechanisms

– Decomposed into many elementary steps

• Reactions between neutral species

– Predominance of bimolecular reactions

– Presence of uni- and trimolecular reactions (but few)

• Very low ionized medium

– Combustion in air: small quantities of NO⁺

• Non-linear systems of equations

– Numerical resolution of stiff systems

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4 . Reaction mechanisms in flames or in combustion processes

4.4 - Numerical resolution of the system of equations

Chemkin

Evolution of the concentrations of the chemical species in different reactors

• Shock tube (SENKIN)

• Laminar flame (PREMIX)

• Perfect Stirred Reactor (PSR)

• etc…

Example : methane/air

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SENKIN

Concentration profiles behind a shock wave

for the mixture: CH₄ / air

47

P₂, T₂, ρ₂ P₁, T₁, ρ₁

Profiles behind a shock wave

48 1E-010 1E-009 1E-008 1E-007 1E-006 1E-005 0.0001 0.001

T e m ps (s)

0 0.005 0.01 0.015 0.02 0.025

Fraction Molaire de NO

Methane - Air P=1bar

[N O]_équil=4,74E-03, P=5bars

[N O]_équil=4,36E-03 P=10bars

[N O]_équil=4,14E-03 P=15bars

[N O]_équil=3,99E-03 P= 25bars

[N O]_équil=3,89E-03

1,82x10^-2 2,2x10^-2 2,36x10^-2 2,45x10^-2 2,51x10^-2

Influence of initial pressure on NO formation in a CH₄ / air mixture submitted to a shock wave

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PREMIX

Concentration profiles

through a laminar flame front

for the mixture: CH₄ / air

50

Burnt gas

P₁, T₂

Fresh gas ^P₁^{, T}₁

Fresh Gas

P₁, T₁

Burnt gas P₁, T₂

Laminar flames: 2 cases

Flat flame on a burner Spherical flame in a bomb

-0.5 0 0.5 1 1.5 2

Distance (cm)

0 0.04 0.08 0.12 0.16 0.2

Fractions Molaires des Réactifs

1E-017 1E-016 1E-015 1E-014 1E-013 1E-012 1E-011 1E-010 1E-009 1E-008 1E-007 1E-006 1E-005 0.0001 0.001 0.01

Fractions Molaires de OH et NO

FRESH GAS BURNT GAS

O 2 OH

NO

CH₄

T

Methane/air ; ER = 1 ; P = 100 kPa

Concentration profiles through a laminar flame front in a CH₄/air mixture

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5. Formation of nitrogen oxides in combustion 5.1 - Mechanisms of formation of NO

• Nitric oxide NO is an important minor species in combustion, because of its contribution to air pollution

• In the combustion of fuels that contains no nitrogen, NO is formed by 4 different chemical mechanisms that involve N2 from the air:

– The thermal-NO mechanism (called Zeldovich mechanism) – The prompt-NO mechanism (called Fenimore mechanism) – The N₂O-intermediate mechanism

– The NNH-intermediate mechanism

• Certain fuels contain N in their molecular structure, like coal that contains bound N up to ~ 2% by mass. In this case, there is a 5th mechanism for the bound nitrogen in such fuels that converts nitrogen into HCN (hydrogen cyanide) and NH₃ (ammonia):

– The fuel-NO mechanism

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5. Formation of nitrogen oxides in combustion 5.1 - Mechanisms of formation of NO

5.1.1 Mechanism of thermal-NO (1): called Zeldovich mechanism – Proposed by Zeldovich, 1946, completed by Fenimore, 1971

– It concerns the formation of NO from the molecular nitrogen contained in air

– It dominates in high-T combustion over a wide range of equivalence ratios

(1) N₂ + O  NO + N θ₁ = 38200 K (= Ea/R) (-1) NO + N  N₂ + O θ_-1= 0 K

(2) NO + O  N + O2 θ2 = 19500 K (-2) N + O₂  NO + O θ_-2= 3100 K (3) N + OH  NO + H θ₃ = 0 K

(-3) NO + H  N + OH θ_-3= 20000 K

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5. Formation of nitrogen oxides in combustion 5.1 - Mechanisms of formation of NO

5.1.1 Mechanism of thermal-NO (2)^: called Zeldovich mechanism

(1) N₂ + O  NO + N θ₁ = 38200 K ^{(= Ea/R)} (-1) NO + N  N2 + O θ-1= 0 K

(2) NO + O  N + O₂ θ₂ = 19500 K (-2) N + O₂  NO + O θ_-2= 3100 K (3) N + OH  NO + H θ₃ = 0 K

(-3) NO + H  N + OH θ-3= 20000 K

• Reaction (1) is the limiting step (that is the slower one, except at high temperature) and has the highest Ea

• It determines the overall reaction rate

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5. Formation of nitrogen oxides in combustion 5.1 - Mechanisms of formation of NO

5.1.1 Mechanism of thermal-NO (3): called Zeldovich mechanism

(1) N2 + O  NO + N θ1 = 38200 K ^{(= Ea/R)} (-1) NO + N  N₂ + O θ_-1= 0 K

(2) NO + O  N + O₂ θ₂ = 19500 K (-2) N + O₂  NO + O θ_-2= 3100 K (3) N + OH  NO + H θ₃ = 0 K

(-3) NO + H  N + OH θ-3= 20000 K

• Reduction of thermal-NO:

– Decrease the flame temperature, the residence time

– Decrease the oxygen concentration in the region of the temperature peak