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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 30-31, 2012
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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 or in combustible processes
5. Formation of nitrogen oxides in combustion
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1. Fundamentals of chemical kinetics
1.0 - Introduction
Study the rate of chemical reactions and of chemical mechanisms
Aim:
• Determine the time-evolution laws of chemical species (reactants, products, intermediate species) that takes part in a reaction
• Interpret the time-dependent laws: An important factor: TIME
Necessary condition: For a given 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
Two important parameters: TEMPERATURE and 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:
ν1A1 + ν2A2 + ... 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 [Ai]
νi dt = + 1 d [A’i]
νi’ dt νiV dt νiV2 dt if V is time-dependent
1 dni + ni dV - =
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1. Fundamentals of chemical kinetics
1.1 – Reaction rate
1.1.2 - Expression of reaction rate at constant V
ν1A1 + ν2A2 + ... ν1’A’1 + ν2’A’2 + ...
With constant reaction volume V: ni . dV νiV2 dt 1
d [Ai] νi 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 – Reaction order, rate constant, activation energy, half-life time 1.2.1 - Reaction order: m
For the reaction: νAA + νBB Products
v = k [A]mA [B]mB (v expressed in mol m-3 s-1)
with k: rate constant ; mA and mB: partial orders mA + mB = m: overall order
If: mA = νA and mB = νB
↔ ‘
elementary reaction’
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1. Fundamentals of chemical kinetics
1.2 – Reaction order, rate constant, activation energy, half-life time 1.2.2 – Rate constant: k
For the reaction: νAA + νBB Products
v = k [A]mA [B]mB
with: k = k0 exp (- Ea / RT) Arrhenius law
v: reaction rate (mol m-3 s-1)
k: rate constant ; k0: pre-exponential factor ; k and k0: same units as v 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 – Reaction order, rate constant, activation energy, half-life time 1.2.3 – Activation energy: Ea
For the reaction: k = k0 exp (- Ea / RT)
Determination of Ea from:
- the linear representation: ln k = f (1 / T) k0, Ea
- the measurements of v or k at two different temperatures T1 and T2
if T1 ≠ T2 : v1/v2 = k1/k2 = (k0)1/(k0)2 exp[-Ea/R (1/T1 – 1/T2)]
if T1 # T2 : (k0)1 # (k0)2 ; (k0)1/(k0)2 # 1 Ea
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1. Fundamentals of chemical kinetics
1.2 – Reaction order, rate constant, activation energy, half-life time
1.2.4 – Half-life time: t½
A + B Products at t = 0 a b
at t a – x b – x
The half-life t½ is the time corresponding to the half of reactant initial concentration a or b:
at t = t½ 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: t½ = ?
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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: t½ = ?
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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 (νA = νB = 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: t½ = ?
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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 (νA = 1) A Products
at t = 0 a 0 at t a – x
Reaction rate: v = ?
Concentration: [A] = f (t)?
Units for k: ?
Half-life: t½ = ?
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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 (νA = νB = 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: t½ = ?
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 (νA = 1)
1.3.6 – Order 3: (m = 3) with a 2 reactants (νA = 2 ; νB = 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 (P = Products)
with νA = mA = 1 et νB = mB = 1 (≡ elementary reaction of order 2)
• v = - d[A]/dt = - d[B]/dt = + d[P]/dt
• v = k [A]1 [B]1
• Generally: k = k0 exp[-Ea/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 ZAB is evaluated on the basis of the kinetic theory of gases (assuming that the chemical species are like hard spheres):
ZAB = σAB cAB [NA/V ] [NB/V ] [expressed in coll. m-3 s-1] with: dAB = ½ (dA+dB) σAB = π (dAB)2 cAB = (8 kBT/π µAB)1/2
B
B
A cAB
σAB B
B
2. Elementary reactions
2.2 - Collision Theory for gaseous reactions
where 1/µAB = 1/mA+1/mB NA/V = nA
NB/V = nB
ZAB = [NA/V ] [NB/V ] (8 kBT/π µAB)1/2 π (dAB)2
with NA/V = nA and NB/V = nB
nA, nB: numbers of molecules A and B per volume unit
ZAB = nA nB (8kBT/π µAB)1/2 π (dAB)2
• Each collision is not a reactive process: v << ZAB
• Two limiting factors :
- Energetic factor: f = exp (-Eexp (-EAA/RT) /RT) - Steric factor: p
v v = - dn= - dnAA/dt = Z/dt = ZAB AB p exp(-Ep exp(-EAA/RT) = k n/RT) = k nAA n nBB
k = (8 kBT/π µAB)1/2 π (dAB)2 p exp(-Eexp(-EAA/RT) = k/RT) 0 exp(-EA/RT)
With: k0 = (8 kBT/π µAB)1/2 π (dAB)2 p
2.2 - Collision Theory for gaseous reactions
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Finally :
- d[nA]/dt = nA nB σAB cAB p exp (-EA/RT) = k nA nB
2. Elementary reactions
2.2 - Collision Theory for gaseous reactions
Rate constant : Rate constant :
k k = = σσAB AB c cAB AB p p exp (-Eexp (-EAA/RT)/RT)
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Validity of the collision theory for gaseous reactions ?
How to evaluate EA ? 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‡ P P = Products
with K‡ : pseudo-equilibrium constant:
K‡ = [AB‡] c°/ [A] [B]
v = + d[P]/dt = ν‡ [AB‡] = ν‡ K‡ [A] [B] / c°
v = kII [A] [B] kII : 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 (in the International Unit System)
2. Elementary reactions
2.3 – Activated-Complex Theory
kkIIII = = 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 Qi
K‡ = (QAB ‡ / QA QB) exp (-E‡0 /RT)
with: Qi = (qe qn qtr3 qrota qvib3N-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‡ = (QAB ‡ / QA QB) exp (-E‡0 /RT)
If: h ν‡ << kB T
QAB‡ = Q’AB‡ / [1 – exp (- hν‡/kBT)] # Q’AB‡ kBT / 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 ; kB: 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 Qi
2. Elementary reactions
2.3 – Activated-Complex Theory
kII = (Q’AB‡ / QA QB) (kBT/h) (1/c°) exp(-E‡0 /RT) Calculation of kII: kII = ν‡ K‡ / c° becomes:
(from A.G. GAYDON and H.G. WOLFHARD, Chapman and Hall, 4th 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, 4rd 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 in a:
– 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) ΔrH°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 R:
d[R]/dt = 0 Since they appear and disappear, [R] = constant with t
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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, we 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
H2 (g) + ½ O2 (g) H2O (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 vr: vr = d[H2O]/dt = kpr [H2][OH]
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4 . Reaction mechanisms in flames or in combustion processes
4.2- Branching chain reactions
A R• (initiation) vi = {d[R•]/dt}i
R• + A R• + P (propagation) vp = kp [R•] ; {d[R•]/dt}p = 0 R• + A αR• (branching) vb = kb [R•] = (d[R•]/dt)/(1-α)
R• + A B (termination) vt = kt [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) = vi + (α-1)vb – vt = vi + {kb(α-1) - kt }[R•] = vi + 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 = vi + Φ [R•] Φ = kb(α-1) - kt
* Stationary state possible if Φ < 0 = transmission factor [R•]steady = - vi /Φ
• Integration of d[R•]/dt = vi + Φ [R•]
[R•] = (vi /Φ) [exp(Φt) - 1)] with t: time
• Overall rate : Vr = + d[P]/dt
Vr = kP [R•] = kP (vi /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
vr = kP [R•] = kP (vi /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
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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
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Burnt gas
P1, T2
Fresh gas P1, T1
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 the ‘Zeldovich mechanism’
– The prompt-NO mechanism (called the ‘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 in 1946, completed by Fenimore in 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