Combustion Kinetics
From Chain Reactions to Explosions to Pyrolysis
by Ryan Moore
Chain Reactions
Generally, chain reactions can be described as a reaction where "an intermediate is produced in one step that generates another intermediate in a subsequent step, then that intermediate generates another intermediate, and so on…" Now in most combustion these intermediates are radicals (radical chain reactions), called chain carriers, and are responsible for chain propagation. The steps in a chain reaction are broken down to:
INITIATION - PROPAGATION - BRANCHING - RETARDATION
- TERMINATION/INHIBITION
Where chain carriers are formed. e.g.
Br2 + M -> 2Br. + M
where the Br. is the chain carrier for the chain reaction
The step which chain carriers attack a reactant to form another chain carrier. This can also be called the branching step due to the number of chain carriers that can be produced. If one is produced, the reaction is a Straight Chain Reaction, if 2 are produced the reaction is a Branched Chain Reaction. e.g.
When a chain carrier attacks a product molecule formed already, thus reduces the net concentration of product formed. e.g.
In this case a molecule of product is reduced and a molecule of reactant is reformed.
When the radicals combine and end the chain, either by forming with other radicals or the vessel walls or even a foreign radicals.
We’ve met Straight Chain reactions before with the study of H2 + Br2 -> 2HBr before. Each step either involves the making of one chain carrier (except the initiation) and/or a termination step. This reaction is a simple one and only involves at most 5 steps.
In Branched Chain reactions the mechanism is much more complex. The formation of 2 chain carriers causes the chain reaction to branch out in many ways and provide an almost infinite reaction paths. The chain length can be expressed as:
L = {rate of disappearance of reactants} / {rate of chain carrier formation by initiation}
Another term can be introduced N , which is a net branching factor. The mathematics of it are pretty complex, simply:
N = g - f
Where g is rate of branching and f is
rate of termination. When N >
____ branching occurs more rapidly than termination, leading to
exponential growth and explosion. When N <
_____ termination dominates. For example the classic formation of
H2O reaction.
It is so complex that the entire mechanism is not yet understood. For the formation of water (as depicted above) there are approximately 40 steps theorized that can account for the observations. In most conditions it can be described in generally 5-6 steps.
| Reaction | Reaction Type | A / cm3 molecule s-1 | E / kJ mol-1 |
| [1]H2 + O2 -> 2OH | Initiation | 2.8 e –11 | 200 |
| [2]OH + H2 -> H + H20 | Propagation | 4.2 e –11 | 22 |
| [3]H + O2 -> OH + O | Branching | 3.8 e –10 | 70 |
| [4]O + H2 -> OH + H | Branching | 4.8 e –11 | 42 |
| [5]H + O2 + M -> HO2 + M | Termination | 5.8 e –30 x T-1 | |
| [6-8] H, O, OH -> Wall | Termination | ||
| [9] HO2 + H2 -> H + H2O2 | Restore the Chain at High Temperature | 1.0 e –12 | 77 |
| [10]2HO2 -> H2O2 + O2 | 7.0 e –10 | 50 | |
| [11]H2O2 -> 2OH | 1.0 e –7 | 1110 |
A complicated answer for the reaction can be:
Explosions:
The rapid increase of chain carriers in branched chain reaction, if the reaction is exothermic and there is no reservoir for the output of energy, the rate of reaction increases exponentially, which then, in turn, increases the temperature exponentially, which in turn increases rate exponentially and so on and so on. A great example of this is leaving oily rags around. If you were to throw a bunch of oily rags in a closed bin the slow oxidation of the oil occurs. Initially this reaction occurs slowly, but as there is no place for the output of the thermal energy released, except to increase the rate, the rate starts to increase, which causes more reactions, which releases more heat which…. EXPLOSION, or fire. Another example of this is with water again. Supposed we use the following mechanism for the oxidation of Hydrogen to form water.
1. Initiation H2 + O2 -> 2OH. k1
2. Propagation OH. + H2 -> H2O + H. k2 -fast, exothermic
3. Branching H. + O2 -> OH. + O k3 -slow, endothermic
4. Branching O + H2 -> OH. + H. k4 -fast (k4 > k3)
5. Termination H. + wall -> inert H species k5 -H. removed
6. Termination H. + O2 + M -> HO2. + M k6
Applying steady state conditions:
and adding (1) + (2) + (3) we solve to get:
[H.]steady state = {2k1[H2][ O2]} / {k5 – 2k3[O2] + k6[O2][M]}
here we find a Pressure/Temperature relationship like:
Where if we take it for one temperature we find a
rate reaction a little different than an exponential curve. What
we find is:
Reasons for this are:
Pyrolysis
Thermal decomposition in the absence of air. These reactions can get quite complicated at higher molecules, and there are lots that aren’t fully explained yet. Typically the reactions either involve the hydrogen abstraction from the fuel (leaving the organic backbone in tact) or breaking the organic backbone. We can consider these with a typical Arhenius equation(s):
RH + O2 -> R + HO2 k1 = 1x1014 exp(-25000/T)
Or
RH -> R1 + R2 k2 = 5x1016 exp(-42000/T)
The relative rates can be expressed thus:
k1/k2 = 2x10-3 exp(17000/T)[O2]
We can see the exponential depedance on the route for reaction (which route will take place). Below 1000K we would have the first reaction taking place and above the latter. But above this temperature (where most combustion occurs) we get the chain breaking. This is a homolytic cleavage of the bond and leaves alkyl radicals. Though short lived these play an important role in pyrolysis, by either acting as a propagating step for hydrogen abstraction (then leaving it to react as an alkene) or can even sometimes form with a reactant to make a longer branched radical. Even for a simple organic molecule the decomposition is fairly complicated. Most of it being somewhat of a linear chain reaction. For example the pyrolysis of ethane:
| Reaction | Classification |
| C2H6 -> CH3 | Initiation |
| CH3 +C2H6 -> CH4 + C2H5 | Propagation (minor) |
| C2H5 -> H + C2H4 | Propagation (major) |
| H + C2H6 -> H2 + C2H5 | Propagation (major) |
| C2H5 + C2H5 -> C4H10 | Termination |
| C2H5 + C2H5 -> C2H4 + C2H6 | Termination (minor) |
(The Rice-Herzfeld mechanism is similar except it ignores the termination step and propses a new one H. + C2H5. -> C2H6 which is just reactants)
Pictorally:
The same sorts of treatments on these can be used as in straight chain reactions. One thing to notice in this reaction was the formation of C4H10, which is a common occurrence in combustion reactions. In the combustion of propane we can find butane being a common product formed.
A good exercise would be the pyrolysis of ethanal (CH3CHO). The experiments show a kinetic order of 3/2, and major products being methane and carbon monoxide.
Sources