013 part 4 – chemical kinetics of combustion and pollutants formation

8/3/2019 013 Part 4 Chemical Kinetics of Combustion and Pollutants Formation

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Part IV Chemical Kinetics ofCombustion and Pollutants Formation

2103555 Engine Emissions and Control


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Combustion Theory

Why study combustion?

combustion of fossil fuels is currently, and should remainfor the foreseeable future, the main source of the worldsenergy. It is therefore a fundamental driver of almost allhuman activity.

it is also now generally accepted that the combustion offossil fuels is the major cause of global warming via therelease of carbon dioxide CO2 into the atmosphere.Given that fossil fuel combustion is currently essential tothe world economy, the more benign use of this resourceis of increasing concern.


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Combustion Theory

Basic definitions

combustion reactions are one form of chemical reaction

1. combustion is defined as the oxidation of a fuel,with large amounts of released energy

2. the oxidiser is in most cases air (or more specifically,O2 in air) because of its abundance.

3. a fuel is any material that can be burned to releaseenergy. Hydrocarbon fuels of the form CxHy are themost common.


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Combustion Theory

Basic definitions

many hydrocarbon fuels are mixtures of many differenthydrocarbons although they mainly consist of thefollowing:

gasoline ~ octane, C8H18 diesel ~ dodecane, C12H26

methanol = methyl alcohol, CH3OH

LNG (liquefied natural gas) ~ methane, CH4 LPG (liquefied petroleum gas) ~ propane,

C3H8


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Combustion Theory

Composition of air

on a molar (or volume) basis, dryair iscomposed of: 20.9% oxygen O2

78.1% nitrogen N2 0.9% CO2, Ar, He, Ne, H2, and others

a good approximation of this by molar or volume

is: 21% oxygen, 79% nitrogen thus, each mole of oxygen is accompanied

0.79/0.21 = 3.76 moles of nitrogen.


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Combustion Theory

Composition of air

at ordinary combustion temperatures, N2 is inert,but nonetheless greatly affects the combustionprocess because its abundance, and hence its

enthalpy change, plays a large part indetermining the reaction temperatures.1. this, in turn, affects the combustion chemistry, as we

shall see later.

2. also, at higher temperatures, N2 does react, formingspecies such as oxides of nitrogen (NOx), which are asignificant pollutant.


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Combustion Theory

Stoichiometry and air/fuel ratios

the amounts of fuel and air taking part in a combustionprocess are often expressed as the air to fuel ratio:

where:

mfuel, mair = mass of fuel or air (kg),

equivalent, and widely used, terms to the AFRare thefuel/air ratio FAR, the equivalence ratio, , and thelambda ratio :

stoichFAR

FAR1

==

fuel

air

m

m

AFR =


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Combustion Theory

Thermodynamics of Combustion When molecules undergo chemical reaction, the reactantatoms are rearranged to form new combinations. Thechemical reaction can be presented by reaction

equations. However, reaction equations represent initialand final results and do not indicate the actual path ofthe reaction, which may involve many intermediate stepsand intermediate species. This approach is similar to

thermodynamics system analysis, where only end statesand not path mechanism are used. The dissociation of the products into species with a

higher enthalpy of formation occurs in many combustion

reactions of practical importance. In such cases, thetemperature of the products is lower than theundissociated temperature, because some of the energyreleased by the original combustion reaction is absorbed

by endothermic, dissociative reactions.


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Combustion Theory

Thermodynamics of Combustion The concept of chemical equilibrium must be introduced

in order to quantify the degree of dissociation.

Chemical equilibrium occurs when the Gibbs freeenergy of a chemical mixture is at a minimum i.e. therehas been sufficient time for all reactions to reach

completion. This latter condition may seem ratherrestrictive in many combustion reactions of practicalimportance, such as those involving the transient flow of

fuel and air through an internal combustion engine. However, combustion reactions are generally very fast,

and equilibrium or near equilibrium is achieved in many

cases.


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Chemical Equilibrium

To obtain thermodynamic equilibrium, it is necessary tohave complete equilibrium between the molecularinternal degrees of freedom, complete chemicalequilibrium, and complete spatial equilibrium.

Internal molecular energies are the way that moleculesstore energy.

The major form of energy for polyatomic molecules are translational, vibrational, and rotational energy,

electronic energy excitation, and nuclear spin.

For most engineering combustion application it is safe toassume equilibrium among the internal degree offreedom.


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One case where it is not safe to assume equilibrium is inshock waves.

The times for relaxation of the various internal degreesare typically:

translation 10-13 s,

rotation 10-8s, and

vibration 10-4 s.

Thus, for a very sudden change in temperature therotational energy will not reach equilibrium until about10-8s and the vibrational until about 10-4 s.

Therefore, the translational energy will briefly overshootthe equilibrium value, and one cannot strictly assumeinternal equilibrium until 0.1 ms has elapsed.


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Chemical equilibrium is achieved for constanttemperature and pressure systems when the rate ofchange of concentration go to zero for all species.

In a complex reaction some species may come to

equilibrium rapidly due to fast reaction rates or a verysmall change in concentration, while others approachequilibrium more slowly.

For example, consider the flow of high-temperature

hydrogen in a nozzle. Suppose that at the stagnationtemperature the hydrogen is all dissociated to H atoms. If the expansion is very slow, the reaction 2H ---> H2 will

follow the dropping temperature rapidly enough to give a

series of equilibrium values (called shifting equilibrium). If the expansion is very rapid, hardly any reaction can

occur and the result will be an essentially constantconcentration of H atoms (frozen equilibrium).


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Between these two extremes the concentration will bedetermined by the rate of reaction and is said to bekinetically limited.

This is important because chemical equilibrium does not

exist in the flame zone. In the flame zone, temperature gradient are very steep

and many short lived species are found there.

In the postflame zone, many of combustion products arein chemical equilibrium or possibly shifting equilibrium.

An example of practical interest is nitrogen oxide

production. The major species may follow an essentially equilibriumpath while the NO reacts too slowly to stay in equilibriumas the temperature is lowered by heat transfer or

expansion.


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Chemical Equilibrium Criterion Thermodynamics alone cannot determine what species

may be in the product mixture.

However, given an assumed set of constituents,thermodynamics can determine the proportion of eachspecies which exist in the equilibrium mixture.

Once the composition is determined, thethermodynamics properties of the mixture, such asu,h,etc., may be calculated.


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Chemical Equilibrium Criterion

For a system of J species in chemical equilibrium, thepressure and temperature do not change, equilibriumcriterion may be specified by stating that the Gibbs freeenergy of the system (G=H-TS)does not change.

(1)

Where(2)

And where . Since

(3)

and (4)

( ) 0,

=pT

dG

==J

j jjgNG

1

jjj sThg ==

=

o

jo

jjppRss ln

dtT

cs

T

T

po

j

o

=


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Chemical EquilibriumChemical Equilibrium Criterion

the Gibbs free energy for species j can be written as


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The equilibrium constant at constant pressure Kpis nota functionof the total pressure, but onlya function of temperature.

When solving for equilibrium products using Eq. 13, the reactions tobe considered are identified, and the equilibrium constants areevaluated at the specified temperature.

Then the atom balance constraints are specified for the system andan equilibrium equation is written for each of the specified reactions

using the form of Eq. 12. This set of equations is solved simultaneously to obtain the species

mole fractional and other thermodynamic properties of the system.


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For combustion products, important gas phase equilibrium reactionsinclude:

Reactions (i), (ii), (v), (vi), and (vii)are dissociation reactions.

Reaction (iii)is the so called water-gas shift reaction.

Reaction (iv)accounts for equilibrium OH formation, which is animportant species in chemical kinetics reactions.

Reaction (viii)accounts for equilibrium NO, an important air pollutant.

C


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An example of the thermodynamic equilibrium productsfrom kerosene-air combustion is shown in Figures 1 and 2.

Major products of lean combustion are H2O, CO2, O2, andN2; and for rich combustion the major products are H2O,CO2, CO, H2, and N2.

At stoichiometric conditions at the flame temperature O2,

CO, and H2 are present, whereas for the assumption ofcomplete combustion, i.e., no dissociation, these threespecies are zero.

Minor species equilibrium of combustion products at theflame temperature includes O, H, OH, and NO.

Carbon monoxide is a minor species in lean products,

while O2 is a minor species in rich products.

Ch i l E ilib i


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Figure 1 Equilibrium composition and temperature for adiabatic combustionof kerosene (CH1.8) as a function of equivalence ratio.

Ch i l E ilib i


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Figure 2 Variation of equilibrium composition with temperature forstoichiometric combustion of kerosene, CH1.8

Ch i l E ilib i


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Several thermodynamic equilibrium calculations can alsobe done with a calculator rather than with a computer asshown in an example given below.

The equilibrium constant method is used because it isconceptually and computationally straightforward whenonly one equilibrium reaction is involved.

An example on using the method of minimizing Gis alsogiven.

P ti f C b ti P d t


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Properties of Combustion Products

P ti f C b ti P d t


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The effect of dissociation is not large except at hightemperatures.

This is illustrated in Figure 3, where enthalpy is plotted

versus temperature for a product of a stoichiometric methaneand air reaction.

The line of constant pressure coincides at lower temperaturewhere dissociation is small.

At higher temperature the changing composition due todissociation cause the lines of separate.

For a fixed temperature, dissociation is largest at lowpressure and becomes quite small at very high pressures.

In general, Le Chateliers rule states that if the moles ofproducts exceed the moles of reactants, then an increase inpressure decreases the dissociation as shown by Eq. 12.



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Figure 3 Absolute enthalpy of products from stoichiometricmethane-air reaction.



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Properties of Combustion Products Figure 3 can be used illustrate the effects of dissociation on a simple

adiabatic throttling process. Neglecting changes kinetic energy, h1 = h2. If enthalpy is a function

of Tonly, then T1 = T2. This is true for the ideal gas mixture of Figure 3 in the nondissociated

region. However, at the higher temperatures the moles fraction of the ideal

gas constituents vary with both Tand p, so that his a function of bothTand p.

Throttling cause a drop in pressure resulting in some energy being

used to break molecular bonds and lowering the downstreamtemperature.

For example, throttling the products in Figure 3 from 3000 K and 150atm to 1 atm gives a downstream temperature of 2700 K.

Note that this energy is recovered by a constant pressure coolingprocess to a nondissociated state provided that we assume shiftingequilibrium.

The processes do however cause a loss in available energy. Becausethe throttled gas may go from state 1 to state 2 in a very short time

the assumption of shifting equilibrium may not hold for all species.

013 part 4 – chemical kinetics of combustion and pollutants formation

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