Course Outline

Fundamentals and Combustion Systems

Part I• Chemical Equilibrium• Chemical Kinetics• Fuels

Part II• Flames• Gas-Fired furnace combustion• Premixed-charge engine combustion

Part III• Spray formation and droplet size• Oil-fired furnace combustion• Gas turbine spray combustion

Dr Hatem Omar

Dr Essam Abo-Serea

Prof. Abdel Motalb

Dissociation and Equilibrium

Objectives

The objectives of this Lecture are:

· To present the concept of dissociation.

· To introduce the concept of equilibrium constants.

· To calculate the composition of combustion products at equilibrium.

Chemical equilm occurs when a reaction and its reverse reaction proceed at the same rate.

In a system at equilibrium, both the forward and reverse reactions are being carried out; as a result, we write its equation with a double arrow N2O4 (g) 2 NO2 (g)

Concept of Equilibrium

Introduction

Dissociation and Equilibrium

We use combustion in order to release heat and then, for example, to drive

a turbine or move a piston. As engineers, we want to know the

temperature that the combustion products will have and the heat release.

An estimate was done in the previous academic year, by using the products

of complete combustion. Unfortunately, chemical equilibrium of the flame

products affects the species mass fractions and hence, by virtue of the First

Law, the adiabatic flame temperature will be different than that calculated

by assuming complete combustion. Hence the products composition needs

to be studied in detail. In this way, we can also make an estimate of the

amount of major pollutants (NO and CO) released from combustion.

DissociationAt high temperatures, the main products of combustion will

decompose or dissociate into other species. For example, complete

combustion of hydrocarbons with air gives CO2, H2O, N2 (and O2 if

lean) as products. But dissociation of these and reactions between

the resultant species from the dissociation may lead to many other

species, for example O, H, OH, N, NO, and others.

Dissociation and Equilibrium

Important dissociation reactions are:

Dissociation

Dissociation and Equilibrium

and we will use some of these to introduce the concept of equilibrium later.

Dissociation of a molecule occurs at high temperatures because it is only

then that significant numbers of the molecules have enough kinetic energy

during a collision to break one or more internal bonds. At typical

combustion temperatures, dissociation affects mostly CO2 and H2O,

although other species will also be affected at higher temperatures. The

presence of CO and H2 in the products means that oxidation is not complete

and hence that the final temperature is less than the adiabatic flame

temperature calculated based on the products of complete combustion.

Description of Chemical equilibrium concept

Dissociation and Equilibrium

Consider an adiabatic closed box filled with CO and O2 in stoichiometric

proportion. No other species are present initially. As the reaction

proceeds, more and more CO2 will appear. Experiment, however, shows

that the reaction stops before all the CO and O2 disappears, because

dissociation of CO2 (back towards O2 and CO) begins. Hence there is a

point where reactants and products coexist in equilibrium and their

concentrations do not change any more.

In the language of Thermodynamics, chemical equilibrium is a Second-Law

concept. For the system above, the equilibrium point will be the one that

gives the maximum entropy of the whole mixture

CO + O2CO +O2

decrease

CO2

increaseCO + O2 + CO2

initially As reaction proceeds At Equilibrium

Only reactants existIn the vessel at startOf reaction

As reaction proceedsReactants decrease and Products increase

At Equilm, reaction stopsand no change in compositions for reactants and products

Dissociation and Equilibrium

Description of Chemical equilibrium concept

Criteria for chemical equilibrium for a fixed mass at a specified temperature and pressure.

Equilibrium criteria for a chemicalreaction that takes place adiabatically.

Chemical equilibrium criterion

Dissociation and Equilibrium

Equilibrium constantsConsider a fixed-mass isothermal, constant pressure system with many species.

The criterion for equilibrium is: dGmix=0 at const P,T and mass (3.1)

Remember Gibbs energy is the capacity of a system to do non-mechanical work and ΔG measures the non-mechanical work done on it. Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium

with G=H-TS, the Gibbs free energy or Gibbs function. For a mixture of

N species containing ni kmols of each, (3.2)

(3.3)

Dissociation and Equilibrium

Using Eqs. (3.2) and (3.3) in (3.1), the condition for equilibrium of the mixture becomes

The second term is zero since the pressure and temperature are constant and hence (3.4) becomes

(3.4)

Now, we bring in the fact that the species are engaged in a chemical reaction. Take the general equilibrium reaction

(3.5)

Substituting in (3.5), we obtain

a1R1 + a2R2+.... b1P1 + b2P2 + ….

Dissociation and Equilibrium

with the definitions

The quantity Kp is called the equilibrium constant for the particular reaction

(3.7)

(3.6)

𝐾 𝑃=𝑋𝑃 1

𝑏1 𝑋𝑃 2𝑏2 ....

𝑋𝑅1𝑎1 𝑋𝑅 1

𝑎1 .... ( 𝑃𝑚

𝑃 0 )∑𝑖 𝑏𝑖−∑𝑖𝑎𝑖

Dissociation and EquilibriumFeatures of Kp

1- From Eq. (3.6), since the standard Gibbs functions are a function of temperature only, the

equilibrium constant Kp is also a function of temperature only.

2- It is tabulated for various reactions (not only for dissociation reactions).

Dissociation and Equilibrium

Equilibrium products for Hydrocarbon combustion

Dissociation and Equilibrium

If we specify the pressure and consider only eleven product species,

there are twelve unknowns: the temperature and the species

concentration coefficients b to o. We have four equations from the atom

balances and one equation from the first law of thermodynamics.

Equilibrium products for Hydrocarbon combustion

We therefore need seven chemical equilibrium relationships among the various product species. An acceptable set is given by Eqns. ER1-ER7:Also we have the first law of thermodynamics (the energy equation). If T is specified, Q – W is unknown. If Q - W is specified, T is unknown.

Dissociation and EquilibriumEquilibrium products for Hydrocarbon combustion

Equilibrium Products of Hydrocarbon Combustion: Temperature & Major Species

for low temperature (<1800 K) systems with negligible dissociation

Equilibrium products for Hydrocarbon combustion

Solved Example