Post on 22-Dec-2015
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