Course Outline

1. Fundamentals and Combustion Systems Course Outline • Part I • Chemical Equilibrium • Chemical Kinetics • Fuels • Part III • Spray formation and droplet size • Oil-fired furnace combustion • Gas turbine spray combustion Dr Hatem Omar Prof. Abdel Motalb • Part II • Flames • Gas-Fired furnace combustion • Premixed-charge engine combustion Dr Essam Abo-Serea

2. 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.

3. N2O4 (g) 2 NO2 (g) Concept of Equilibrium Chemical equilmoccurs 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

4. Dissociation and Equilibrium Introduction 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.

5. Dissociation and Equilibrium Dissociation At 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 O2if 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. Important dissociation reactions are:

6. Dissociation and Equilibrium Dissociation 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.

7. Dissociation and Equilibrium Description of Chemical equilibrium concept 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

8. Dissociation and Equilibrium Description of Chemical equilibrium concept CO2 increase CO +O2 decrease initially As reaction proceeds At Equilibrium CO + O2 + CO2 CO + O2 At Equilm, reaction stops and no change in compositions for reactants and products As reaction proceeds Reactants decrease and Products increase Only reactants exist In the vessel at start Of reaction

9. Chemical equilibrium criterion Equilibrium criteria for a chemical reaction that takes place adiabatically. Criteria for chemical equilibrium for a fixed mass at a specified temperature and pressure.

10. Dissociation and Equilibrium Equilibriumconstants Consider 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) with G=H-TS, the Gibbs free energy or Gibbs function. For a mixture of N species containing nikmols of each, (3.2) (3.3) 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

11. Dissociation and Equilibrium Using Eqs. (3.2) and (3.3) in (3.1), the condition for equilibrium of the mixture becomes (3.4) The second term is zero since the pressure and temperature are constant and hence (3.4) becomes (3.5) Now, we bring in the fact that the species are engaged in a chemical reaction. Take the general equilibrium reaction a1R1 + a2R2+.... b1P1 + b2P2 + …. Substituting in (3.5), we obtain

12. Dissociation and Equilibrium (3.6) with the definitions (3.7) The quantity Kp is called the equilibrium constant for the particular reaction

13. Dissociation and Equilibrium Features 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).

14. Dissociation and Equilibrium Equilibrium products for Hydrocarbon combustion

15. Dissociation and Equilibrium Equilibrium products for Hydrocarbon combustion 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.

16. Dissociation and Equilibrium 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.

17. Equilibrium Products of HydrocarbonCombustion: Temperature & Major Species

18. Equilibrium products for Hydrocarbon combustion for low temperature (<1800 K) systems with negligible dissociation

19. Solved Example