1. SINGLE STEP AND MULTISTEP MECHANISM FOR METHANE COMBUSTION
BY SHREYA RAJE

2. MOTIVATION PROJECT GOAL
Different Fuels are now a days being introduced in the automotive industry because of shortage of the present natural resources and also because of the rising prices of the present fuels. These newly introduced fuels should be tested for their rise in temperature and pressure during the combustion process. This had motivated me to choose natural gas to compare with Diesel. But as the mechanism was complex, I consider methane for my project as it contributes highest percentage in natural gas.
Many researches are going in finding the efficiency of the engines as well as reduction of NOx emission using natural gas as a fuel.
PROJECT GOAL
To find the molar concentration of species, temperature and pressure for single step and multistep mechanism of methane combustion.

3. OBJECTIVE Approach To find The temperature rises Pressure Rises
Molar concentrations
Approach
Literature Review
Physical Model
Mathematical Model
Result and Conclusion

4. LITERATURE REVIEW
Turns, An introduction to combustion
This helped in understanding the constant volume reactor as well as gave me structure of single step mechanism.
Glassman, Combustion
This was relevant for basic understanding of chemical kinetics.
C C Pounder, Marine Diesel Engines
This was relevant because I could get the engine specifications as well as operation of engine.
Crina I. Heghes, C1-C4 Hydrocarbon Oxidation Mechanism
This was relevant because it had the reaction kinetics of different hydrocarbons
LIM Pei Li, The Effect of Compression Ratio on the CNG-Diesel Engine
Le Corre Olivier, Nox emissions reduction of a natural gas SI Engine under lean conditions: comparison of the EGR and RGR concepts.

5. PHYSICAL MODEL Valve Top dead centre (TDC) Spark Plug
Engine Specifications:
Wartsila DF 50
Cylinder Bore – 500 mm
Stroke – 580 mm
Engine Speed – 580 rpm
Compression ratio - 15
T0,P0 , P1,T1
T0= T1, P0=P T2,P2
Spark Plug
T0= T2 ,P0=P T3,P3
Bottom dead centre (BDC)
Cylinder
Piston

6. MATHEMATICAL MODEL CH4 +2O2 CO2 +2H2O ф=1 INITIAL CONDITIONS:
Inlet temperature and Pressure= 298 K, 1 atm
Mole Fractions- χCH4, χO2 ,
χCO2, χH2O = 0
T0=TBDC *(compression ratio)γ-1
P0=PBDC*(compression ratio) γ
[CH4]0 = χCH4 *P0/RT0
[O2]0 = χO2 *P0/RT0
[CO2]0 = 0 , [H2O]0 = 0

7. MATHEMATICAL MODEL Single step Mechanism
(A/F)s=(Nair/NCH4)*(MWair/MWCH4)
Assumptions:
Adiabatic (Q/V)=0
Reaction Rates are as follows:
d[CH4]/dt=-A*exp(-Ea/RTi)[CH4]m[O2]n
d[O2]/dt=-(A/F)s*(MWCH4/MWO2)*A*exp (- Ea/RTi)[CH4]m[O2]n
d[CO2]/dt= ((A/F)s+1)*(MWCH4/MWCO2)*A*exp (- Ea/RTi)[CH4]m[O2]n
d[H2O]/dt= ((A/F)s+1)*(MWCH4/MWH2O)*A*exp (-Ea/RTi)[CH4]m[O2]n
dT/dt= RTi∑ ẁi - ∑(hiẁi)/(∑[Xi](Cpi-R))
dP/dt= RTi∑ ẁi + R∑[Xi] dT/dt
Here A, Ea, m, n are taken from table 5.1 from Turns.
Cp and enthalpy varies with varying temperature and volume.

8. MATHEMATICAL MODEL
Multi Step Mechanism
This is taken from Glassman Appendix B. There are 11 reactions and 17 species involved.
Here we know the initial concentration of fuel and oxidizer and also the kf . kb is calculated using the formula
Kp= kf /kb
where Kp = (NcυcNdυd)/(NaυaNbυb ) *(P/∑N) υd+ υc- υb-υa
Concentration of intermediate and final species is taken zero initially
Species are CH4, CH3, H, H2, O, OH, H2O, O2, HO2, H2O2, HCO, CO, CH2O, CH3O, CH3OH, CH2OH, CH2
dT/dt and dP/dt are solved using earlier equations.

9. MATHEMATICAL MODEL
These equations of Single as well as Multi Step mechanism are integrated numerically using Matlab ODE 45 function.
k, kf , kb also varies with temperature.

10. Molar Concentration for Single Step Mechanism
H2O
CO2 O2
CH4
Within 2 milliseconds molar concentration of fuel and oxidizer are converted to products

11. Temperature for Single Step Mechanism
The adiabatic temperature attained is approximately 3990 K

12. Pressure for Single Step Mechanism
The pressure reaches is approximately 7.5x107 N/m2

13. CONCLUSION
For single step mechanism as the temperature, pressure and volume are updated each time the conversion of fuel to product takes place at a faster rate.
At the same time there is an increase in adiabatic temperature and pressure.
In terms of improvement, multistep mechanism needs to be more worked on for Matlab coding. Also this can be extended for varying ф.
I would like to extend this by taking all the components present in the natural gas and try to find the molar concentrations, temperatures and pressures attained in actual gas engines.