Combustion Process
The combustion process typically involves the burning of a hydrocarbon along with on oxidizer. Most commonly the oxidizer used is atmospheric air, which consists of 21% oxygen and 79% nitrogen on a molar basis. As such, for every mole of oxygen in air there are a matching 3.76 moles of nitrogen. The presence of nitrogen in air can become a problem at high temperatures where it can form harmful substances with other reacting chemicals.
The general form for a combustion reaction with air is as follows:
C_xH_y+a(O_2+3.76N_2)\to bCO_2+cH_2O+3.76aN_2
The moles of air required per mole of fuel is therefore:
n_{air}=4.76(x+0.25y)
The air-fuel ratio can be defined in terms of moles or mass:
AF_{mass}=\dfrac{m_{air}}{m_{fuel}}
AF_{mol}=\dfrac{n_{air}}{n_{fuel}}
AF_{mass}=AF_{mol}\dfrac{M_{air}}{M_{fuel}}
- Theoretical Air: The amount of air required to theoretically complete the combustion process.
- Excess Air: The amount of extra air required to actually complete the combustion process. Can also be used to control the reaction temperature.
Enthalpy of Formation
Application of the first law upon a simple combustion process will result in the following:
Q+H_R=H_P
Where H_R denotes the enthalpy of reactants and H_P denotes the enthalpy of products.
\displaystyle H_R=\sum_R n_i\bar{h}_i
\displaystyle H_P=\sum_P n_e\bar{h}_e
Since enthalpy is measured from an arbitrary reference point we can assume that H_R=0. The following is measured when assuming zero reactant enthalpy for the formation of carbon dioxide:
C+O_2=CO_2
\dfrac{Q}{n_{CO_2}}=\dfrac{H_{CO_2}}{n_{CO_2}}=-393522\text{ kJ/kmol}
Since Q is negative the reaction is releasing heat to the surrounding environment. The resulting measurement is termed the enthalpy of formation:
\bar{h}^0_{f,CO_2}=-393522\text{ kJ/kmol}
The enthalpy of formation is dependent on the product as well as the pressure and temperature at which the reaction takes place. Atmospheric conditions, superscript 0, are atmospheric pressure and 25 degrees Celsius.
\bar{h}_{T,P}=\bar{h}_f^0+(\bar{h}_f-\bar{h}_f^0)_{T,P}
\bar{h}_{T,P}=\bar{h}_f^0+\Delta\bar{h}_{T,P}
The enthalpy of formation for a substance is tabulated in any standard thermodynamics textbook.
A couple notes on enthalpy of formation:
- \bar{h}_f^0=0 for pure elements like C, O_2, H_2, N_2, S
- The enthalpy of formation for stable compounds is negative and for unstable compounds is positive
Enthalpy and Internal Energy of Combustion
The enthalpy of combustion is the heat released when combusting a fuel, therefore it is the difference between the enthalpies of products and reactants.
H_{RP}=H_P-H_R
\displaystyle H_{RP}=\sum_Pn_e(\bar{h}_f^0+\Delta\bar{h})_e-\sum_Rn_i(\bar{h}_f^0+\Delta\bar{h})_i
Similar to the enthalpy of combustion, the internal energy of combustion is defined as the difference in product and reactant internal energies.
U_{RP}=U_P-U_R
\displaystyle U_{RP}=\sum_Pn_e(\bar{h}_f^0+\Delta\bar{h}-P\bar{\nu})_e-\sum_Rn_i(\bar{h}_f^0+\Delta\bar{h}-P\bar{\nu})_i
For ideal gases we can utilize the ideal gas law:
\displaystyle U_{RP}=H_{RP}-\bar{R}T
Heating value refers to the amount of heat transferred during combustion at a constant temperature. The higher heating value is the heat transferred by the liquid portion of product water. Likewise, the lower heating value is the heat transferred by the gaseous portion of product water.
Adiabatic Flame Temperature
The adiabatic flame temperature (AFT) is the corresponding product temperature for a combustion process when W=0, Q=0, \Delta KE=0, and \Delta PE=0. The AFT decreases as excess air increases.