Question 9.6.1: Calculation of a Heating Value A natural gas contains 85% me......
Calculation of a Heating Value
A natural gas contains 85% methane and 15% ethane by volume. The heats of combustion of methane and ethane at 25°C and 1 atm with water vapor as the assumed product are given below:
Calculate the higher heating value (kJ/g) of the natural gas.
Since the heating value per unit mass of the fuel is desired, we will first calculate the composition on a mass basis:
1 mol fuel \Longrightarrow \begin{matrix} 0.85 mol CH_{4} \Longrightarrow \\ 0.15 mol C_{2}H_{6} \Longrightarrow \end{matrix} \begin{matrix} 13.6 g CH_{4} \\4.5 g C_{2}H_{6}\\\hline 18.1 g total \end{matrix}
Thus x_{CH_{4}} = 13.6 g CH_{4}/18.1 g = 0.751 g CH_{4}/g fuel
x_{C_{2}H_{6}} = 1 – x_{CH_{4}} = 0.249 g C_{2}H_{6}/g fuel
The higher heating values of the components are calculated from the given heats of combustion (which are the negatives of the lower heating values) as follows:
The higher heating value of the mixture is from Equation 9.6-3:
HV= \sum{x_{i}(HV)_{i}} (9.6-3)
HHV=x_{CH_{4}}(HHV)_{CH_{4}} + x_{C_{2}H_{6}}(HHV)_{C_{2}H_{6}} \\ =[(0.751)(55.6) + (0.249)(52.0)] kJ/g =\boxed{54.7 kJ/g}