Question

Natural gas consists of a mixture of several gases. One example is 84% methane, 14.8 ethane, 0.7% carbon dioxide and 0.50% nitrogen by volume. Calculate the specific heats, the molecular weight and the k value of the mixture

Answer 1

For methane, specific heat at constant pressure Cp = 2.22 kJ/kg/K

For ethane, specific heat at constant pressure Cp = 1.75 kJ/kg/K

For CO2, specific heat at constant pressure Cp = 0.844 kJ/kg/K

For N2, specific heat at constant pressure Cp = 1.04 kJ/kg/K

For methane, specific heat at constant volume Cv = 1.70 kJ/kg/K

For ethane, specific heat at constant volume Cv = 1.48 kJ/kg/K

For CO2, specific heat at constant volume Cv = 0.655 kJ/kg/K

For N2, specific heat at constant volume Cv = 0.743 kJ/kg/K

For methane, k = 1.304

For ethane, k = 1.187

For CO2, k = 1.289

For N2, k = 1.4

For methane, molecular weight = 16 kg/kmol

For ethane, molecular weight = 30 kg/kmol

For CO2, molecular weight = 44 kg/kmol

For N2, molecular weight = 28 kg/kmol

Quantity of methane in 1 kmol of natural gas = 0.84 * 16 = 13.44 kg

Quantity of ethane in 1 kmol of natural gas = 0.148 * 30 = 4.44 kg

Quantity of CO2 in 1 kmol of natural gas = 0.007 * 44 = 0.308 kg

Quantity of N2 in 1 kmol of natural gas = 0.005 * 28 = 0.14 kg

Total quantity = 13.44 + 4.44 + 0.308 + 0.14 = 18.328 kg

Mass fraction of methane = 13.44 / 18.328 = 0.733

Mass fraction of ethane = 4.44 / 18.328 = 0.242

Mass fraction of CO2 = 0.308 / 18.328 = 0.017

Mass fraction of N2 = 0.14 / 18.328 = 0.008

Cp of natural gas = 2.22 * 0.733 + 1.75 * 0.242 + 0.844 * 0.017 + 1.04 * 0.008 = 2.074 kJ/kg/K

Cv of natural gas = 1.7 * 0.733 + 1.48 * 0.242 + 0.655 * 0.017 + 0.743 * 0.008 = 1.622 kJ/kg/K

k of natural gas = 1.304 * 0.733 + 1.187 * 0.242 + 1.289 * 0.017 + 1.4 * 0.008 = 1.276

Molecular mass of natural gas = 16 * 0.733 + 30 * 0.242 + 44 * 0.017 + 28 * 0.008 = 19.954 kg / kmol