Question

Calculate the emissions reduction if a natural gas power plant is converted to biogas. 81 % of the biogas emissions are absorbed by regrowing the source material.
Fuel properties:
• methane content of Natural gas: 72 %
• calorific value of methane: 55 GJ/t
• ethane content of Natural gas: 20 %
• calorific value of ethane: 51 GJ/t
• remainder of Natural gas is CO2
• methane content of biogas: 54 %
• remainder of biogas is CO2
Calculate the percentage savings (e.g., if natural gas emitted 200 units of CO2 and the resulted in a net emission of 120 units, then the percentage savings would be (200-120)/200 = 40%).
Give the answer in % rounded to the nearest ±1%

Answer 1

To solve the question, let's assume that we want to produce 100 GJ/year of energy by burning either biogas or natural gas.

Let's first calculate the amount of natural gas required to produce 100 GJ of energy:

Fuel required = Energy Required / calorific value

The first step is to calculate the calorific value of natural gas as follows:

Where,

  , , and are the calorific values of natural gas, methane, ethane and carbon di-oxide in , respectively

, and are the fractions of methane, ethane and carbon di-oxide in natural gas, respectively

We know that the mass fraction of CO2 in natural gas is (1- mass fraction of methane - mass fraction of ethane) = 1-0.72-0.54 = 0.08

Therefore,

Fuel required = Energy Required / calorific value

This implies that the amount of natural gas required:

  

Similarly for biogas:

Fuel required = Energy Required / calorific value

This implies that the amount of natural gas required:

  

The Second step is to calculate the amount of CO2 emitted by burning and of Natual gas and biogas, respectively.

Let's start by writing the combustion reaction for methane and ethane:

CH₄ + 2O₂ - > CO₂ + 2H₂O

C₂H₆ + 3.5O₂ - > 2CO₂ + 3H₂O

Therefore, each mole of methane and ethane emits 1 and 2 moles of CO2, respectively.

Let's calculate CO2 emissions from burning of Natural gas:

Amount of methane in of Natural gas is given by: . Therefore, converting this into moles of methane: (Here, I've converted tonnes into grams by multiplying by 10^6 and 16 is the molecular weight of methane).

Amount of ethane in of Natural gas is given by: . Therefore, converting this into moles of methane: (Here, I've converted tonnes into grams by multiplying by 10^6 and 30 is the molecular weight of ethane).

Therefore, Total moles of CO2 emitted by burning the natural gas = moles of CO2 emitted by burning the methane +moles of CO2 emitted by burning the ethane + moles of CO2 inherently present in natural gas

This implies Total moles of CO2 emitted by burning the natural gas = moles of CO2 emitted by burning one mole of methane * moles of methane burned + moles of CO2 emitted by burning one mole of ethane * moles of ethane burned + mass of natural gas burned * mass fraction of CO2 in natural gas/Molecular weight of CO2

This is written as follows:

Let's calculate CO2 emissions from burning of biogas:

Amount of methane in of Natural gas is given by: . Therefore, converting this into moles of methane: (Here, I've converted tonnes into grams by multiplying by 10^6 and 16 is the molecular weight of methane).

Therefore, Total moles of CO2 emitted by burning the biogas = moles of CO2 emitted by burning the methane + moles of CO2 inherently present in natural gas

This implies: Total moles of CO2 emitted by burning the natural gas = moles of CO2 emitted by burning one mole of methane * moles of methane burned + mass of biogas burned * mass fraction of CO2 in biogas/Molecular weight of CO2

This is written as follows:

Since, 81 % of the CO2 emissions from biogas burning are re-absorbed, the net emissions from biogas are as follows:

Therefore, Percentage savings by burning biogas instead of natural gas are given as :

Since, the question asks for an answer in % rounded figure, the answer is 77 %

Hope this helps!