There are two popular comparisons of greenhouse gas effects of leaked methane versus CO2 from burning fossil fuel. They involve 20 or 100 year periods, and comparison of the gasses for the same weight.
Neither time period has a basis in actual warming and lifetimes of the gases. Even worse, the number of greenhouse molecules produced is not directly equal to the actual weight of the gases. The real comparison should be on the basis of the lifetime of CO2 in the atmosphere, which is several hundred years, not a hundred. It should also be on the basis of the ratio of energy generated by each source, and the number of molecules produced in burning or as leaked “fugitive” gas. Then this should be compared by the relative generation of energy per molecule of methane versus carbon atom in coal. Then we can figure out what percent of leakage of methane with new efficient methane plants would match the greenhouse warming of just using coal in present old plants. Keeping methane leakage to a small fraction of the limit would lead to only 28% greenhouse gas effect per unit energy than the coal pollution it would replace, as shown in the previous post in this blog.
On a hundred year basis, including effects of aerosols, for the same gas weights, methane is said to be 34 times as warming as CO2. The hundred year period was arbitrarily chosen for long lived CO2, but its true lifetime is several hundred years and unknown. We will call its actual lifetime a constant “tc” times 100 years (see footnote).
Methane, CH4, has a lifetime of 12 years in the atmosphere, where Oxygen or OH radicals convert it to a molecule of CO2 and water. Its short lifetime has already been factored into its comparison with CO2 by unit weight, on the hundred year basis, to give the factor of 34. Despite the short lifetime, it takes around 60 years for the pulse of CH4 to reduce enough to match the greenhouse gas effect of an equivalent number of CO2 molecules.
We now convert the ratio for both CH4 and CO2 per carbon atom from the ratio per weight. A molecule of CO2 has an atomic weight C:12 + O:16 + O:16 = 44. So CO2 has one carbon atom per 44 units of weight: 1C/44 wt. A molecule of CH4 has an atomic weight C:12 + 4xH:1 = 16. So CH4 has one carbon atom per 16 units of weight: 1C/16 wt.
Converting the greenhouse ratio by weight of (34 / wt CH4) / (1 / wt CO2) by multiplying (16 wt CH4 / C) / (44 wt CO2 / C) = 34 x 16 / 44 = 544 / 44 = 12.36. Thus the greenhouse ratio per contained C atom is about 12.4.
With “tc” being the number of centuries for CO2 to be disposed of, the greenhouse ratio per contained C atom is about
R = 12.4 / tc.
The approximation of just dividing by tc is only approximate, for small tc. For example, for a 500 year CO2 lifetime (tc = 5), the initial greenhouse gas factor of CH4 to CO2 is reduced from 25 to 7.6, or by the factor 0.30, not 0.20, as the simple formula would indicate. The formula would be correct for the excess warming by the initial CH4 pulse, before the C in it got converted to CO2.
The question we now have is what amount of leakage of methane will just balance the savings of CO2 pollution from replacement of coal plants by natural gas plants. This depends on the relative efficiencies of the two types of plants, and the fact that one CH4 molecule burns to about the same energy as two carbon atoms, and therefore makes half the CO2, if their respective plants had the same efficiency.
In the previous post we showed that replacing an old coal plant at 33% efficiency with a new combined cycle natural gas plant at 60% efficiency, reduced CO2 down to 28%, rather than just 50%. So for each 100 coal atoms we burn, we only have to burn 28 CH4 atoms, each of which makes a CO2 molecule. Another way to say this, is that if there is not CH4 leakage, greenhouse gas pollution can be reduced by 72% by replacing old coal plants with new combined cycle natural gas plants.
We then ask how many fugitive CH4 atoms can we tolerate to restore us back to the same effective greenhouse gas emissions as the 100 coal atoms. The difference is 100 – 28 = 72 CO2 molecules missing from the CH4 burning. But each fugitive CH4 molecule is equivalent to 12.4/tc CO2 atoms in greenhouse strength. So we divide the 72 CO2 molecules by 12.4/tc = 5.8 * tc molecules. The fraction of fugitive methane to the 28 burned methane molecules at break-even is then
Feven = 5.8 * tc / 28 = 0.21 * tc.
So we can tolerate 21% x tc leakage and still break even in our replacement of an old coal plant with a new combined cycle natural gas plant. This is far greater than the 4% or 3% leakage break-even fraction calculated with the old naive pollution ratio of 25 or 34 in the useless units.
As an example, if leakage is 10% and tc is 2 for 200 years CO2 retention, the fraction of Feven is
f = 0.10 / (0.21 * 2) = 0.10 / 0.42 = 0.24,
or 24% of the break-even is leaked away. So the greenhouse savings of 72 CO2 molecules has to be reduced by 24% to 55 molecules, meaning there is a savings of 55% greenhouse gases over just the old coal burning plant. So instead of 3% or 4% leakage being the old break-even point, even 10% leakage now could give us the near 50% savings as with no leakage in the old, incorrect calculation. No leakage in the new calculation gives us 72% savings in greenhouse gases.
We give a table of greenhouse gas emission reductions for CO2 lifetimes of 100 years and 200 years, and leakage rates of 0%, 3%, 5%, and 10%.
Greenhouse Gas Emission Reductions Converting Old Coal to New Natural Gas Plants:
|CH4 Leakage -
|CO2 100 years lifetime
|CO2 200 years lifetime
Richard Muller, of UC Berkeley, in “Fugitive Methane and Greenhouse Warming” has a similar argument, and comes up with a 14% fugitive cap, below which warming is reduced for the same energy produced. He only considers the 100 year CO2 period, but also includes the added efficiency of new combined cycle natural gas plants at 60%, versus new efficient coal plants at 43%. He also has general formulas for calculating the cap including plant efficiency and general greenhouse gas ratios.
Footnote: The CO2 is actually absorbed by carbon incorporated into phytoplankton grown in the top ocean layer that then falls to be sequestered at the bottom of the ocean. Since growing ocean acidity is already making the growth of oyster shells difficult, increasing acidity will cause less plankton to form and increase the lifetime of CO2. This is a positive feedback to the amount of greenhouse gases. It also makes the lifetime of CO2 releases today actually unknown, and dependent on how much we slow greenhouse gas production.