Calculating carbon intensity

calculating-carbon-intensity.md

Calculating Carbon Intensity

So terms like "oil" and "coal" are somewhat confusing, when you go to look for properties. These are names for sets of compounds that share similar, but not equivalent characteristics.

So when I went looking for the carbon intensity of oil (that is, mass ratio of CO₂ produced to fuel burned for a fuel), I found myself stymied; Wikiepedia did not have a simple number, and the papers on the subject elicited by a google search tended to avoid giving actual numbers on the subject.

Not to be discouraged, I figured you could calculate it yourself, and get something in the right ballpark.

Petroleum is made up of largely "alkanes" - molecules with this ladder-like formula:

  H H H
  | | |
H-C-C-C....-H
  | | |
  H H H

Alkanes are named for the number of carbon atoms in each molecule. You'll be familiar with many of the low-carbon molecules: methane, ethane, propane, butane, hexane, heptane, octane. "Oil" is made up entirely of those molecules that are liquid at room temperature: hexane and up. "Natural gas", by contrast, is almost entirely methane and ethane. The formula for an alkane can be derived from its carbon number (N): C_NH_{2N + 2}.

Combustion is a simple formula for almost any hydrocarbon:

a Fuel + b O₂ => c H₂O + d CO₂

For Alkanes, we can work out what a, b, c, and d are pretty concretely:

(2) C_NH_{2N + 2} + (3N + 1) O₂ => (2N + 2) H₂O + (2N) CO₂

We can then work out the masses of the fuel, oxidizer, and products on a per-mole basis, by simply substituting out the element names for their masses. (units: amu/mol)

Input Fuel: (2) * ((12 * N) + (1 * (2 * N + 2))) = 28N + 4
Input Oxygen: (3 * N + 1) * (16 * 2) = 96N + 32
Output Water: (2 * N + 2) * (1 * 2 + 16) = 36N + 36
Output CO₂: (2 * N) * (12 + 16 * 2) = 88N

Carbon intensity is then easily parsed by dividing the output CO₂ mass by the input fuel mass:

CO₂:Alkane(N) = 88N / (28N+4)

And simplifying:

CO₂:Alkane(N) = (22N)/(7N+1)

Using some basic calc, we can work out the limit of that function:

CO₂:Alkane(inf)
= lim (N->inf) (22N)/(7N+1)
= (22/7) * (lim(N->inf) N/(N+1/7))
= 22/7 ~= 3.1428

Since we know the lightest of the alkanes called "oils" is hexane (N=6), we can just run that one for our lower limit:

CO₂:Alkane(6) = (226)/(76+1) = 132/43 ~= 3.06976

TL;DR

The carbon intensity of oil is between 3.07 and 3.14 (for all linear isomers of C_nH_{2n + 2} alkanes where n>6).