How much water has been created by burning fossil fuels?

A back-of-the-envelope calculation

I was out walking other day and a seaplane flew overhead. My mind did some somersaults and out popped a question: How much more water exists on earth today as a result of burning fossil fuels?

For good reason CO2 is the product of fossil fuel burning that is primarily talked about, but another product of combustion of petroleum-based fuels and natural gas is H2O. So, I figured I'd do some back of the envelope calculations to estimate the volume of water generated from burning fossil fuels. There are a lot of approximations in here so the only thing certain about the answer is that it's wrong to some degree.

Let's do some sums.

How much water does combustion generate?

There are two main sources of H2O-generating combustion: burning natural gas, and burning petroleum-based (liquid) products.

Gasoline combustion (other petroleum fuels vary, but have similar chemical equations)

C8H18 + 12.5 O2 → 8 CO2 + 9 H2O

Natural gas combustion

CH4 + 2O2 → 2H2O + CO2

So for petroleum combustion H2O is produced roughly 1:1 with CO2, but for natural gas the ratio is 2:1.

Cool, so how much CO2 has man emitted by burning fossil fuels in total?

Total CO2 emissions since 1850

Sources [1] [2] estimate that mankind has added on the order of 1500 gigaton of CO2 to the atmosphere since the beginning of the industrial revolution. Now, this has been generated not only by burning petroleum, but also coal which doesn't really produce a whole lot of H2O. For this estimation we'll assume that the 50% of the total CO2 was generated by burning coal, the rest petroleum and natural gas [3].

Mass of water generated from liquid & gas combustion

With the 50% approximation above, this leaves us with 750 gigaton (7.5 x 1014 kg) of CO2 from liquid (petroleum) and gas sources.

The mass of a CO2 molecule is 44 atomic units (or 44 x 1.66 x 10-27 kg). Therefore, the total number of CO2 molecules created from burning solid and liquid fossil fuels is (7.5 x 1014) / (44 x 1.66 x 10-27) = 1040.

Of this, ~40% was generated from gas combustion, and 60% from petroleum fuels [4]. On aggregate, we can then say that each CO2 molecule generated from burning liquid and gas fossil fuels has created 1.4 H2O molecules (40% x 2 + 60% x 1). This means a grand total of 1.4 x 1040 H2O molecules have been created from burning fossil fuels.

The mass of an H2O molecule is 18 atomic units, or 3 x 10-27 kg. So the total mass of water created is 0.4 gigaton.

Is that a lot?

0.4 gigaton seems like quite a lot, but it's also a lot less than the mass of CO2 generated (1500 gigaton). Let's try and visualise this amount of water as volume.

The density of water is 1000 kg / m3, so 0.4 gigaton of water is equivalent to 400 km3. That's a 400 km high column of water with a cross-section of 1 m2.

Put another way, if you were to dump it all on the United States (and assumed it didn't immediately run into the sea, it would cover the entire country in 4 cm of water.

Put yet another way, if you put it all in the sea it would raise sea levels globally by ~ 1mm.

So is it a lot? Sure, objectively that is a lot of water but compared to the sea level rises expected from climate change it's a literal drop in the ocean.