Having spent a while studying the potential for replacing fossil fuels with solar fuels in the world economy, I’m prone to thinking about hidden energy flows that support the things I do. While I’m lining up to board an unavoidable flight, for example, in between thoughts about how airports are looking ever more like shopping malls, I’m thinking about things like how much ancient oceanic phytoplankton went into producing the kerosene in the plane’s fuel tanks. More specifically, I’m wondering how much ancient seawater was needed to grow the little bugs that were later slow cooked into crude oil, harvested by humans millions of years later, and will soon be burned to carry me through the sky at half the speed of sound. After flying home from Amsterdam to Stockholm last night, I decided to try to figure it out.

The following is quick and dirty, and intended to provide only a rough idea.

According to Carbon Independent, a Boeing 737-400 (typically used for short international flights) uses 36.6 g of fuel per passenger kilometre (p-km). A 747-400 (long international flights) is slightly more efficient at 32.2 g of fuel per p-km. Dukes (2003) estimated that 31 t (metric tonnes) of ancient biomass was required to produce 1 kg of modern gasoline, accounting for losses in both formation and harvesting. The average molecular weight of kerosene (jet fuel) is only slightly higher than that of gasoline, so for convenience I adopt the same conversion factor. Accordingly, each passenger burns about 1100 kg of ancient biomass (roughly the mass of a small car) per kilometre flown on a short flight, or 1000 kg/ p-km on a long flight. For simplicity, I use the latter.

Microbial biomass density varies widely in modern oceans. Based on slide 24 here, I make a very rough estimate of 1×10^(-5) kg/m3 of productive ocean, and assume the same for the ancient oceans. Each p-km of modern flight therefore needs about 1×10^8 m3 of productive ancient seawater. This is the same volume as 40,000 olympic-sized swimming pools. Almost all photosynthetic productivity occurs in the top 100 m of the ocean, so 1×10^6 m2 or 100 hectares of ocean surface were needed to power each p-km of flight. This assumes instantaneous, complete biomass harvest for input into oil-production processes (ignoring growth dynamics and potential for repeated harvest over time in a smaller area).

There is a sense in which the ancient oceans were 100 m-thick solar panels for the modern economy. My flight from Amsterdam to Stockholm last night was roughly 1100 km, so an ‘ancient-oceanic solar panel’ of 110,000 ha was needed to power my personal trip. This is comparable to the size of greater London (150,000 ha). Had I flown from London to Sydney (17,000 km), I (and every other passenger on board) would have needed a ‘panel’ of 1,700,000 ha. This is nearly half the area of the Netherlands (4,150,000 ha).