HOW I CALCULATE CARBON DIOXIDE EMISSION FROM THE COMBUSTION OF RP-1 (Rocket Propellant 1)

Determining the amount of carbon dioxide produced from the combustion of methane is fairly straightforward. However, many rockets use RP-1—or have moved to RP-2 a newer formulation but still a hydrocarbon fuel—whose chemical makeup is quite complex, and difficult to ascertain.

As such, determining the carbon dioxide emissions from the combustion of this propellant is not straightforward. RP-1 is a highly refined form of kerosene with a chemical formula that seems to elude the vast knowledge of the internet.

However, it is generally known to be CnH1.953n (Magee et al., 2007). This multiplier will help me in determining a representative chemical formula as we'll discuss. According to a gas chromotographic analysis of RP-1 by the National Institute of Standards and Technology (NIST), the propellant is made up of 16 different hydrocarbons.

Their carbon chains range from 6 to 16 atoms, with 2,2 dimethylbutane ("neohexane") at the lightest end of this range (C6H14), and hexadecane (C16H34) at the heaviest end. It's important to note that the multiplier does not apply to each hydrocarbon species, but to the mean (colloquially called an “average”) of all species taken together.

The Falcon 9 and Falcon Heavy rockets use RP-1 as fuel and liquid oxygen (LOx) as oxidizer. According to SpaceFlight101.com, the RP-1 capacity of the Falcon 9 first stage is 123,570 kg. Its LOx capacity is 287,430 kg. This is a 1:2.326 ratio of RP-1 to LOx. Its second stage has RP-1 and LOx capacities of 32,300 kg and 75,200 kg respectively. This is nearly the same ratio (1:2.328). The Falcon Heavy core stage and boosters each have RP-1 and LOx capcities of 123,570 kg and 287,430 kg respectively.

Again, these are 1:2.326 ratios. From MacGee (2007), I take the multiplier of 1.953 hydrogens per carbon not because this will reveal the specific hydrocarbon species actually in the RP-1 mix, but because whatever species I come up with will have the mean carbon to hydrogen ratio. So, what I've done is look at hydrocarbons with 6 through 16 carbons that closely match the multiplier.

For example, 8 carbons are associated with 16 hydrogens (C12H23 = cyclooctane). 10 carbons are associated with 20 hydrogens (C10H20 = cyclodecane) etc. Based on the RP-1-to-LOx ratio, I then mass balanced each of the hydrocarbons of CnH1.953n formulation until I found one that requires a hydrocarbon-to-oxygen ratio that matches (or closely matches) the ratio of RP-1-to-LOx used on the Falcon rockets to balance.

This worked best with C6H12 (cyclohexane) very nearly to this target ratio (1:2.286). The balanced perfect combustion equation for cyclohexane is:

C6H12 (l) + 6O2 (l) -------> 6CO2 (g) + 6H2O (g)

As noted above, this is a mass ratio of 1:2.286, which is very close to the 1:2.326 ratio of RP-1-to-LOx on the Falcon rockets.

I did not expect a perfect match since RP-1 is not a single hydrocarbon, but a mixture of 16 different species according to the NIST. The idea here is simply to determine which hydrocarbon might best be used to simplify the combustion equation to get a representative mass total of carbon dioxide produced per launch of a given rocket with a known RP-1 capacity. This will not give an accurate CO2 figure, but a reasonable result.

RP-1 is light on alkenes and aromatics. Cyclohexane is alicyclic, not an aromatic, and while it is an isomer of alkene, it consists only of single bonds. Of course, I encourage anyone reading this to fact check my numbers, and remain critical of my assumption that cyclohexane might be a good representative of RP-1 in terms of using its chemical formula for calculating CO2 production from its combustion reaction with LOx.

With that said, the laws of thermodynamics tell us no engine can perform perfect combustion. As such, I'll presume a propulsive efficiency of 60% for rocket engines. While this is considerably more efficient than most vehicles, I use it because of the high combustion temperatures, high pressures, and long converging-diverging nozzles used on rocket engines lend themselves to higher efficiencies.

And while these efficiencies slightly vary with altitude due to changing atmospheric pressure and mass loss from fuel burn, an efficiency of 60% seems a reasonable assumption to make given the fact some rocket engines are known to be as much as 70% efficient. Since no rocket engine is perfectly efficient, we'll also consider the incomplete combustion equation for cyclohexane for guestimating the amount of carbon monoxide (CO) produced. The incomplete combustion of cyclohexane is:

C6H12 (l) + 6O2 (l) -----> 6CO (g) + 6H2O (g)

For every mole of liquid cyclohexane plus 6 moles of liquid oxygen, produces 6 moles of carbon monoxide gas, and 6 moles of water vapor. Carbon monoxide (CO) exhaust is an unfortunate product of incomplete combustion, and while it isn't directly a greenhouse gas, it will interact with UV at altitude and atmospheric oxygen (O2) to form carbon dioxide (CO2).

As such, I'll conservatively and arbitrarily add an additional 5% to the total CO2 produced which means taking 65% of the total mass of CO2 produced from perfect combustion as my final number.

In situations where CO2 production estimations are being calculated for failed launches of rockets that do not burn all their fuel, consider burn time before failure before taking a linear approach to fuel burned per unit time, as rockets burning RP-1 (or RP-2) throttle down at Max-Q and MECO. There are other considerations as well, but the focus here is a very general consideration of CO2 production from RP-1 combustion.

Here I'll provide an example of how I would roughly determine how much gaseous carbon dioxide a rocket burning RP-1 would produce from a successful launch. The Falcon Heavy carries 123,570 kg of RP-1 in its core stage, plus an additional 247,140 kg in its two boosters, and 32,300 kg in its second stage, for a combined total RP-1 mass of 403,010 kg.

To make calculations easier, we'll convert this to grams, which gives us a total RP-1 mass of 403,010,000 grams. Here we'll substitute RP-1 with cyclohexane, which has a molar massof 84 g/mol. 403,010,000 grams/84 g/mol = 4,797,738.1 moles of cyclohexane. We know from the perfect combustion equation for cyclohexane that for every mole of cyclohexane 6 moles of carbon dioxide are produced.

Therefore we multiply 4,797,738.1 moles of cyclohexane by 6 and get 28,786,428.6 moles of carbon dioxide. The molar mass of carbon dioxide is 44 g/mol. 28,786,428.6 mol x 44 g/mol = 1,266,602,858.4 grams of carbon dioxide, or 1,266,602.9 kg. We then take 65% of this by multiplying by 0.65 and get a total of 823,291.9 kg of carbon dioxide produced per launch. This would be a ballpark figure for the Falcon Heavy.

If you've worked with RP-1 or RP-2 and have additional information to share, please use the contact form to let me know. I would greatly appreciate anyone who is willing to share their knowledge with me, and have it presented here. Thanks for reading.

-Rook Andalus

Originally Published: Aug. 18, 2019

References

Magee J.W., Bruno T.J., Friend D.G., Huber M.L., Laesecke A., Lemmon E.W., et al.
Thermophysical properties measurements and models for rocket propellant RP-1, phase I.
NISTIR 6646, 2007.