Can you burn pyrolytic carbon? Part 5 of lunar station

Part 5 of a series.  Part 4 was here.

First of all, where did that question come from?  In part 4, I was wondering about which fuel to use.  So, I decided to look elsewhere as opposed to using solid rockets.

So I started reading the Wikipedia article on the Sabatier reaction, to answer that question.  Pyrolytic carbon can be produced by pyrolyzing methane.  The point of pyrolyzing methane is to obtain the hydrogen. This is all anticipated as a way to close the carbon-water cycles in outer space for life support.  If you do that, you can remove a lot of the mass that has to be taken along.  That mass is in the form of food, which is eaten and produces carbon dioxide and water in respiration.

Anyway, this didn't start out as a life support thought experiment.  The idea is if you can obtain methane via pyrolytic carbon.  If you can do this with that form of carbon, can you do it with other forms of carbon?  My hunch is yes, but I'm not sure.

Why would you care about obtaining methane from carbon?  Well, if you have a source of carbon, as what exists in asteroids, then you can make methane as fuel.  That's provided that the said asteroid has water. NASA wants to send an asteroid to lunar orbit, so that's where the asteroid will come from.

The carbon can indeed be burned using carbon dioxide.  So, you would need a source of carbon dioxide to burn the carbon which produces carbon monoxide.  This requires an energy source to accomplish. Provided that you have such a source, just use this process to produce the carbon dioxide by burning the carbon monoxide thus produced.  In other words, the carbon dioxide is generated, but you need some in the first place in order to jump start the process if there's none available from the asteroid.

Once you have the carbon dioxide, you can make the methane and LOX for a rocket.  The methane is produced from the Sabatier Reaction.  LOX is obtained from the lunar surface or the asteroid by cracking water from the moon or the asteroid.  Or it can be obtained from the regolith on the moon.  In that case, hydrogen will have to be brought down.

Now the only thing you need is a carbon source and a water source.  There's water on the moon, but you have to get it to a handy location.

Now you can use a rocket to send down the raw materials, but that defeats the whole purpose doesn't it? Can we mitigate that to some extent?

Maybe you could just de-orbit the carbon, which is pretty indestructible stuff.  Collect the carbon after it is crashed into the lunar surface.  You'd have to be pretty precise so that you don't hit anything important and it's not too far away that you can't get to it.

Next problem is finding the water.  There's water on the moon, but it is hard to get at.  You'd have to get it from the poles or by baking it out of the regolith.  The second option will take an enormous amount of energy.  Third option is bringing it down via the asteroid.  Any old way you look at it, this part won't be easy.

If you brought the hydrogen down from the asteroid, you'd have to make some for the trip down too.  You'd make the LOX on the surface and generate the methane from the carbon that was crashed into the surface.

Then you'd have a way of transport from the surface to the asteroid and back.  This could use the same vehicle over and over again.

On each excursion, you'd build up your space station.  Eventually, you will have enough carbon and water to make the LOX to fill up the fuel tanks and blast your newly built station into lunar orbit.