It would be based on biochar of vegetable origin which is ploughed into agricultural land where it will be sequestered permanently. (Known as Terra Preta)

During pyrolysis some hydrocarbons could be given off and collected.

The underlying premise is that these hydrocarbons can be used as a fuel, but there will be a net removal of carbon from the atmosphere.

There is a bonus that adding carbon to soils can enhance fertility.

It seems unlikely that the scale of production of these fuels could be built up to replace fossil fuels in the near future, but plausible that enough could be produced to allow long-haul aviation to continue.

Alternative fuels for long-haul flights

There seems to be very little scope for alternatives to hydrocarbons for long haul flights. The range of these depends on the energy-to-weight ratio of fuel, and hydrocarbons are the best we have.

Hydrogen would be good for low carbon output, but storage is a problem. Storage under pressure requires tanks which weigh too much. Hydrogen can be liquefied at very low temperatures, but the density of the liquid is very low, meaning that the volume needed takes up significant passenger space.

Ammonia is a possibility, the energy to weight is lower than aviation fuel and the technology is under development.

Elsewhere, I have proposed Mg-air batteries could in theory have a similar energy to weight hydrocarbons, but the technology has not yet been developed and they get heavier during discharge.