Methane (CH4) is available naturally. Propane (C3H8) is derived from Methane. Is there a process for synthesizing propane applicable to a micro-farm environment?
AFAIK there is no sustainable method to turn methane into propane, but I must admit I'm no expert on this topic. I do know that it is possible to use use CO2, water and electricity to generate methane on a small scale. When the electricity comes from (the spare capacity of) sustainable energy sources then this process is sustainable and can be used to reduce CO2. More info on this on this site.
Also, in this article they claim they built a small portable refinary that turns
plastics, paper, and other residual waste into methane and low-grade propane.
However, from the article it isn't clear to me how the process works exactly and how sustainable it really is. The article does say that the refinery requires diesel fuel for the first hours to run.