I suspected the amount of energy needed to concentrate oxygen would dwarf the amount of energy of the combustion so I did the calculation:
I took the following device[1]: 350W to produce up to 5L of Oxygen per minute.
5L of dioxygen means roughtly 6 gram or 0.18 mol per minute.
Pure carbon combustion produces 393 kJ or energy per dioxygen molecule, whereas dihydrogen produces 572kJ per dioxygen molecule.
Wood has roughtly as much Carbon as di-hydrogen (glucose, the basic block for cellulose is 6 carbon for 12 hydrogen, I'm voluntary ignoring the oxygen here since I want an upper bound), so when burning wood, for each of our dioxygen molecule we can take ~500kJ/mol as an approximation.
That means your device can only produce enough oxygen to sustain a fire generating around 1,5kW of power. (I was wrong)
So, even though my intuition was wrong, spending 350W of electricity to get less than 1,5kW of heat out of the wood you're burning doesn't sounds like a great deal.
You're much better off with a heat pump at that point…
> Or you could do this:
> https://en.m.wikipedia.org/wiki/Chemical_looping_combustion
I had never heard about that, this is so cool!
[1]:https://oxystore.fr/concentrateurs-d-oxygene-stationnaires/5...