There are some very interesting new approaches to this problem which have the potential to dramatically change the calculus for point-of-emissions CO2CO2 capture and storage.
First, a technique using liquid gallium and silver-gallium nanorods in an ultrasonic bath acts to electrochemically reduce solute CO2CO2 into O2O2 gas and solid C particulates. The input energy of 230kWh per tonne of CO2CO2 makes this an interesting possible route for the scenario you propose. source: https://onlinelibrary.wiley.com/doi/epdf/10.1002/adma.202105789
Secondly, another technique pyrolyzes bulk plastic waste particles into a carbonaceous substrate having pores sized to enable it to absorb a significant % of it own weight in CO2CO2, at low temps, and re-release CO2CO2 gas above 75°c75°C.
The low temperature absorption performance may make it somewhat viable to use in capture-and-sequester home systems. but systems which recirculate the material for repeated extraction/concentrated/release may be able to use this as a cost effective stage to isolate diffuse CO2CO2 from flue gas streams and further process that concentrated CO2CO2 into more stable/more economically useful compounds. source: https://pubs.acs.org/doi/pdf/10.1021/acsnano.2c00955 Plastic Waste Product Captures Carbon Dioxide in Nanometer Pores
Turns out the 'secret sauce' is pyrolyzing the plastic in the presence of potassium acetate. That, and really high temperatures -600°c600°C/1112°F.
So, to the extent of my awareness, there are no commercially available 'bolt-on' solutions to household carbon capture from your HVAC.
If one wanted to use HVAC specific CO2CO2 streams to enrich a greenhouse atmosphere, so long as the appropriate precautions against CO poisoning and CO2CO2 safe human respiration levels are in place and operating properly, is not an impossibility given a large enough greenhouse.
Net CO2CO2 reduction, by such means as supporting long term, persistent natural carbon sequestration through rewilding or other actions to reverse habitat loss may be the best, most immediate response to the continued use of CO2CO2 emitting home heat sources.
As has already been state; an answer to this for new installations may be ground thermal heat pumps, to avoid burning petroleum for heat in the first place. I think though, for existing installations, were maybe a few years away from the 'CO2'CO2 non-emitting' add-on for gas powered home HVAC.
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