Hi Melissa, interesting question, so input is biogas which consists of CO2 and Ch4 (and maybe other components) and output is biogas with a higher share of CH4 and less CO2? What do you do to reduce the CO2 content, do you have an absorber e.g.? Is the CO2 released elsewhere or bound, somehow? You do not model the creation of biogas probably?
How can I model the avoided emission of CO2 and the avoided exctraction of natural gas that will produce the same amount of energy
There are several possibilities, one would be to model three systems, natural gas, biogas "raw" and biogas CH4-enriched, for producing the same amount of heat, and compare them, you will then see fewer CO2 emissions from the CH4-enriched gas (assuming CO2 is truely bound). You should also consider leakages though.
I hope this helps! Best wishes, Andreas