I am well aware methane is not currently generated from CO₂, as we are still using fossil fuels, not generating enough surplus energy to make the reverse proces

I am well aware methane is not currently generated from CO₂, as we are still using fossil fuels, not generating enough surplus energy to make the reverse process economical. Do you have any numbers on synthesis energy efficiency? It is inherently energy intensive, as it is storing energy. Rare metal membranes may be current state of the art, but Nickel catalysts seem a popular alternative.