As we have thoroughly documented in reports from Penn State University, and others, Carbon Dioxide can be recycled, through the process of "Tri-reforming", wherein it is combined with Methane in a reaction sequence that yields complex hydrocarbons, including some which can be used as, or refined into, liquid fuels.
We have also cited reports, including one most recently from the Pittsburgh, PA, office of the USDOE, demonstrating that Methane, alone, can be converted both into the liquid fuel and gasoline synthesis raw material, Methanol, and, even more directly, into gasoline-range hydrocarbons.
We have thoroughly documented that Carbon Dioxide can be used as a raw material from which Methane can be synthesized, especially via the Nobel-winning Sabatier process, as is now being further developed by NASA; and, other technologies, that we've referred you to, patented by corporate proxies of our US Department of Defense.
We have also reported, via citation of multiple, credible sources, some dating back to the 1950's, that Methane can, as well, be manufactured by processes of Coal gasification.
Herein, in a more recent report, only a quarter-century old, the fact that Coal can be converted into Methane is affirmed by no less a hydrocarbon fuel authority than Exxon.
As per the excerpt:
"Title: Dynamic simulation of Exxon's Catalytic Coal-Gasification process
Authors: Franklin, H.D.; Parnas, R.S.; Kahn, C.; Gaitonde, N.Y.
Affiliation: Exxon Research and Engineering Co., Texas
Publication: Presented at the Annual Meeting of Heat Transfer and Energy Conversion, Los Angeles, 14 Nov. 1982
Abstract: A dynamic simulation of the Catalytic Coal Gasification (CCG) process was done to determine whether the process interactions presented any controllability problems as well as to help design a control scheme for the process. While there were previous dynamic simulation of both fixed and fluidized bed coal gasifiers, these simulations were all performed for noncatalytic gasification processes, and thus would not show the process dynamics implications resulting from the unique features of the CCG process. Unique features of closed control loop responses are given. The Exxon Catalytic Coal Gasification process is a novel method for producing methane directly from coal. Its key features from a process dynamics standpoint are use of a catalyst which causes both the highly endothermic gasification and exothermic methanation reactions to occur in the same reactor, separation of product gas in a highly heat-integrated cryogenic section, and recycle of product carbon monoxide and hydrogen back into the reactor."
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So, yes, in case you had any remaining doubts: If we want Methane for use in the recycling of Carbon Dioxide into valuable hydrocarbons, as can be accomplished via the "Tri-reforming Process" described by Penn State University; or, if we want Methane to convert directly into liquid fuels in a process such as that described by researchers Noceti, et. al., at the Pittsburgh DOE center, we have available, according to Exxon, a "method for producing methane directly from coal".
Why aren't we now employing that "method"?