Via the link and the attached file, you can access a US Patent from early in the last century explaining technology for the conversion of Methane and, by explicit extension, Coal, into liquid hydrocarbon fuel.
Comment follows excerpts from:
"United States Patent 1,922,918 - Production of Liquid, in Particular Aromatic Hydrocarbons
Date: August 15, 1933
Inventors: Fritz Winkler, Hans Haeuber and Paul Feiler
Assignee: I. G. Farbenindustrie
Description (highly abbreviated):
The present invention relates to improvements in the production of liquid, in particular aromatic hydrocarbons.
We have found that liquid ... aromatic hydrocarbons ... are obtained in a particularly advantageous manner by the thermal treatment ... of methane or gaseous hydrocarbons comprising more than 80% of methane.
The said methane or gas rich in methane may be from any source, as for example, from the reduction of oxides of carbon with hydrogen or obtained by partial liquefaction and fractionalization of coke oven gas or coal gas.
The favorable effect ... (is) ... that no carbon is deposited on the catalyst.
The process is usually carried out at atmospheric pressure.
The resulting hydrocarbons may be employed as motor fuels."
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As in "the reduction of oxides of carbon", i.e. the Sabatier-type, or related, recycling of Carbon Dioxide, and the "fractionalization of coke oven gas or coal gas"; we can obtain Methane from either Carbon Dioxide or Coal, and then convert that Methane into "hydrocarbons" which "may be employed as motor fuels".
