ScienceDirect - Fuel : Reaction of methane with coal 
In an earlier dispatch detailing the US Gas Research Institute's US Patent 4609440, wherein Carbon Dioxide is converted into Methane, we indicated that, among other valuable potentials, Methane can be employed in indirect coal conversion processes, by addition to the synthesis gas generated from Coal, to enhance the quality of the syngas prior to catalysis, and thereby improve the quality and quantity of the liquid fuels produced.
It can, in fact, supply the additional Hydrogen needed to effect the conversion of highly-carbonaceous raw materials, such as Coal, into hydrocarbon liquids.
Herein, we document that Exxon, at work with Australian collaborators, knows it.
Following are excerpts from:
"Reaction of Methane with Coal
Kezhan Yang, Barry D. Batts; Macquarie University, Macquarie, NSW 2109, Australia
Martin L. Gorbaty, Peter S. Maa; Exxon Research and Engineering Company, Annandale, NJ, USA
Mervyn A. Long; University of New South Wales, Sydney, NSW 2052, Australia; et.al.
Abstract: The reactivities of Australian coals and one American coal with methane or methane-hydrogen mixtures, in the range 350–400°C and a range of pressures (6.0–8.3 MPa, cold) have been examined. The effects of aluminophosphates (AlPO) or zeolite catalysts, with and without exchanged metals, on reactivity have also been examined. Yields of dichloromethane extractable material are increased by using a methane rather than a nitrogen atmosphere and different catalysts assist dissolution to various extents. It appears that surface exchanged catalysts are effective, but incorporating metals during AlPO lattice formation is detrimental. Aluminium phosphate catalysts are unstable to water produced during coal conversion, but are still able to increase extraction yields. For the American coal, under methane-hydrogen and a copper exchanged zeolite, 51.5% conversion was obtained, with a product selectivity close to that obtained under hydrogen alone, and with only 2% hydrogen consumption. The conversion under methane-hydrogen was close to that obtained under hydrogen alone, while a linear dependence of conversion on proportion of methane would predict a 43% conversion under methane-hydrogen. This illustrates a synergistic effect of the methane-hydrogen atmosphere for coal liquefaction using this catalyst system."
In their experiments, it does appear that they still used some, more expensive, elemental Hydrogen, as can be obtained, for instance, via water electrolysis. But, Methane can replace some, or most, if we understand "with only 2% hydrogen consumption" correctly,  of the elemental Hydrogen which might otherwise be required to maximize liquid hydrocarbon productivity from coal-derived synthesis gas.
And, yet again, as we have thoroughly documented: Methane can be synthesized via the Sabatier recycling of Carbon Dioxide; and, the steam, or hydro, gasification of Coal.

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