From what I understand (after reading the wikipedia page about it) the crater probably isn't putting out much more methane than the rest of the ground in the surrounding area. Wikipedia says the flames are seen there because the shape of the crater allows the gas to accumulate into concentrations that support flames, while in the rest of the area the gas leaking from the ground is rapidly diluted by the wind, but is nevertheless being released.

Looking at the thing, this makes some sense to me. There are flames coming out the side of the walls of the crater all along the perimeter, from only a few meters below where the surface of the ground would be. The gas is obviously very shallow below ground in that region, and unless the top layer of soil is impermeable to gas I think a ton of it must be leaking out all over the area.

Doesn’t seem too big to cap with a concrete dome rolled in place on rails (similar to the Chernobyl sarcophagus install), with the methane captured and burned off (perhaps even used for electrical generation).

The Chernobyl New Safe Confinement took abot 8 years to build at near 2B USD cost[1]. If fire is put out, a simple geoengineering tarp with piping underneath and dirt on top will do the job. Those are used a lot in covering up old landfills to capture the gas and avoid water leaking in.

[1] https://en.wikipedia.org/wiki/Chernobyl_New_Safe_Confinement

Isn't that effective like what the crater is currently doing? It's effectively already concentrating the methane and burning it off before it fills the atmosphere.

Dig a deep enough ditch around it to cut off the fuel. I'm sure Bob the Builder could do an excellent job for not alot!

Or, like, a tarp, but either way you have to worry about the gas going around if you're not capturing it just right.

Can a tarp withstand the heat currently generated? I suppose any material with high heat resistance, low weight, and not too gas permeable would do. Snuff the fire (once capped, it should naturally burn out from a lack of available oxygen), pump and productively burn the gas.

Since this comment chain was about the worry of methane release after stopping the fire, I'm assuming the fire would already be put out if necessary.

Perhaps there is a nearby source of sand.