The consequences of that can include: Russia's economy being broken due to a main export literally vanishing into thin air. And worse: Green house gases getting into the atmosphere in vast amounts.
As far as I know, the methane from the permafrost is not commercially exploited. It's left there frozen, so this doesn't affect the Russian economy unless one of this "explosions" hits a building.
This PDF contains a few numbers for those interested: http://www.arlis.org/docs/vol1/ICOP/40770716/CD-ROM/Proceedi...
I have no idea ho much methane can be released, since I don't even know how much Russia is mining or anything like that...
But it sounds a lot (since in Ukraine crisis Russian gas is a big point), so if all that leaks out it would greatly accelerate global warming no? (thus releasing even more gas!)
Methane produces a much stronger greenhouse effect than CO2, so the obvious solution is to capture it and use it for fuel, which will convert it to CO2.
The idea is to capture it before it escapes its previously permafrosted enclosure.