I don't believe oil & gas prices can be decoupled by much in the long run. A BTU is a BTU (a joule is a joule). Both fuels are perfectly substitutable for a large enough number of uses (starting with electricity generation) so that their prices cannot remain too far apart for too long - not as long as boilers can be converted from one to the other.

Short term variations will be uncorrelated, but the overall trend will remain similar.

In the long run, we're all dead. John Maynard Keynes