The technique could "propel Scotland towards the top of the global league table in terms of oil and gas production", Scottish business body N56 said.
Hydraulic fracturing, also known as fracking, has been heralded as a new source of energy in UK but onshore reserves in Scotland are thought to be limited.
N56, led by Yes Scotland adviser Dan Macdonald, has now seized on a new proposal by petroleum geophysicist Dr Christopher Cornford to export fracking techniques to the North Sea.
The new technique - unveiled at the Unconventional Resources and Technology conference in Denver, Colorado, last month - could almost double the amount of recoverable oil from the industry's high end estimate of 24 billion barrels to 45 billion barrels.
The extra reserves could yield an additional wholesale value of £1 trillion to £2 trillion depending on oil prices, according to N56.
The target is the Kimmeridge Clay formation, an Upper Jurassic organic rich shale which is the major oil and gas source rock for the Central and Northern North Sea.
Danish state-owned oil company Nordsofonde has described the technique as "a potential game changer", N56 said.
Trapoil's CEO Mark Groves Gidney said: "Offshore unconventional oil and gas could materially change the UK economy, let alone the North Sea oil and gas industry."
Professor Richard Selley, emeritus professor of petroleum geology at Imperial College, London, said: "The in place resources of oil and gas in the Kimmeridge Clay in the North Sea are vast.
"The technology to extract it is tried and tested.
"The kit - platforms and pipelines - are becoming available as the conventional fields deplete."
Dan Jarvie, chief geophysicist at EOG Resources, the USA's largest shale oil producer, said: "This is an intriguing possibility and while out of the ordinary should be investigated further."
Martyn Tulloch, of Tulloch Energy, said: "The prize available to the UK or Scottish Government through unconventional oil and gas could be colossal and as a nation we could be sitting on a fortune of black gold that will last for another century, well after conventional oil and gas runs out.
"Should the proposal outlined in Denver prove to be viable, then we must grab the opportunity it presents with both hands, prolonging the life of the North Sea as well as creating an oil fund on the scale of the Norwegian oil fund, to serve both this and future generations."
N56 adviser Graeme Blackett, from BiGGAR Economics, said: "Scotland's public finances would be given a colossal boost through access to these new oil and gas reserves.
"These finds are reminiscent of the early North Sea discoveries from over 40 years ago, such as the Brent Field, and would propel Scotland towards the top of the global league table in terms of oil and gas production."
Scottish Conservative energy spokesman Murdo Fraser said: "It's remarkable an organisation whose founder sits on Yes Scotland's board has discovered £300 billion worth of oil just weeks before the referendum.
"I'm sure if these reserves existed, the Scottish Government would have been falling over itself to announce it before now.
"We are firmly in favour of fracking, and believe the possibilities for extracting unconventional oil should be explored.
"But people will see right through this study as an SNP move to ease concerns over dwindling oil revenues."