The leak on the Elgin PUQ platform, about 150 miles off the coast of Aberdeen, led to the evacuation of all 238 workers. Total have also stopped production and part-evacuated its nearby Franklin platform.
The company said that it could take as long as six months to drill a relief well to stop a gas leak at an offshore platform.
Shell also evacuated workers from one offshore installations nearby as a 'precautionary' measure.
Jake Molloy, Regional Organiser of the OILC union, told STV that there may be a risk of explosions and of the poisonous gas hydrogen sulphide, although added that the evacuation had been quick and efficient.
Mr Malloy, has said that the slightest spark could trigger a massive explosion at the Elgin PUQ rig in the North Sea. He said that engineers were dealing with an unprecedented situation since gas is leaking from outside the casing walls.
Total has flown in 10-20 specialist engineers to tackle the leak and enlisted the services of Wild Well Control, which was heavily involved in the BP's Deepwater Horizon oil spill in the Gulf of Mexico in 2010.
David Hainsworth of Total E&P UK, which operates the Elgin PUQ oil rig, admitted that the release of gas could go on "for a significant period of time". He said:
Dr Martin Preston, marine pollution specialist and research fellow at the University of Liverpool has said that a gas leak at one of operator Total's offshore platform could harm marine life. Dr Preston said that the process to drill a relief well may take months. He said: