The damaged well at SoCal Gas' Aliso Canyon storage facility has been releasing environmentally damaging natural gas since Oct. 23.
BP said it expected the damaged well to be completely sealed by Saturday.
"It's not a matter so much of if, as when," Mr. Wells said of the effort, which will involve pumping heavy mud and cement through the relief well into the damaged well to plug the damaged well permanently.
Shares in BP fell 4.7% today after possible oil and gas leaks were detected near the damaged well, to which BP fitted a cap last Thursday.
Most fishing restrictions in the gulf have been lifted, with only about 1,000 square miles nearest to the damaged well remaining closed.
The next phases will deal with efforts to seal the damaged well and questions of environmental damage and health effects related to the cleanup.
Relief wells, which provide access to the blown-out well beneath the seabed, provide the best hope to seal the damaged well.
BP also said that workers drilling one of the relief wells, meant to help seal the leaking well, came within 200 feet of the damaged well on Friday.
And a permanent solution, drilling a relief well that can be used to plug the damaged well with cement, will take several months.
