THEODORE, Ala. – A relief well being drilled deep into the seafloor to shut down the gushing Gulf of Mexico oil well could be completed ahead of a long-set deadline of mid-August only if conditions are ideal, government and BP officials said Thursday.

The relief well is currently the best hope for stanching the oil leak set off by the April 20 explosion aboard the Deepwater Horizon drilling rig, which killed 11 workers and began an environmental catastrophe.

National Incident Commander and retired Coast Guard Adm. Thad Allen said Thursday that the relief well is expected to intercept and penetrate the Deepwater Horizon well pipe about 18,000 feet below sea level within seven to 10 days.

But they won’t know how long it will take to stop the oil until they get there. The gushing well has several concentric rings, and oil could be coming up through multiple rings, Allen said.

The plan is to pump heavy mud and then cement into the well to overcome the upward pressure of the huge oil reservoir below.

If the oil is coming through the outer ring of the well, then they will have to pump in mud and cement to stop that layer first. Then they would have to drill through the hardened cement and repeat the process in each ring until they reach the center pipe and do it again.

That scenario would push into the middle of August, which is the timeline the company and government officials have held to for weeks, despite repeated reports that the drilling was ahead of schedule and the oil could be stopped as soon as late July.

If the oil is only coming up the center pipe, then it’s possible to stop the leak sooner.

“We’re a bit ahead of schedule, but it just takes one storm to change that,” BP spokesman Scott Dean said.

Alhough workers are getting “tantalizingly close to the well,” they are also entering a delicate part of the operation that requires slow, methodical action, Dean said.

Shaving even days off the timeline would stop millions of gallons of oil from escaping into the Gulf.

BP’s stock is closing in on a second straight weekly gain as the relief wells get closer to the gusher and BP has taken steps to reassure business partners in the Middle East and Russia that it remains a viable company.

Another tropical depression was closely following the path of Alex to the coast at the border of Texas and Mexico. It was expected to have little effect on the eastern Gulf. Improved weather was forecast this weekend before more rough weather comes, offering a precious window to capture more leaking oil.

Also on Thursday, BP announced it will use a centrifuge developed by actor Kevin Costner’s company, Ocean Therapy, to clean some of the crude that has fouled the Gulf of Mexico.

A vessel, the Ella G, was retrofitted to receive oil and water from a skimmer, separate the oil and place it in storage tanks, and return the cleaned water to the Gulf. It was previously an offshore supply barge.

The system was built in 10 days, and BP chief operating officer Doug Suttles says it offers many advantages. He says it can remove more oil, stay at sea indefinitely, and skim in seas up to 10 feet. Most skimmers can’t work in seas higher than 4 feet.