“The one thing about this method that we’re about to go into — it will and should measure the majority of the flow,” he said.

Mr. Dudley said that the original estimates by the government and BP officials of 5,000 barrels a day were based on satellite pictures and that the current estimate of 12,000 to 19,000 barrels was “issued without an actual flow measurement.” If the leak is not contained or slowed and continues at the higher estimated flow rate of 19,000 barrels a day until Aug. 20 — four months after the accident — it could amount to close to 2.3 million barrels spilled into the gulf.

After more than a month of diagnostic tests and the pumping of tens of thousands of barrels of drilling fluids — and everything from golf balls to shards of rubber — into the broken blowout preventer, engineers are still debating about what they think may be the inner contours of the five-story stack of pipes and how to best contain its leaking gashes.

In the end, all the mysteries of what went wrong and caused one of the greatest environmental calamities of history may not be known until the well is finally killed and the ill-fated blowout preventer is brought up from the bottom of the sea.

The final plugging of the well will have to wait until August, when the two relief wells are scheduled be completed. Those wells are being drilled diagonally to intersect with the runaway well and inject it with heavy liquids and cement. Work could be slowed by storms in what is expected to be an active summer hurricane season.

Officials from BP and the administration announced on Saturday that the top kill was a failure and had been abandoned, and that engineers were once again trying to solve the problem with a containment cap. A similar operation was tried nearly four weeks ago, but it failed because a slush of icy water and gas, known as hydrates, filled the large containment device, blocking the escaping oil from entering it. This time, engineers will pump hot sea water around the new, smaller device to keep hydrates from forming, and there will be far less space between the cap and the well for any hydrates that do form to flow in.

BP officials expressed optimism on Sunday about the new operation, though one technician working on the project warned that there were concerns that hydrates could again stymie the containment effort. The technician and outside experts also warned that by cutting the riser, the engineers may increase the flow of escaping oil.