HOUSTON (Dow Jones)--Integrity testing on BP PLC's (BP, BP.LN) broken well should begin Tuesday afternoon resulting in the shut down of the two production vessels which have been keeping oil from flowing into the U.S. Gulf of Mexico, said U.S. Coast Guard Retired Adm. Thad Allen. If the first six hours or so of testing show that the pressure on the well is too low, than BP will most likely decide that the new cap they placed on the well Monday is not strong enough to seal off the runaway well entirely, Allen said in a news conference here. If the tests show high pressure readings, BP will continue monitoring the situation for at least another 42 hours, Allen said. At that point, BP could decide to use the new cap to shut-in the well entirely, Allen said. He said the time frame given are merely estimates. However, if the well cannot sustain high pressures throughout the testing, than BP will not use the cap to shut-in the well. Instead, the U.K. oil giant will use the cap to siphon off oil from the well to ships on the surface, Allen said. -Susan Daker, Dow Jones Newswires, 713-547-9208; [email protected] Order free Annual Report for BP plc Visit http://djnewswires.ar.wilink.com/?link=BP or call 1-888-301-0513 (END) Dow Jones Newswires July 13, 2010 11:40 ET (15:40 GMT)