BP is continuing tests on the cap that's stopped oil leaking from its broken well into the Gulf of Mexico, just as the cost of dealing with the spill approaches $4bn (£2.6bn)."At this time, the well integrity test on the MC252 exploratory well continues," the rumoured bid target said Monday. "During the test, the three ram capping stack has been closed, shutting in the well."Pressure inside the well recently has been measured at about 6,792 pounds per square inch and continues to rise slowly. Information gathered during the test will be used to determine next steps.There was no mention of reports yesterday that engineers monitoring the situation had noticed some seepage on the ocean floor. A relief well, started on 2 May, has reached target depth and "ranging runs" will be now used to guide the drill bit to a MC252 well intercept point. Operations will then begin to kill the flow of oil and gas from the reservoir by pumping specialized heavy fluids down the relief well. The second relief well has been temporarily halted so it won't interfere with the ranging runs on the first relief well. "Although uncertainty remains, the first half of August remains the current estimate of the most likely date by which the first relief well will be completed and kill operations performed," BP said.Meanwhile, the cost of the disaster that claimed the lives of 11 workers on the Deepwater Horizon rig, has reached $3.95bn, with 116,000 claims resulting in over 67,500 payments worth $207m.