MERIDIAN —     The relief well being drilled to ensure crude never again spills into the ocean from BP’s paralyzed well in the Gulf of Mexico has been dubbed the ultimate solution to the drama that’s unfolded over the past three months.

    It’s the final, suspenseful act as one man guides a drill more than two miles beneath the sea floor and three miles from the surface, trying to hit a target less than half the size of a dartboard. The drill is about as wide as a grapefruit, and the target now lies less than 100 feet away.

    If John Wright misses, BP engineers will pull the drill bit up, pour concrete in the off-track hole and then try again. Wright is 40-for-40 , though, having helped capped wells across the world in four decades of work. And he seemed confident in a June video put out by BP that he could make it 41-for-41.

    ‘‘Out of 40 relief wells that I’ve drilled, we’ve never missed yet,’’ Wright said. ‘‘I’ve got high confidence we will take care of this problem as soon as we can get there.’’

    Work began during the weekend to finish drilling the well, and company and government officials say they could hit their target as early as Friday. If it hits, engineers will perform a ‘‘bottom kill’’ by pouring in mud and cement to permanently seal the blown-out well that’s spewed an estimated 207 million gallons since April.

    In three months, the relief well has been run more than 17,900 feet from its rig. But drilling the final stretch, a section slightly





longer than the distance from third base to home on a baseball field, will be a time-consuming and careful process.

    Crews dig about 20 to 30 feet at a time, then run electric current through the relief well. The current creates a magnetic field in the pipe of the busted well, allowing engineers to calculate exactly where and how far they need to drill.

    A ‘‘static kill’’ last week pushed mud and cement into the top of the crippled well, leaving very little chance oil could leak into the Gulf again, said retired Coast Guard Adm. Thad Allen, the government’s point man overseeing the cleanup operation. Neither he nor BP officials have been willing to declare victory yet — but Allen said that day isn’t far off.

    ‘‘This step, in our view, will permanently seal the well,’’ he said Monday.

    Finishing a relief well can be tricky. It took five tries last fall for crews trying to stop a blown well in Australia to hit the target.

    But the area around this well has been thoroughly mapped and carefully tracked, said Eric Smith, associate director of the Tulane Energy Institute.

    ‘‘I think they know exactly where they need to go,’’ Smith said. ‘‘I think they can get this on the first try.’’

    BP, however, has only emphasized the caution being used and won’t talk about its chances of hitting the target the first time.

    ‘‘We are doing everything we can to ensure success,’’ company spokesman John Curry said.

    As engineers work to finish the relief well, Allen is planning a three-day trip to Louisiana, Mississippi and Alabama this week to talk with local officials about how to speed up cleanup efforts as the peak of hurricane season approaches.

    BP and the Coast Guard currently are keeping an eye on thunderstorms over Florida that forecasters say should move across the Gulf near the site of the leak this week. They say the system has a small chance of becoming a tropical storm, but there are no plans yet to suspend drilling operations.

    Meanwhile Monday, BP announced it has spent $6.1 billion responding to the spill since the April 20 explosion on the Deepwater Horizon killed 11 workers, sending the rig to the bottom of the sea and oil spewing 5,000 feet underwater.

    Also, the Justice Department and BP announced they have finished negotiations to implement a $20 billion fund for victims of the Gulf oil spill and that BP has made a $3 billion initial deposit.

     BP says it has received 145,000 claims for lost income because of its blown-out well and has paid out $324 million without denying a single claim.

    But the company said Monday it also has 39,000 claims pending — and some of those have been hanging for months. BP says those claims are being reviewed and might need more paperwork from the people who filed them before they can be paid.

    Some Gulf Coast residents say the company is simply putting off denying claims until the federal claims administrator takes over the process. And BP does say it wants the administrator to rule on questionable cases.

    The spill has taken its toll on the tourism and seafood industries, but there have been encouraging signs that things are returning to normal. Fishing waters have started to reopen. Beaches have begun reopening this weekend on Grand Isle, a popular vacation spot on a Louisiana barrier island, after closing in May.

    ‘‘It’s certainly a sign of recovery,’’ Jefferson Parish Councilman Chris Roberts said Monday. ‘‘The sad part is the busiest time of year for Grand Isle is typically between May and September.’’

    Following the ongoing impact of the global recession and the Gulf oil spill, U.S. inbound tourism has seen a decline of up to 24 percent, according to skyscanner.com.

    Comparing the flight searches from June to July this year, Scot Carlson, Skyscanner’s U.S. Country Manager said: “We would expect to have seen a fall in searches for flights around the area affected by the oil spill, however what our data actually shows is a definite decline in searches for major airports across the whole country. However, while domestic travel has taken a real hit with searches in this period decreasing by an average of 24 percent, international searches have fallen at a far lesser rate, with July searches seeing a 10 percent decline on the previous month.

     “What I find really interesting is that flights to Orlando have seen the smallest drop in international searches with a 2 percent fall, while domestic searches have plummeted by over 30 percent. Therefore perhaps it is only domestic travelers who are being put off by the threat of the oil spill hitting Florida’s beaches and, ultimately, international tourists will protect our tourism businesses.”