BP is betting big on the U.S. shale patch to raise its worldwide production and accelerate drilling while keeping a tight capital budget. The UK-based supermajor is doing something few other pure shale producers are doing. Shale drillers have been slowing drilling activity, or at least not spending too much on raising production, amid volatile oil prices that have dropped below the estimated break-even levels too many times to count in the past few months. For example, Diamondback Energy, one of the biggest names in the patch, plans to keep activity…