LONDON — BP expects to be back drilling in the Gulf of Mexico, where a rig explosion last year killed 11 men and caused the biggest offshore oil spill in U.S. history, in the second half of this year. After BP PLC reported Wednesday that net profits rose 16 percent in the first quarter, company officials acknowledged the company has applied for permits to restart drilling in the Gulf. The U.S. government lifted a moratorium on deepwater drilling in the Gulf earlier this year, citing improved security standards and the need to protect communities and workers whose livelihoods depend on drilling. The costs of the spill have driven BP to make numerous asset sales, boosting net profits in the first quarter to $7.2 billion.