A Reuters poll of nine analysts gave an average forecast of $5.70 billion for the company's replacement cost (RC) net income, excluding one-off items, a 1 percent rise on the same period last year.
This compares with a predicted 22 percent rise in profits calculated on the same basis at Royal Dutch Shell Plc
RC net income excludes unrealized gains or losses related to changes in the value of oil inventories and so is comparable to net income under U.S. accounting rules.
The meager rise in profits comes despite a 38 percent rise in Brent crude in the quarter compared with the same period last year, due to strong global demand and political upheaval in the Middle East, and a tripling in global refining margins.
BP's production is predicted to have fallen around 12 percent after it sold oil fields to raise money to pay for the spill, which it said in February was likely to cost $40.9 billion to clean up and meet compensation payments and fines.
Investors are hoping the quarter will mark the end of a constant ratcheting up in the estimated cost of the spill.
They will also be watching out for any updates in BP's spat with its Russian partners in TNK-BP
BP may also give updates on the planned sales of assets including the Texas City and Carson refineries in the United States.
As the first big oil company to report, BP will also be watched closely as an indicator of performance across the sector. ConocoPhillips
BP last week filed lawsuits against the contractors it employed to help it drill the doomed Macondo well and managers may face questions about this on an analyst call.
(Editing by David Holmes)