The American Petroleum Institute (API) estimated on Wednesday a surprise crude oil inventory build of 1.57 million barrels for the week ending January 17, compared to analyst expectations of a 1.009-million-barrel draw in inventory. Last week saw a build in crude oil inventories of 1.1 million barrels, according to API data. The EIA’s estimates, however, were of a draw of 2.5 million barrels for that week. Oil prices were down earlier in the day prior to the afternoon data release, despite continued unrest in oil-rich Iraq and a near-complete…