The 60,000-bpd hydrocracker was shut on March 1 for the planned overhaul, the two sources said. The 80,000-bpd PTR-4 catalytic reformer is also shut for work.
Exxon spokesperson Lauren Kight declined on Monday to discuss operations at the Beaumont refinery.
Exxon also plans to shut the 35,000-bpd CHD-1 hydrotreater for two weeks of work in April, according to the sources.
Hydrocrackers use high heat and pressure in the presence of hydrogen to convert gas oil into diesel and other motor fuels.
Reformers convert refining byproducts into octane-boosting components to make premium grades of gasoline.
Hydrotreaters use hydrogen to remove sulfur from motor fuels to comply with U.S. environmental rules.