A method for disposing of solid refinery waste is disclosed. The method includes removing solid waste constituents from inside a refinery tank using excavating machinery, delumping the solid waste constituents, and conveying the delumped solid waste constituents into a mobile tank. The method further includes transporting the delumped solid waste constituents in the mobile tank to a burning facility, adding at least one diluent, mixing, and pumping from the mobile tank a flowable mixture of refinery waste and the at least one diluent at the burning facility.