A method of transporting solid refinery waste includes loading solid refinery waste into a mobile tank having at least one sloped floor wall and a plurality of compartments separated by at least one buffer. The method may also include maintaining a head space between a top level of the solid refinery waste and a top wall of the mobile tank. The method may also include delivering the mobile tank to a burning facility that maintains a reserve of diluent and that is equipped with an agitator configured for lowering into the mobile tank through a manhole opening, to thereby permit the diluent to be conveyed into the headspace and mixed with the solid refinery waste, thereby enabling a resulting mixture to be off-loaded for burning at the burning facility.