Certain fatty acid amide-based surfactants such as cocamide DEA (also known as “coco(nut) diethanolamide” or “coco(nut) DEA”) when dissolved or dispersed in a cutting oil (diesel, light cycle oil, naphtha, and such other petroleum distillates) produce a petroleum distillate having significantly enhanced solvency for heavy residuals. Such solutions or dispersions are especially useful for cleaning vessels and similar equipment in refineries by circulating the solution or dispersion in the vessel, optionally with the application of heat.