In an embodiment is provided a process to re-refine used oil that includes introducing a used oil and a solvent to a separation unit under separation conditions selected to produce a purified oil product, the separation unit comprising a porous membrane, a semiporous membrane, or both; and separating the used oil to obtain an effluent comprising a purified oil product. In another embodiment is provided an apparatus for re-refining used oil that includes a separation unit comprising a porous or semiporous membrane; a used oil feed coupled to an inlet of the separation unit; and an inlet of a diffusate collection unit coupled to an outlet of the separation unit. In another embodiment is provided a composition generated from a membrane separation process that includes a base oil, the composition having a soot content of about 0.05% or less.