The present invention provides a method for separating conjunct polymers and sulfolane from a mixture containing conjunct polymers, sulfolane, and hydrofluoric acid comprising the sequential steps of:(a) separating hydrofluoric acid from said mixture to provide an intermediate stream containing less than about 30 percent hydrofluoric acid by weight;(b) gravitationally separating said intermediate stream into a sulfolane-enriched stream and a conjunct polymer-enriched stream;(c) contacting said sulfolane-enriched stream with a polar extraction solvent to provide an extract stream enriched in sulfolane and a raffinate stream enriched in conjunct polymers;(d) stripping the polar extraction solvent from said sulfolane-enriched extract stream; and(e) recovering sulfolane from said enriched stream of step (d).