Separation method and apparatus

A separation method and apparatus that separates a component from a feed stream by use of a membrane in which separation is driven, at least in part, by a sweep stream. The sweep stream may be pumped to a supercritical pressure and then heated to at least near supercritical temperature, at least in part, through heat exchange with a component laden sweep stream being discharged from the membrane. A multi-component mixture can also be used that will produce the sweep stream as a vapor as a result of the heat exchange. The component laden sweep stream, due to cooling through the indirect heat exchange, will form a two- phase fluid that can be phase separated into a vapor phase enriched in the component that can be taken as a product and a residual liquid that can be recirculated in the formation of the sweep stream in the liquid state.