An enrichment apparatus and process for enriching a hydrogen sulfide concentration in an acid gas stream to create a hydrogen sulfide rich stream for feed to a Claus unit. The process comprises: (a) separating an acid gas stream to create a hydrocarbon rich stream and a purified acid gas stream; (b) separating the purified acid gas stream to form (i) a carbon dioxide rich stream and a carbon dioxide lean stream having a concentration of hydrogen sulfide, or (ii) a hydrogen sulfide lean stream and a hydrogen sulfide rich stream having a concentration of hydrogen sulfide, subsequently separating the hydrogen sulfide rich stream to form a carbon dioxide retentate and an enriched hydrogen sulfide stream; and (c) feeding (i) the carbon dioxide lean stream or (ii) enriched hydrogen sulfide stream to the furnace of the Claus unit and (d) feeding the (i) carbon dioxide rich stream or (ii) carbon dioxide retentate to the catalytic converters of the catalytic stage of the Claus unit.