An acid gas purification system is described herein that includes a primary membrane system with a CO2- and H2S-enriched permeate stream effluent and a hydrocarbon stream effluent; a first compression stage arranged to receive the CO2- and H2S-enriched permeate stream and produce a compressed stream; and a cryogenic separation system to receive the compressed stream, the cryogenic separation system including a cooler followed by a fractionator, wherein the fractionator produces a CO2- and H2S liquid stream and a hydrocarbon gas stream.