NOVELTY - The system comprises: a first loop of co-current contacting systems configured to remove hydrogen sulfide (H2S) and carbon dioxide (CO2) from a natural gas stream; and a second loop of co-current contacting systems configured to remove the H2S from the CO2. The first loop of co-current contacting systems comprises a first series of co-current contacting systems to remove the H2S and the CO2 from the natural gas stream by contacting the natural gas stream with a solvent stream and providing for incorporation of the H2S and the CO2 from the natural gas stream into the solvent stream.    USE - The system is useful for separating H2S and CO2 from a natural gas stream (claimed) in offshore oil and gas production applications.    ADVANTAGE - The compact system has reduced weight, so that the system is easy to transport and to install at the offshore oil and gas production site, and economically separates H2S and CO2 from the natural gas stream.    DETAILED DESCRIPTION - The system comprises: a first loop of co-current contacting systems configured to remove hydrogen sulfide (H2S) and carbon dioxide (CO2) from a natural gas stream; and a second loop of co-current contacting systems configured to remove the H2S from the CO2. The first loop of co-current contacting systems comprises: a first series of co-current contacting systems configured to remove the H2S and the CO2 from the natural gas stream by contacting the natural gas stream with a solvent stream and then providing for incorporation of the H2S and the CO2 from the natural gas stream into the solvent stream; and a second series of co-current contacting systems configured to remove the H2S and the CO2 from the solvent stream, where the solvent stream is recirculated to the first series of co-current contacting systems. The second loop of co-current contacting systems comprises: a third series of co-current contacting systems configured to remove the H2S from the CO2 by contacting the H2S and the CO2 with an H2S-selective solvent stream and then providing for incorporation of the H2S into the H2S-selective solvent stream; and a fourth series of co-current contacting systems configured to remove the H2S from the H2S-selective solvent stream, where the H2S-selective solvent stream is recirculated to the third series of co-current contacting systems. The first series of co-current contacting systems is arranged to contact a sour natural gas stream comprising CO2 and H2S with a lean solvent stream to generate a sweetened natural gas stream and a rich solvent stream comprising the CO2 and the H2S. The second series of co-current contacting systems is arranged to contact the rich solvent stream with a stripping gas to regenerate the lean solvent stream and generate a first gas stream comprising the CO2, the H2S and the stripping gas. The lean solvent stream is recirculated to the first series of co-current contacting systems. The third series of co-current contacting systems is arranged to contact the first gas stream with the lean H2S-selective solvent stream to generate a rich H2S-selective solvent stream comprising the H2S and a second gas stream comprising the CO2 and the stripping gas. The fourth series of co-current contacting systems is arranged to contact the rich H2S-selective solvent stream with the stripping gas to regenerate the lean H2S-selective solvent stream and generate a third gas stream comprising the H2S and the stripping gas. The lean H2S-selective solvent stream is recirculated to the third series of co-current contacting systems. Each of the first series of co-current contacting systems, the second series of co-current contacting systems, the third series of co-current contacting systems and the fourth series of co-current contacting systems comprises co-current contacting systems connected in series. Each of the co-current contacting systems comprises a co-current contactor located in-line within a pipe, and a separation system is configured to remove liquid droplets from the gas stream. The co-current contactor includes: a mixer comprising an annular support ring configured to maintain the mixer within the pipe; radial blades configured to allow a liquid stream to flow into the mixer; a central gas entry cone configured to allow a gas stream to flow through a hollow section within the mixer; and a mass transfer section downstream of the mixer. The mixer and the mass transfer section provide for efficient incorporation of the liquid droplets formed from the liquid stream into the gas stream. The separation system comprises a cyclonic separator. A downstream portion of the central gas entry cone comprises a blunt ended cone, and a tapered ended cone. A CO2 separation system removes the CO2 from the second gas stream to recover a final CO2 product. The stripping gas from the second gas stream is recirculated to the second series of co-current contacting systems. A H2S separation system removes the H2S from the third gas stream to recover a final H2S product. The stripping gas from the third gas stream is recirculated to the fourth series of co-current contacting systems. An INDEPENDENT CLAIM is included for a method for separating CO2 and H2S from a natural gas stream.    DESCRIPTION OF DRAWING(S) - The diagram shows a flow diagram of a chemical solvent-based gas processing system.    Contactor (106)    Subsurface reservoir (108)    Inlet separator (110)    Oil recovery system (116)    Liquid glycol stream. (118)