Method and system for compressing a fluid in a gas phase and for pumping the fluid in a dense phase. The system includes a compressor part having an impeller; a compressor part inlet that receives the fluid in the gas phase; a compressor part outlet that provides the fluid in the gas phase; a temperature changing device that changes a phase of the fluid; a pump part having an impeller; a pump part inlet that receives the fluid in the dense phase from the compressor part outlet; a pump part outlet that outputs the fluid in the dense phase from the system; a single bull gear configured to rotate around an axial axis with a predetermined speed; plural pinions contacting the single gear bull and configured to rotate with predetermined speeds, and a pump shaft configured to rotate the at least one impeller of the pump part.