An apparatus and method for flow management and CO2-recovery from a CO2 containing hydrocarbon flow stream, such as a post CO2-stimulation flowback stream. The apparatus including a flow control zone, a gas separation zone, a pretreatment zone, and a CO2-capture zone. The CO2-capture zone is in fluid communication with the pretreatment zone to provide CO2-capture from a pretreated flowback gas stream and output a captured CO2-flow stream. The CO2-capture zone includes a first CO2-enricher and at least one additional CO2 enricher disposed downstream of the first CO2 enricher and in cascading relationship to provide a CO2-rich permeate stream, the CO2-capture zone further including at least one condenser to condense the enriched CO2-stream and output the captured CO2-flow stream.