A membrane permeation system and process accommodates varying acid gas inlet concentrations over time while utilizing only the initially installed equipment and still maintaining the non-permeate gas specification. The system and process provide flexibility to operate efficiently over a wide range of inlet CO2 concentrations by adjustments to primary permeate, secondary permeate, and recycle gas operations. The glassy polymer membrane devices used in the system and process are selected so removal duty efficiency increases as acid gas concentration increase. Designing the system and process to handle about a 15% increase in acid gas concentrations over initial conditions effectively treats acid gas concentrations well above that 15% increase, thereby eliminating the need for additional equipment or for additional downstream amines and physical solvents.