A system and method for separation of a gas, e.g., carbon dioxide, from a gaseous mixture using a hollow fiber membrane module. The module contains an absorbent solution that is effective in absorbing the gas for an extended period, e.g., eight hours, without regeneration or replacement. The absorbent solution is then regenerated by passing a sweep gas through the hollow fibers in the module. The separation system is particularly useful for fuel cell and battery applications.