A method for processing flue-gas, in an exemplary embodiment, includes providing an absorber unit having a membrane contactor, channeling a combustion flue gas along a first surface of the membrane contactor, and channeling an ammonia-based liquid reagent along a second opposing surface of the membrane contactor. The method also includes partially separating the ammonia-based liquid from the flue gas such that the ammonia-based liquid and the flue gas contact at gas-liquid interface areas, defined by a plurality of pores of the membrane contactor, to separate CO2 from the flue gas by a chemical absorption of CO2 within the ammonia-based liquid to produce a CO2-rich ammonia-based liquid.