Oil and gas industries have high carbon dioxide (CO2) emissions, which is a great environmental concern. Monoethanolamine (MEA) is widely used as a solvent in CO2 capture and storage (CCS) systems. The challenge is that MEA–CCS itself is an energy-intensive process that requires optimum configuration and operation, and numerous design parameters and heat demands must be considered. Thus, the current work evaluates the energy distributions and CO2 removal efficiency of a CCS installed in floating production storage and offloading units under different operating conditions of a power and heat generation hub. The optimization procedures are implemented using highly accurate surrogate models for the following responses: (1) overall power consumption of CCS, (2) CCS separation performance, and (3) CCS heating and cooling demands. The input variables considered in the present research include the following: (1) the exhaust gas compositions and mass flowrate, (2) the operating pressure and temperature parameters of CCS and the injection compression unit, (3) the structural parameters of absorber and stripper columns, and (4) MEA solution parameters. The optimum CCS configuration significantly reduces the total heating and cooling demands by 62.77% (7 × 106 kW) and the overall power consumption by 8.65% (1.8 MW), and it increases the CCS separation performance by 4.46% (97.46%) and mitigates the CO2 emissions of proper CCS by 1.02 t/h compared with conventional operating conditions.