Oil and gas production in FPSOs (floating, production, storage, and offloading) faces a dual challenge: meeting variation in energy demand while decreasing its negative environmental impact. The present article integrates thermodynamic analysis of oil and gas processing plants and screening analysis to determine the most important operational parameters to lower energy demand and increase efficiency and production. Therefore, the main goals of this study are to identify the contribution of the total effect of the operating parameters in an FPSO with CCUS (CO2 capture, utilization, and storage). Twenty-seven thermodynamic and structural design variables are selected as input parameters for the sensitivity analyses. Four machine learning-based screening analysis algorithms such as smooth spline-analysis of variance (SS-ANOVA), PAWN, gradient boosting machine (GBM), and Morris are adapted to achieve the following objectives: (1) overall power consumption of FPSO, (2) CO2 removal efficiency of carbon capture and storage (CCS), (3) power consumption of CCS, and (4) total oil production. The influence of three real crude oil compositions with variations in gas–oil ratio (GOR) and CO2 content is assessed. The combination of thermodynamic and screening analyses showed that the optimal operating pressure parameters of CCS significantly reduce the energy consumption and exergy destruction of the key main and utility plants. Furthermore, the results indicated that total power consumption, CCS efficiency, and CCS power consumption are much more sensitive to the CO2 content of the fluid reservoir than GOR, while the total oil production is influenced only by the GOR content. Finally, for scenarios with high CO2 or GOR content, the effect of design variable interactions is decisive in changing the separation efficiency and/or the compression unit performance.