The International Maritime Organization (IMO) has implemented new sulfur content regulations for marine fuels in response to growing environmental concerns, including global warming. These regulations severely and costly restrict refinery operations. Oxidative desulfurization (ODS) is an attractive desulfurization method that has advantages such as mild operating conditions and a hydrogen-free process over traditional processes such as hydrodesulfurization (HDS). One can employ oxidative desulfurization in addition to or instead of hydrodesulfurization. Organic sulfur molecules undergo oxidative desulfurization, which results in the formation of polar sulfones. The refined fuel oil is then separated from the oxidized sulfones using methods such liquid-liquid extraction, distillation, and absorption. This work examines and simulates the process of separating sulfur-containing oxidized chemicals from fuel oil utilizing oxidative desulfurization technology. Acetic acid served as the catalyst and hydrogen peroxide as the chosen oxidant. This effort involved simulating the oxidative desulfurization of fuel oil and then using absorption methods to separate the oxidized sulfones. Subsequent procedures including absorption and distillation were used to separate and recover the resultant effluent, solvent, and oxidant from the remaining components. According to the simulation results, the procedure was run at 80 °C and a modest pressure of less than 5 bar. Sulfur content in the original hydrocarbon fuel was 3.5% by weight; at the output, it was less than 0.5% by weight. The findings of the sensitivity analysis of a few key factors demonstrated that the conversion percentage increased from 84 to 98% when the reactor’s diameter was changed from 0.5 to 1.2 m and its length was extended to the desired amount. The reaction conversion percentage has increased significantly when the mass flow rate of hydrogen peroxide is increased from 0.5 to 1.5 kg/h, the pressure is increased from 1.5 to 5 bar, and the temperature is raised to 30 °C. According to the process optimization data, the ideal state had an exergy efficiency of 55.57%, a solvent waste rate of 1.75%, and a sulfur content of 0.22% in the fuel.