In this work, CO2 conditioning processes for ship-based CCS sequestration are modelled using the software APSEN HYSYS V11. This study uses the captured CO2 gas from the 3D project as the feed. The feed stream contains water, H2S, and CO as contaminants. The purification processes for dehydration, desulfurization, and CO removal are reviewed. Two liquefaction approaches, the open-cycle and the closed-cycle liquefaction, are modelled and compared for transport pressures 7 and 15 bar. It is found that the energy requirement of the open-cycle process is higher than that of the closed-cycle liquefaction process. For the closed-cycle design, two refrigerants, ammonia and propane, are considered. Results show that the energy requirement of the process using ammonia is lower than that of propane. When comparing the two transport pressures, it is found that liquefaction at 15 bar requires less energy than 7 bar. On top of that, both refrigerants are unsuited for the liquefaction of CO2 at 7 bar, as their operating pressures are below 1 atm. Several optimization concepts are tested on the closed-cycle liquefaction design. The net power consumption of the closed-cycle liquefaction is reduced when CO2 is precooled using the intermediate pressure ammonia streams and the cold from the CO stripper.