## 1 Introduction  
Carbon capture utilization and storage (CCUS) refers to a wide-ranging set of techniques that can be used to mitigate anthropogenic CO\({}_{2}\) emissions. Utilization methods include enhanced oil recovery (EOR), enhanced coal bed methane (ECBM), mineral carbonation, biological algae cultivation, conversion into synthesized fuels and chemicals feedstock. A recent review of the patents being published in field of CCUS concludes that, although the most patents concern utilization of CO\({}_{2}\) in the production of fuels and chemicals, there are also a large number of patents published on algae cultivation, EOR, and ECBM [1]. The aim of many CCUS technologies is the re-use of CO\({}_{2}\) emissions in the location where they are generated thereby eliminating any need for transportation and driving the development of a more circular economy. However, in the case of EOR and ECBM, a transportation step is usually needed, which can represent a significant challenge to the implementation of these types of CCUS projects [2; 3]. Although there exists around 8000 km of CO\({}_{2}\) pipeline in the world today, it is estimated that over 200,000 km of pipeline will be required by 2050 [4]. In addition, as the variety of CO\({}_{2}\) sources considered in CCUS projects becomes more diverse, the challenges associated with transporting CO\({}_{2}\) can be expected to multiply. The transportation of CO\({}_{2}\) by sea on a small scale has been a commercial practice in Europe for several years, where ships are used to transport food-quality CO\({}_{2}\) from production plants to coastal distribution terminals [5]. The current commercial vessel sizes vary between 1000 and 1500 m\({}^{3}\) and the transport pressure is in the range 14-20 bara [6]. Although the use of shipping in many CCUS projects would require a considerable scale-up in transport capacity, there are no technical barriers and shipping has long been identified as a potential option for the long-distance transport of CO\({}_{2}\). The IPCC special report on CCS [5], for example, identifies shipping as the lowest cost option for distances over 1700 km. Other studies such as [PERSON] et al. [7] and [PERSON] et al. [8] have found that the trade-off distance for shipping could be much lower. As a result, shipping of CO\({}_{2}\) is a standard feature in the modelling of CCS transportation networks and a significant number of studies have been made into the technical and commercial aspects of the liquefaction processes required, for example, the studies of Mitsubishi in 2004 [9], [PERSON] et al. in 2007 [10], and [PERSON] et al. in 2014 [11]. When transporting CO\({}_{2}\) in ships, the energy consumption of the liquefaction process is significant, implying high operating costs. As a result, many studies have considered the design of the liquefaction process, particularly with a focus on reducing energy consumption. [PERSON] [6] states that \"in principle, there are two process alternatives\" and goes on to suggest that when low temperature cooling water is available, CO\({}_{2}\) should be used directly as a cooling medium, but above a trade-off temperature, an in-direct ammonia (NH\({}_{3}\)) refrigeration process becomes the best option. Subsequent studies have considered the selection of the optimal process flow scheme for the liquefaction of CO\({}_{2}\) in more detail. Although the majority of work is focused on either open cycle CO\({}_{2}\) processes or closed cycle NH\({}_{3}\) refrigeration processes, others have also studied more novel approaches such as the use of absorption refrigeration [12], cascade refrigeration [13], and the application of turbo expanders [14]. Some have also compared a broad range of schemes. [PERSON] et al. [13], for example, compares simple refrigeration schemes, cascade refrigeration schemes, and absorption refrigeration schemes using waste heat. Most studies, however, focus on the performance of one or two schemes and one set of operating conditions.