## 1 Introduction  
Carbon dioxide (CO\({}_{2}\)) is a primary anthropogenic gas contributing to the global climate. The International Energy Agency (IEA) indicates that limiting global warming to 1.5 \({}^{\circ}\)C above pre-industrial levels necessitates achieving net-zero global CO\({}_{2}\) emissions by approximately 2050 [1]. This aligns with the goals outlined in the Paris Agreement [2]. Carbon Capture, Transportation, Utilization, and Storage (CCTUS) technologies are therefore widely recognized as essential tools for achieving deep decarbonization. Among these technologies, maritime transport of liquefied CO\({}_{2}\) (LCO\({}_{2}\)) presents a particularly promising solution when pipeline infrastructure is unavailable or impractical, especially for intercontinental shipping and offshore storage applications. Cryogenic transport of LCO\({}_{2}\) typically involves one of three types of tanks: fully pressurized, semi-refrigerated, or fully refrigerated. Semi-refrigerated C-type tanks are considered a well-balanced option due to their compatibility with the thermodynamic characteristics of CO\({}_{2}\) and their operational feasibility in marine environments [3]. However, during transport, external heat ingress and ship-induced motion may cause liquid sloshing and phase change, leading to the formation of boil-off gas (BOG). The generation of BOG not only increases tank pressure but also poses operational safety risks and raises the energy demand for re-liquefaction systems [4]. While BOG-related phenomena have been extensively studied in the context of liquefied natural gas (LNG) and liquid hydrogen, reliable CO\({}_{2}\)-specific models remain scarce. Several numerical and experimental studies have explored self-pressurization, heat transfer, and evaporation dynamics in cryogenic tanks. For example, [PERSON] [5] and [PERSON] [6] investigated LNG evaporation behavior in large-scale storage tanks, emphasizing the roles of gas-liquid interface dynamics and thermal stratification. [PERSON] et al. [7; 8] developed visualization and transient simulation systems for low-temperature fluids such as liquid oxygen, offering insights into pressurization over time. [PERSON] et al. [9] proposed a one-dimensional model incorporating vapor temperature gradients to enhance tank pressurization predictions. However, these models were largely designed for LNG or oxygen systems with distinct thermophysical properties, limiting their direct applicability to LCO\({}_{2}\), particularly under dynamic marine transport conditions. Recent studies on CO\({}_{2}\) transportation have primarily focused on system-level aspects rather than internal tank behavior. [PERSON] et al. [10] developed a thermal model for insulated CO\({}_{2}\) truck tanks. [PERSON] et al. [11] evaluate technological readiness (TRL) and emphasize the influence of CO\({}_{2}\) source and separation methods, while [PERSON] et al. [12] examine CCUS's socio-technical role in industrial decarbonization, including policy gaps. [PERSON] et al. [13; 14] and [PERSON] et al. [15] addressed ship design and hydrodynamics for offshore CO\({}_{2}\) shuttle vessels. These works provide useful engineering context but lack detailed analysis of internal heat and mass transfer mechanisms. [PERSON] et al. [16] and [PERSON] [17] performed economic assessments across different pressure conditions, but their models were based on steady-state assumptions and omitted transient thermophysical dynamics. [PERSON] et al. [18] and [PERSON] et al. [19] provided valuable experimental data on energy consumption and depressurization safety, yet did not quantify the time-resolved evolution of internal flow and thermal fields. As a result, most existing BOG models rely heavily on analogies with LNG, often overlooking CO\({}_{2}\)'s narrower liquid-phase window, stronger thermal sensitivity, and unique solidification risks near the triple point. Moreover, simplified interface treatments and steady-state assumptions reduce model accuracy, particularly under realistic marine operating conditions.