1. Introduction
The primary energy sources in modern society are fossil fuels such as coal, oil, and natural gas. These hydrocarbon-based fuels inevitably produce water and carbon dioxide as byproducts during combustion. Historically, the emitted carbon dioxide was absorbed within the natural carbon cycle, maintaining an atmospheric balance. However, since the onset of industrialization, fossil fuel consumption has increased dramatically (Marland et al., 1985), resulting in a sharp rise in atmospheric CO2 concentrations and contributing significantly to global warming. To address this issue, the International Maritime Organization (IMO) announced targets to reduce greenhouse gas (GHG) emissions from international shipping (IMO, 2018), followed by the declaration of a Net-Zero goal as part of its strengthened GHG reduction strategy (IMO, 2023). Among emerging solutions, carbon capture, utilization, and storage (CCUS) has gained considerable attention as a pivotal technology. CCUS captures CO2 before it is released into the atmosphere and enables either permanent storage or beneficial reuse. According to Davis et al. (2018), CCUS is considered an essential technology for achieving large-scale decarbonization.
Within CCUS technologies, the transportation has received particular emphasis. Nath et al. (2024) reported that carbon dioxide (CO2) is typically transported via pipelines, maritime vessels, or storage tanks. Pipelines are generally the most efficient option for short-distance, large-volume CO2 transport (Roussanaly et al., 2014), particularly when handling quantities exceeding 5 million tons per year over distances shorter than 200 km. In contrast, for smaller transport volumes-such as approximately 2.5 million tons per year-maritime transport becomes more cost-effective when the transport distance exceeds 500 km (Knoope et al., 2015). Compared with pipelines, CO2 carriers offer greater operational flexibility and are easier to maintain (Kjarstad et al., 2016). As a result, maritime CO2 transport is gaining increasing attention due to its adaptability and suitability for long-distance, scalable operations. In these vessels, liquefied carbon dioxide (LCO2) is stored in insulated cargo tanks to maximize transport efficiency (Jeon & Kim, 2015a). However, heat ingress from the external environment inevitably generates boil-off gas (BOG) within the tank (Jeon & Kim, 2015b), resulting in gradual pressure buildup that may compromise operational safety and system stability.
To safely and economically manage this BOG, research has explored the adaptation of re-liquefaction systems originally developed for LNG carriers to CO2 transport vessels (Jeon et al., 2016). However, according to Kim and Kim (2024), re-liquefaction technology for LCO2 carriers remains at an early stage of development. At present, open refrigerant cycles are the most widely studied configuration. Yoo (2017) analyzed an open-cycle system that utilizes LNG cold energy using Aspen HYSYS. While such process simulators are effective for evaluating thermodynamic states and steady operating conditions, they are limited in their ability to capture time-dependent interactions among heat ingress, vapor generation, and safety-valve operation in cryogenic storage systems.
Building on this foundation, the present study investigates the performance of a CO2 re-liquefaction system designed for non-LNG-fueled maritime vessels, employing Thermal Desktop for the numerical simulation. Thermal Desktop was selected because it allows direct simulation of transient thermal–fluid coupling, which is essential for analyzing pressure rise, boil-off gas generation, and relief-valve cycling under realistic heat-load conditions. Thermal Desktop is a computer-aided design (CAD)-based thermal analysis software that integrates the finite difference method (FDM) and finite element method (FEM) to model conduction, convection, and radiation heat transfer (Panczak et al., 1998). The software maps FDM thermal nodes directly onto CAD geometry and evaluates conductive, convective, and radiative heat exchange among complex surfaces using the SINDA/FLUINT thermal solver. In addition, Thermal Desktop incorporates FloCAD, a one-dimensional flow analysis module capable of simulating transient behavior and two-phase flow phenomena (Lusby et al., 2023).
In a previous study, Krenn et al. (2015) employed Thermal Desktop to analyze air leakage within the insulation layer of cryogenic liquid hydrogen (LH2) storage tanks, demonstrating the software’s capability for evaluating the thermal and safety performance of cryogenic storage systems. Similarly, Zhang et al. (2001) conducted a thermal analysis of compressible CO2 flow for major equipment in a fire-detection system, showing that Thermal Desktop is capable of modeling CO2 choked-flow behavior as well as simulating Joule–Thomson cooling effects. These studies collectively indicate that Thermal Desktop can accurately represent compressible gas dynamics and cryogenic thermophysical processes. Building on this foundation, the present study extends the use of Thermal Desktop to the analysis and safety verification of cryogenic LCO2 storage tanks and their associated re-liquefaction systems.
2. LCO2 Re-Liquefaction System Modelling
For maritime transportation of CO2, it is essential to manage the pressure increase caused by BOG generation (Lee et al., 2024). Tao et al. (2025) reported that, in some cases, BOG is vented into the atmosphere to prevent excessive tank pressure. However, this approach leads to economic losses and may result in environmental penalties. Therefore, when considering both operational safety, economic feasibility and environmental protection, the implementation of a re-liquefaction system becomes a critical requirement for CO2 carriers.
To evaluate the operational safety of the re-liquefaction process, a general open type refrigerant cycle was designed (Seo et al., 2015). The basic configuration of the system is shown in Fig. 1. Liquefied CO2 is stored in a 20 m3 cryogenic storage tank, a representative size selected based on commercially supplied LCO2 cargo tank designs from Korean manufacturers and on typical volumes adopted in preliminary design studies for small to medium CO2 carriers. Tanks in the 15 to 30 m3 class are commonly used as reference units in system level modeling because full scale LCO2 carriers have not yet been commercialized and publicly available design envelopes remain limited. This volume therefore provides a realistic basis for evaluating pressure evolution, boil off gas generation, and relief valve cycling under IMO conforming low pressure storage conditions (IMO, 2016).
Boil off gas generated through LCO2 vaporization inside the tank is routed to a compressor, where it is pressurized before passing through an after cooler and condenser for cooling and re-liquefaction. The high pressure, low temperature LCO2 then passes through a Joule–Thomson valve, where its pressure is reduced to a cryogenic low level. During this expansion, irreversible losses occur due to the Joule–Thomson effect, resulting in partial re-vaporization of the LCO2. A separator subsequently divides the liquid and vapor phases. The separator volume of 0.6 m3 was selected to match the capacity range of industrial LCO2 separators currently manufactured for stationary and prototype marine CO2 re-liquefaction systems. Separator sizing in practice is determined by flash vapor separation requirements, transient liquid holdup, and level control stability rather than by a fixed scaling ratio to the main cargo tank. The adopted volume therefore reflects realistic equipment sizing used in existing CO2 re-liquefaction designs. When the liquid level in the separator reaches a predefined threshold, a relief valve automatically opens, allowing the re-liquefied CO2 to flow back into the main storage tank and completing the re-liquefaction cycle.
In addition, the operating parameters assigned to the re-liquefaction components such as compressor mass flow capability, condenser UA, and refrigerant inlet and outlet temperatures were not arbitrarily chosen. These values were drawn directly from manufacturer design data used in the ongoing development of CO2 re-liquefaction equipment and are consistent with the operating ranges reported in previous LCO2 system studies (Jeon & Kim, 2015a, 2015b; Jeon et al., 2016). As such, the component specifications used in this model reflect realistic engineering design inputs and ensure that the resulting thermodynamic behavior represents that of an operable re-liquefaction system rather than a hypothetical configuration.
The LCO2 storage tank consists of concentric inner and outer cylindrical shells, each featuring different head thicknesses. Accordingly, the shells were modeled as separate thermal domains. Tables 1 and 2 summarize the radiative thermal properties and thermophysical properties of the selected materials, respectively.
In defining the environmental boundary conditions, the radiative boundary was assigned a temperature of 45 °C, whereas natural convection from the surrounding air was modeled at 25 °C. This approach follows the guidance in IGC Code 4.2.6.2, which specifies 45 °C as the reference temperature when tank pressure is governed by ambient thermal loading, while explicitly allowing the use of lower ambient temperatures for ships operating in restricted regions or over limited voyage durations, taking into account the presence of insulation. Because the present study represents operating conditions typical of the Korean coastal environment, an ambient air temperature of 25 °C was selected, while retaining the conservative radiative temperature of 45 °C to account for solar heating effects.
As summarized in Table 3, CO2 within the re-liquefaction system was modeled as a compressible fluid. The after-cooler was operated using compressible water, while the condenser was modeled with compressible R410A refrigerant. Radiative heat transfer was calculated using the Monte Carlo method, with the radiation source temperature set to 45 °C and the Pay Per Node value set to 5000. All pipelines were assumed to be thermally insulated. With the exception of designated pipes and flow sections, the cross-sectional area of the remaining flow lines was uniformly set to 1436 mm2.
3. Initial and Boundary Conditions
3.1 LCO2 Storage Tank
The LCO2 storage tank mesh was generated using SpaceClaim. A relative mesh size of 0.07 was applied to both the LCO2 storage tank and the separator, with a triangular surface mesh configuration. The maximum deviation-to-chord length ratio was set to 0.2, and the refinement limit to 0.8. A surface mesh was adopted using a curved control-volume approach to accurately capture the tank geometry.
Parameters such as mesh size, node count, skewness, and aspect ratio were selected empirically based on meshing experience. Because Thermal Desktop operates as a 1-D fluid and lumped-parameter thermal analysis tool, refining the surface mesh does not improve the accuracy of the internal fluid calculation, which depends on vapor- and liquid-phase lumps rather than spatially resolved flow fields. Therefore, choosing mesh parameters that provide a practical balance between computational cost and numerical accuracy is more appropriate than pursuing a highly refined grid.
Although many marine LCO2 carriers employ type C bi-lobe tanks, publicly available experimental or numerical data directly comparing bi-lobe and cylindrical tanks remain limited. Consequently, numerous previous studies on cryogenic LCO2 have adopted simplified cylindrical tanks as a standard modeling geometry, particularly when the primary objective is to examine fundamental thermodynamic behavior rather than to reproduce the exact structural configuration of a specific vessel. This approach is further supported by experimental investigations using vertical cylindrical CO2 cargo tanks (Yoo, 2011) and thermodynamic modeling studies of vertical LCO2 storage systems (Nam et al., 2024), both of which demonstrate that simplified cylindrical configurations sufficiently capture the dominant thermal-fluid mechanisms governing cryogenic LCO2 storage. Therefore, while the geometry does not replicate the full structural complexity of a type C bi-lobe tank, it remains appropriate for analyzing the general thermodynamic trends of interest. Fig. 2(a) shows the resulting tank geometry and mesh configuration.
The operating-pressure configuration in this study was first established based on the thermodynamic characteristics of CO2. Since the triple point of CO2 is 5.18 bar, pressures above this threshold are required to maintain a stable liquid phase. Vopak et al. (2011) recommend 7–9 bar as the optimal range for liquid CO2 storage, which aligns with standard low-pressure transport practices. Accordingly, an 11-bar design-pressure tank was selected to provide a sufficient safety margin, and 8 bar was adopted as the maximum operating pressure to ensure both stability and operational efficiency.
Based on this operating-pressure framework, the initial tank conditions for the simulation were set to −45 °C and 8.51 bar. The relief valve was modeled as a control valve with a flow area of 1436 mm2 and was programmed to open at 8.5 bar and close once the pressure decreased to 8 bar. To ensure that the simulation began with the valve in the open state, the initial pressure was set slightly above the opening threshold at 8.51 bar. Natural convection at an ambient temperature of 25 °C and radiative heat transfer at 45 °C were applied as external boundary conditions.
3.2 Separator
The initial temperature and pressure of the LCO2 inside the separator were set to −45 °C and 8 bar, corresponding to the vapor–liquid equilibrium state of CO2 under low-pressure storage conditions. Using a thermodynamically consistent saturation pair ensures that the separator begins from a physically realistic initial state, consistent with values commonly reported in previous LCO2 re-liquefaction studies. Only natural convection with an ambient temperature of 25 °C was applied because the separator is fully insulated, and its thermal behavior is governed primarily by internal phase-change and flow dynamics rather than by external heat loads.
A check valve located at the top of the separator, with a flow area of 1436 mm2, continuously transfers re-vaporized CO2 to the compressor, while a relief valve at the bottom, which has a flow area of 610 mm2, discharges liquid CO2 back to the storage tank. The relief valve is programmed to open at approximately 38 percent liquid level and close at 22 percent, reflecting the high liquid level and low liquid level setpoints used in industrial CO2 separators. These discrete hysteresis bands provide stable liquid holdup, prevent liquid carryover to the vapor line, and ensure sufficient buffer capacity to accommodate the transient liquid surge that occurs after Joule–Thomson expansion. The initial liquid level was therefore set to the normal operating value prescribed in such equipment. The resulting separator geometry and mesh configuration are shown in Fig. 2(b).
A phase separator is an essential component of any CO2 re-liquefaction system because the Joule–Thomson expansion inevitably produces a two-phase mixture of liquid and vapor CO2. Without a separator, liquid entrainment into the compressor suction line would lead to operational instability and a significant risk of liquid slugging, which is unacceptable in shipboard compression systems. Thus, the separator is not an optional buffer tank but a required flash-drum unit that enables safe and reliable phase separation downstream of the Joule–Thomson valve.
3.3 Compressor
The BOG generated in the LCO2 storage tank is directed to the compressor, where it is pressurized to enable subsequent CO2 liquefaction. The compressor performance curve shown in Fig. 3 was taken directly from the manufacturer’s design data for the compressor unit used in marine CO2 re-liquefaction systems. The compressor is designed to operate at a head pressure of 21.4 bar with a mass flow rate of 0.5 kg/s. In practical operation, compressor performance declines when the flow rate exceeds the design specification, and this behavior was reflected by implementing progressively reduced efficiency values beyond the design point. The compressor inlet flow area was set to 1436 mm2. For the upstream piping connected to the compressor inlet, an initial pressure of 8.49 bar and an initial temperature of −45 °C were applied, consistent with the thermodynamic state of BOG supplied from the storage tank.
3.4 After-Cooler
The after cooler reduces the temperature of the BOG after compression. It was modeled as a heat exchanger directly connected to a pipe for heat transfer calculations. The overall heat transfer coefficient, UA, was set to 1246 W/K, and the heat exchange configuration was defined as counterflow. Fresh water was used as the cooling medium, with a refrigerant pipe cross sectional area of 2214.5 mm2. The inlet temperature and pressure of the cooling water were set to 36 °C and 3 bar, while the outlet temperature and pressure were 38°C and 2.9 bar. A mass flow rate of 2.27 kg/s was maintained to ensure continuous coolant circulation and stable heat transfer performance. Because the software cannot compute outlet conditions without an explicitly defined downstream state, the refrigerant outlet temperature in the condenser was assigned based on the manufacturer’s thermal design specifications for the refrigeration module. This provides the boundary information required for Thermal Desktop to perform the coupled thermal and fluid calculation while still allowing the after cooler heat duty and temperature distribution to be computed consistently within the solver.
3.5 Condenser
The condenser liquefies high-pressure CO2 by removing heat until complete (100%) condensation is achieved. It was modeled as a counterflow heat exchanger, using the same structural configuration as the after-cooler, and was directly connected to the associated piping for thermal interaction. The overall heat transfer coefficient (UA) was set to 11,419 W/K. R410A was employed as the refrigerant, with inlet conditions of −6 °C and 13 bar, and outlet conditions of −4 °C and 12.9 bar. The refrigerant flow passage had a cross-sectional area of 2367 mm2, and a mass flow rate of 0.65 kg/s was maintained to ensure stable heat transfer and phase transition.
In this configuration, R410A operates as a subcooled liquid, because its saturation temperature at 13 bar is approximately 45 °C. Operating significantly below this saturation line ensures that the refrigerant remains in the liquid phase throughout the condenser, providing stable sensible cooling without flash-gas formation. The small temperature glide between inlet and outlet arises naturally from supplying a sufficiently large refrigerant mass flow rate to meet the required heat duty for CO2 liquefaction. This cooling approach is consistent with practical cryogenic re-liquefaction system design, where maintaining a fully liquid refrigerant stream helps ensure predictable and robust condenser performance.
3.6 Joule-Thomson Valve
The Joule-Thomson valve reduces a high-pressure and low-temperature LCO2 to a low-pressure and cryogenic state through an isenthalpic expansion process (De Waele et al., 2017). In this study, the valve was modeled using the orifice valve model, with the downstream pressure maintained at a constant 8 bar. To preserve this condition, the minimum and maximum orifice areas were determined based on the choked flow criterion (Jobson, 1955). The choked flow condition is defined by Eq. (1).
where m ˙
Accordingly, the minimum orifice area was set to 10 mm2, and the maximum orifice area to 125 mm2. The flow area was defined as 1436 mm2, and a travel time of 0.01 s was applied to represent valve actuation dynamics.
3.7 Calculation Condition and Modeling Oveview
The transient simulation was performed for 4,400 s, with data recorded at 1 second intervals. To enhance numerical stability at the initial stage (t = 0 s), a steady state solution with 1,000 iterations was executed prior to the transient run. In addition, both the global time step factor and tube time step factor were reduced to 0.05 in order to improve computational accuracy and prevent numerical divergence.
Fig. 4 shows the complete LCO2 re-liquefaction system modeled in Thermal Desktop, including the thermal and fluid connections between components and the applied boundary conditions. The system operates according to the flow configuration described in Fig. 1. The model simultaneously solves conduction, convection, radiation heat transfer, pressure and temperature change, and phase change phenomena across all components. Sinda/Fluint does not perform CO2 solidification or dry ice calculations, so the analysis is limited to vapor liquid thermodynamic behavior. Through continuous circulation, the system re liquefies the BOG generated inside the storage tank, effectively suppressing internal pressure rise and contributing to overall thermal and operational stability.
4. Results and Discussion
4.1 LCO2 Storage Tank
Fig. 5 shows the coupled evolution of internal pressure, relief-valve discharge, and liquid return from the separator within the LCO2 storage system. At the beginning of the simulation, the tank pressure exceeds the relief-valve opening threshold, initiating BOG discharge. Although the valve is open, the initial pressure differential between the tank and downstream piping remains small, resulting in a limited mass-flow rate. This behavior is consistent with Eq. (2), in which the orifice mass-flow rate increases with the square root of the pressure difference. As the early transient stabilizes and the upstream-to-downstream pressure difference grows, Eq. (2) predicts a larger discharge rate, and the tank pressure decreases more rapidly. Once the internal pressure reaches 8 bar, the relief valve closes and the tank pressure begins to rise again due to continued BOG generation. The pressure recovery is driven by an increase in vapor mass within the headspace as liquid CO2 evaporates under continuous external heat ingress.
In this expression, m ˙
As BOG flows into the re-liquefaction loop, it undergoes condensation in the separator. The resulting phase transition gradually increases the liquid level inside the separator until the level-control threshold is reached at 392 s, triggering the separator relief valve to open. During this interval, liquid LCO2 is returned to the storage tank at a maximum rate of 1.44 kg/s. The inflow of subcooled liquid temporarily perturbs the thermodynamic state of the storage tank but does not significantly influence the overall pressure trajectory because the bulk of the pressure response is governed by the vapor phase. After the separator valve recloses at 494 s, the tank undergoes another cycle of BOG-driven pressurization until the relief valve reopens at approximately 2,284 s.
Following established research practice in LCO2 re-liquefaction studies, the component capacities in our model, including the compressor flow range, condenser UA, and Joule–Thomson valve area, were selected within the operating ranges documented in previous literature (Jeon & Kim, 2015a, 2015b; Jeon et al., 2016). This ensures that the simulated re-liquefaction performance is representative of realistic system operation rather than being influenced by arbitrary component sizing.
This repeated sequence of vapor discharge, pressure reduction, heat-driven mass generation, and periodic liquid return establishes a quasi-steady pressure-flow cycle characteristic of LCO2 storage systems subjected to continuous thermal loading. The small oscillations in mass flow observed during the first few seconds are attributable to numerical stabilization in Thermal Desktop and dissipate rapidly, having no effect on the subsequent thermodynamic behavior. Overall, the figure demonstrates that the dynamic interaction among the storage tank, relief valve, and separator forms a stable cyclic response governed by mass-energy balance and vapor–liquid thermodynamics.
Fig. 6 shows the coupled evolution of pressure and temperature within the LCO2 storage tank. When the relief valve opens, BOG is discharged from the tank, reducing the internal mass of CO2. According to the governing equation of state (EOS), this reduction in mass directly lowers the internal pressure, and the associated decrease in internal energy leads to a simultaneous drop in gas-phase temperature. During the initial stage, the gas temperature gradually decreases toward approximately −46 °C, and a small abrupt increase of about 0.5 °C appears within this interval. This brief fluctuation is interpreted as a momentary numerical divergence during the solver’s early stabilization process rather than a physical heat-transfer mechanism. Because the deviation dissipates quickly and the temperature trend returns to a smooth profile, it does not influence the subsequent thermodynamic predictions.
After the relief valve closes, external heat transfer composed of radiative heating from the 45 °C solar load and convective warming from the 25 °C ambient environment raises the gas-phase temperature. The corresponding temperature increase results in pressure recovery through the thermodynamic coupling defined by the EOS. Throughout this process, the liquid-phase CO2 maintains an almost constant temperature due to its high latent heat of approximately 350.24 kJ/kg, whereas the gas phase, which has a much lower heat capacity of approximately 0.846 kJ/(kg · K) at 300 K, responds more sensitively to pressure changes and external heat ingress. As a result, the observed pressure and temperature variations are predominantly governed by the thermodynamic behavior of the gas-phase CO2.
4.2 Separator
Fig. 7 shows the pressure and temperature evolution within the separator during the re-liquefaction process. Although the initial separator pressure was set to 8 bar, the pressure temporarily increased to 8.45 bar at the start of the simulation due to the higher-pressure CO2 entering from the upstream re-liquefaction line. This behavior is consistent with the system configuration described earlier, where the Joule–Thomson valve downstream is fixed to a back-pressure setting of 8 bar. As the separator equilibrates with the downstream Joule–Thomson valve and internal flow conditions stabilize, the separator pressure gradually converges toward approximately 7.96 bar. This slight difference from the nominal 8 bar is attributed to throttling losses and blowdown effects across the Joule–Thomson valve and connecting piping.
The gas-phase CO2 temperature initially decreases due to expansion effects associated with the transient pressure drop, followed by a stabilization near −28.7 °C after the first relief-valve closure. A further decrease to −30.3 °C occurs after the second closure. These temperature levels reflect the evolving vapor–liquid distribution inside the separator, as the internal vapor fraction diminishes due to continued condensation. The separator does not receive significant external heat transfer other than natural convection from the ambient environment; therefore, the observed temperature changes are primarily governed by internal phase distribution rather than external thermal loading.
Small oscillations in gas temperature immediately following each relief-valve closure correspond to the system seeking hydrodynamic and thermodynamic stability as flow rates through the re-liquefaction loop adjust. These fluctuations rapidly dissipate, after which the temperature converges smoothly. Meanwhile, the LCO2 temperature within the separator gradually increases due to ambient heat ingress and then experiences momentary rises when re-liquefied fluid returns during valve operations. Once the relief valve closes and the mass flow ceases, the pressure and temperature momentarily drop due to expansion effects, consistent with the expected thermodynamic response of CO2 under such transient flow conditions.
Overall, Fig. 7 demonstrates the interplay of transient pressurization, throttling losses, vapor–liquid equilibrium shifts, and flow stabilization within the separator, capturing a realistic thermodynamic response of the LCO2 re-liquefaction process.
4.3 Re-Liquefaction System
Fig. 8 shows the CO2 flow-rate behavior within the re-liquefaction system, which is governed by the mass supplied from both the storage tank and the separator. At the beginning of the simulation, a pronounced surge flow is observed through the separator check valve. This occurs because the separator initially contains vapor-phase CO2 at a pressure higher than that of the re-liquefaction loop. As a result, CO2 is rapidly drawn into the system until the internal pressures reach equilibrium. The early peak therefore reflects the initial pressure imbalance rather than a sustained operating condition.
The flow entering the re-liquefaction system originates from two independent sources, which are vapor-phase CO2 discharged from the storage tank through the relief valve and CO2 supplied from the separator through the check valve. The flow-rate curve of the re-liquefaction loop thus represents the combined mass balance of these two contributions. During cyclic operation, the re-liquefaction loop exhibits an average circulation flow rate of approximately 0.4247 kg/s, reflecting the combined effect of heat-ingress-driven vapor generation, compressor suction behavior, and periodic separator interaction.
The fluctuations that appear around 400 s occur when the separator liquid level reaches its discharge threshold. Once the separator relief valve opens, liquid-phase CO2 is returned to the storage tank, altering the internal phase distribution and causing a brief change in the vapor flow entering the re-liquefaction loop. This interaction produces the characteristic stepwise fluctuation observed in the early period.
When the storage-tank relief valve closes, the re-liquefaction system experiences a temporary cessation of flow because the primary supply path from the tank is interrupted. With no inflow from the tank, the system briefly relies on the separator alone, which cannot maintain the required flow rate. This results in the near-zero flow interval that follows each closure event. Immediately after the valve closes, a short-lived increase in flow from the separator appears. This behavior is caused by the rapid redistribution of internal pressures within the re-liquefaction loop. As the tank-side inflow disappears, the separator becomes the dominant source of CO2 for a moment, creating a transient surge before the system settles.
To provide an external reference for flow-rate validation, an independent HYSYS calculation was performed under the same design-point conditions. HYSYS predicts a steady CO2 flow rate of 0.5086 kg/s for the re-liquefaction loop, which is also marked in Fig. 8. In the present model, the BOG inflow during normal relief-valve cycling is slightly lower than this reference value, consistent with the reduced vapor generation observed under the applied heat-ingress conditions. Conversely, when re-liquefaction does not occur and vapor accumulates in the loop, the model predicts a higher circulation rate of approximately 0.549 kg/s, reflecting the increased vapor availability and reduced condensation load.
Overall, the flow behavior in Fig. 8 demonstrates how the re-liquefaction system transitions among periods dominated by tank-driven inflow, short separator-driven transients, and intervals of flow interruption caused by relief-valve closures. These dynamics form a recurring operational cycle controlled by the separator liquid level, valve activation, and the evolving pressure distribution within the re-liquefaction loop.
Fig. 9 shows the pressure evolution within the re-liquefaction system, which is governed by the interaction between compressor operation, Joule–Thomson throttling, and transient flow redistribution during relief-valve cycling. Although the compressor operates based on a linearly interpolated performance curve around its design head, the downstream Joule–Thomson valve imposes a significant flow resistance due to its limited orifice area. This restriction reduces the flow velocity exiting the re-liquefaction loop, causing flow stagnation and, consequently, a pressure buildup upstream. This mechanism explains why the re-liquefaction system pressure increases to approximately 36 bar while the relief valve is open.
When the storage tank relief valve closes, the CO2 supply path from the tank is abruptly cut off. As discussed in Fig. 7, this sudden loss of incoming mass flow reduces the compressor’s available suction flow, causing the compressor inlet pressure to rise relative to the separator pressure. Because the separator and the re-liquefaction system are directly connected, the resulting pressure imbalance induces CO2 within the separator to flow rapidly into the re-liquefaction loop. This transient redistribution of CO2 resembles a blowdown response, producing a sharp pressure drop within the re-liquefaction system until the internal flow field equilibrates.
The separator pressure evolution has been explained previously in Fig. 7, where it was shown that the pressure stabilizes near 7.96 bar due to the Joule–Thomson valve’s downstream pressure setting. In contrast, the compressor inlet pressure exhibits a more pronounced transient due to its sensitivity to flow availability and suction-side dynamics. The temporary decline to approximately 6.3 bar reflects the combined effects of flow starvation from the storage tank and the momentary redirection of separator CO2 into the re-liquefaction system. Once the internal circulation stabilizes and both supply paths re-establish equilibrium, the system pressures converge toward their respective steady-state values.
Fig. 10 presents the liquefaction ratios achieved in the condenser and across the Joule–Thomson valve. While the relief valve remained open, the condenser generated fully liquefied CO2 (100%) under the applied heat-duty and refrigerant conditions. However, approximately 25% of the liquefied CO2 reverted to vapor across the Joule–Thomson valve due to throttling losses (Yang et al., 2005). This vapor fraction is not an arbitrary loss but the direct consequence of an isenthalpic expansion process in which the fluid state enters the two-phase dome at lower pressure. An independent HYSYS calculation performed under the same operating conditions predicts a flash fraction of 24.29%, which closely matches the value obtained in our model and confirms that the observed vapor fraction reflects a physically accurate equilibrium response.
Fig. 11 further verifies that the Joule–Thomson valve operates under an effectively constant-enthalpy condition: the specific enthalpy immediately upstream and downstream of the valve fully overlaps throughout the transient operation. Because no shaft work or external heat is added, the expansion strictly follows the Joule–Thomson constraint, and the resulting vapor formation represents the flash evaporation required to satisfy vapor–liquid equilibrium at the downstream pressure, not an efficiency loss of the hardware.
In this context, the term “throttling losses” refers to the irreversible entropy generation associated with isenthalpic expansion, which drives the fluid toward a higher-entropy state with part of the mass entering the vapor region. The approximately 25% vapor fraction shown in Fig. 10 therefore represents the thermodynamically required flash fraction at constant enthalpy. The close correspondence between the model prediction and the HYSYS reference result (accuracy approximately 0.97 on a fractional basis) further demonstrates that the predicted liquid fraction is a physically valid thermodynamic outcome rather than a numerical artifact. After the relief valve closes, CO2 continues to circulate through the system; however, without additional inflow from the storage tank, no further cooling load is introduced, and the liquefaction ratio remains unchanged until the next cycle.
4.4 Compressor Power and Condenser Heat Duty Analysis
Fig. 12 shows the transient evolution of compressor power throughout the re-liquefaction cycle. Immediately after each relief-valve closure, short-duration power spikes of up to approximately 80 kW are observed; however, these peaks arise solely from momentary redistribution of mass flow within the loop and do not correspond to actual re-liquefaction operation. During steady re-liquefaction, when vapor-phase CO2 is supplied continuously from the storage tank and the compressor operates within its intended design range, the power consumption remains stable at approximately 20–40 kW. This level of power demand is consistent with values reported for small-to-medium LCO2 re-liquefaction systems and agrees with the compressor performance curve used in the present model, confirming that the simulated operating conditions remain physically realistic.
Fig. 13 presents the condenser heat duty calculated during operation. As with the compressor, transient heat duty peaks, which approach 160 kW, appear only at the moment when the relief valve closes because the inlet flow and thermodynamic state change abruptly at that instant. During normal re-liquefaction, when vapor CO2 enters steadily and condensation proceeds under controlled conditions, the condenser heat duty remains within the range of 90 to 130 kW. This range directly reflects the thermal load imposed by the specified UA value and the operating temperatures of the R410A refrigerant, showing that the modeled condenser performance is consistent with the intended design capacity.
An independent HYSYS calculation performed for the same operating conditions yields a condenser heat duty of 156,900 W. The value obtained in this study is lower than the HYSYS prediction, which indicates that the modeled re-liquefaction loop requires less thermal input to achieve condensation. This result suggests that, under the assumed operating conditions, the re-liquefaction process exhibits favorable energy efficiency relative to the reference HYSYS calculation.
The stable heat duty plateau observed during steady operation confirms that the condenser provides sufficient heat removal to sustain continuous CO2 liquefaction under the specified boundary conditions.
5. Conclusions
The LCO2 re-liquefaction system was numerically analyzed using Thermal Desktop, a one-dimensional thermal–fluid simulation tool. The system configuration includes an LCO2 storage tank, compressor, after-cooler, condenser, Joule–Thomson valve, separator, and the associated piping network. The numerical model incorporated conduction, convection, and radiative heat transfer, as well as phase-change interactions among components. Thermophysical properties of CO2 were obtained from the NIST REFPROP database to ensure accurate representation of real operating conditions.
The results show that the system achieves the intended periodic pressure control behavior driven by the thermodynamic coupling between heat ingress, BOG generation, and relief valve operation. As external heat enters the insulated cargo tank, vaporization of LCO2 gradually increases the internal pressure. When the pressure rises from 8 bar to 8.5 bar, the relief valve opens and discharges BOG, reducing the vapor mass and returning the pressure to 8 bar. This produces a 26 minute pressure rise period consistent with heat ingress driven BOG formation.
Within the re-liquefaction loop, the internal pressure increases to approximately 36 bar while the relief valve is open. This occurs because the compressor continues to compress incoming BOG, whereas the downstream Joule–Thomson valve imposes a strong throttling resistance due to its limited orifice area, causing upstream pressure accumulation. The corresponding mass flow rate of roughly 4.5 kg/s reflects the combined inflow from the storage tank and separator under these transient conditions.
Although the condenser achieves full liquefaction (100%) by removing the required latent heat, only about 75% of the CO2 remains in the liquid phase after the Joule–Thomson expansion. This result is consistent with the isenthalpic nature of Joule–Thomson throttling: the abrupt pressure reduction shifts the refrigerant into the vapor–liquid region, generating a flash-vapor fraction even when the upstream stream is fully condensed.
During steady re-liquefaction, when vapor inflow and cooling capacity remain balanced, the system maintains an internal circulation flow of approximately 0.55 kg/s, and the loop pressure converges toward 21.6 bar. The separator likewise shows stable vapor–liquid separation and reliable liquid-level control, with the relief valve opening and closing precisely at the designated high- and low-level thresholds.
Overall, the simulation results demonstrate that the LCO2 re-liquefaction system maintains both numerical stability and physically consistent thermodynamic behavior under the defined control logic and operating conditions. The analysis provides quantitative insight into transient system responses and pressure-control characteristics, offering foundational data to support future design verification and performance evaluation of CCUS-based marine CO2 transport systems.
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