Design and Thermodynamic Analysis of CO₂ Liquefaction Processes for Onboard Carbon Capture and Storage

Abstract

This study evaluates the thermodynamic performance of the following two CO₂ liquefaction processes for onboard carbon capture and storage (OCCS) on a 174,000 m³ LNG carrier: the Linde–Hampson and vapor compression refrigeration cycles. The cycles were designed based on realistic vessel operating conditions and compared using the specific energy consumption (SEC) as the primary performance indicator, alongside the coefficient of performance (COP). To enable a fair comparison of the two distinct cycles, a complementary COP metric was validated for the open-loop Linde–Hampson cycle by establishing a system-level definition of heat removal. The validity of this metric was confirmed by demonstrating that its optimal point (maximum COP) aligns with that of the primary metric (minimum SEC), ensuring thermodynamic consistency. The analysis reveals that the vapor compression cycle demonstrates superior performance, achieving an 8.35% higher COP and an 11.45% lower SEC than the Linde–Hampson cycle. This work provides a consistent methodology for the comparative assessment of open- and closed-loop liquefaction systems.

1. Introduction

Global warming caused by climate change has become a critical issue, and international efforts to protect the environment have thus been strengthened [1]. The International Maritime Organization (IMO) adopted the revised IMO Greenhouse Gas (GHG) strategy at the 80th Marine Environment Protection Committee (MEPC) [2]. The revised strategy aims to reduce GHG emissions per ship by at least 40% by 2030 compared to 2008 levels, achieve a 70% reduction by 2040, and reach net-zero emissions by 2050 [3,4]. Furthermore, at the 83rd MEPC, amendments to the International Convention for the Prevention of Pollution from Ships (MARPOL) Annex VI were approved to establish the IMO net-zero framework, introducing a GHG fuel intensity (GFI) standard. New regulations regarding onboard carbon capture and storage (OCCS) systems were also included [5,6].

In response to these strengthened international regulations, the maritime industry is accelerating the transition to zero-carbon fuels, such as hydrogen (H₂) and ammonia (NH₃), which do not emit carbon dioxide (CO₂) during combustion [7]. However, their immediate adoption is limited by their low technological maturity and safety concerns. Although liquefied natural gas (LNG) is not a zero-carbon fuel, it emits fewer nitrogen oxides (NO_x) and CO₂ emissions than conventional marine fuels [8]. Moreover, LNG offers advantages such as a high calorific value, a lower environmental risk, and a relatively low fuel cost. Therefore, LNG has been evaluated as a practical fuel that can be commercialized prior to the introduction of zero-carbon fuels [9,10].

The number of LNG-fueled ship orders has been steadily increasing. As of 2024, 169 vessels had been delivered and 264 additional orders placed, with LNG-fueled ships projected to account for 24% of the global merchant fleet by 2050 [11,12]. The application of LNG propulsion to large vessels began in 2012 and has expanded to carriers with capacities of 165,000–175,000 m³ [13].

Until the full-scale transition to zero-carbon fuels is achieved, the increasing number and size of LNG-fueled ships will inevitably result in higher CO₂ emissions. To mitigate this, the adoption of OCCS systems has been proposed [14]. An OCCS system captures CO₂ from exhaust gases during voyages, liquefies and stores it onboard, and subsequently transports it to port facilities for unloading. It is increasingly recognized as an effective solution to reduce carbon emissions and ensure compliance with the energy efficiency design index (EEDI) regulations [15]. OCCS technologies are generally classified into pre-combustion, post-combustion, and oxy-fuel combustion methods. Among these, the post-combustion approach is the most widely applied, due to its compatibility with existing ship engines and propulsion systems [16,17]. The captured CO₂ is liquefied and stored onboard, as liquid storage provides a higher density and thus greater efficiency for long-distance transportation and unloading compared to compressed gas storage [18].

Several studies have examined the design and performance of onboard CO₂ liquefaction systems, with particular emphasis on their energy efficiency, exergy efficiency, and economic feasibility. Chen and Morosuk [19] compared a three-stage vapor compression system and the precooled Linde–Hampson system for a large-scale land-based system for a 500 MW pulverized coal-fired power plant. Their work, simulated using ASPEN HYSYS V11, was focused on a large-scale land-based system for a 500 MW pulverized coal-fired power plant. The results of their simulation indicated that the vapor compression system using R-290 refrigerant at 15 bar provided superior energy efficiency and economic performance. Seo et al. [20] evaluated four CO₂ liquefaction systems applicable to OCCS systems using the Figure of Merit (FOM) and Life Cycle Cost (LCC) and identified the three-stage vapor compression system with ammonia refrigerant at 15 bar as the most efficient system in terms of both the FOM and economic performance. Aliyon et al. [21] conducted a comparative analysis CO₂ liquefaction systems: the Linde–Hampson, dual-pressure Linde–Hampson, vapor compression, and an integrated absorption refrigeration system. They determined that the vapor compression refrigeration system achieved the highest Coefficient of Performance (COP) and exergy efficiency, as well as the lowest LCC. An exergo-economic analysis was also conducted to evaluate potential performance improvements in the main components.

These studies have provided insights into the design and performance of various CO₂ liquefaction systems, often identifying the vapor compression system as highly efficient. Building upon this work, the present study addresses two specific areas for further investigation. First, while prior research has focused on large-scale, land-based applications or general system comparison, this study provides a detailed application-specific analysis for an OCCS system on a 174,000 m³ LNG carrier, considering its specific onboard operation constraints. Second, while previous studies have calculated the COP for open-loop cycles, a methodological validation that reconciles COP with the primary liquefaction metric, Specific Energy Consumption (SEC), has not been a central focus. This research addresses that point by validating a consistent COP framework, ensuring a robust thermodynamic basis for comparing open- and closed-loop technologies.

The remainder of this paper is structured as follows. Section 2 outlines the materials and methods, including the design of the CO₂ liquefaction system and presents the thermodynamics performance indicators and COP evaluation method for the Linde–Hampson refrigeration cycle. Section 3 presents and discusses the results of the comparative analysis of the two liquefaction systems. Finally, Section 4 summarizes the main conclusions.

2. Materials and Methods

2.1. Description of CO₂ Liquefaction

This study provides a comparative analysis of two CO₂ liquefaction systems for onboard applications: the open-loop Linde–Hampson cycle and the closed-loop vapor compression refrigeration cycle. In Linde–Hampson cycle, CO₂ is liquefied through a series of compression, condensation, and expansion processes, using CO₂ itself as the working fluid. It does not require an external refrigerant. The system configuration is illustrated in Figure 1, and its operational procedure is as follows:

(1)

Compression: The captured gas undergoes a three-stage low-pressure compression, followed by a two-stage high-pressure compression. After each stage, the gas is cooled in an intercooler. At the inlet of the first high-pressure compressor, the gas discharged from the aftercooler of the third low-pressure compressor is mixed with the separated CO₂ vapor, which has been heated in the heat exchanger.

(2)

Condensation: The compressed CO₂ becomes saturated in the aftercooler and is subsequently supercooled in the heat exchanger. During this process, heat is transferred from the compressed CO₂ to the separated CO₂ vapor.

(3)

Expansion: The high-pressure supercooled liquid expands through the Joule–Thomson valve, producing a low-temperature vapor–liquid mixture. In the downstream separator, CO₂ is separated into gas and liquid phases. The separated CO₂ vapor is recycled to the inlet of the first high-pressure compressor via the heat exchanger, while the liquified CO₂ is transferred to the storage tank.

Figure 1. Process flow diagram of the Linde–Hampson refrigeration cycle system.

The closed refrigeration system is based on a vapor compression refrigeration cycle, in which ammonia is used as the refrigerant [22,23]. This cycle consists of the following stages: compression, condensation, expansion, and evaporation. The system configuration is shown in Figure 2, and its operation can be described as follows:

(1)

Compression and condensation: The ammonia refrigerant undergoes three stages of compression, which raise its pressure and temperature. Each stage has its aftercooler that dissipates heat from the compressed gas. Then, after the third-stage compressor, the high-temperature and high-pressure refrigerant is condensed into a liquid state in a condenser.

(2)

Expansion: The high-pressure liquid refrigerant is expanded through a Joule–Thomson valve, resulting in a low-pressure mixture of liquid and vapor.

(3)

Evaporation: The low-temperature refrigerant absorbs heat from the captured CO₂ stream through the heat exchanger. This heat input causes the refrigerant to evaporate, completing the cycle and preparing it for compression.

Figure 2. Process flow diagram of the vapor compression refrigeration cycle system.

2.2. Basis of Design

To ensure the practical relevance of the comparative analysis, this study selects an OCCS system installed on a 174,000 m³ class LNG carrier, which currently represents the most widely ordered ship type [24,25]. The ship is equipped with two WinGD 5X72DF-C2.1 propulsion engines (Winterthur Gas & Diesel Ltd., Winterthur, Switzerland), with the engine load assumed to be 50% [26,27]. The exhaust gas mass flow rate was obtained from engine data provided by the WinGD GTD program. The mass flow rate of the captured CO₂ was calculated based on the exhaust gas mass flow rate, the CO₂ concentration in the exhaust gas, and the capture rate. The specifications are summarized in Table 1 [28,29,30].

Table 1. Specifications of the vessel, exhaust gas, and captured gas.

Item	Unit	Value
Cargo capacity	m3	174,000
Main fuel	-	LNG
Engine	-	WinGD 5X72DF-C2.1 (2 set)
Exhaust gas mass flow	kg/h	140,942
Capture rate	%	90
CO2 concentration	mol %	14.98
Captured gas mass flow	kg/h	27,970

Each system was modeled and simulated using Aspen HYSYS V14 (Aspen Technology, Inc., Bedford, MA, USA) with the Peng–Robinson equation of state. The key equipment assumptions and process boundary conditions, selected to reflect a realistic onboard environment, are summarized as follows [19,20,21,29,31]:

• Compressor adiabatic efficiency: 75% [20];
• Maximum compressor pressure ratio: 3 [20];
• Pressure drop across coolers and heat exchangers: 50 kPa [20,21];
• Minimum approach temperature in heat exchangers: 3 °C [21];
• Refrigerant side inlet and outlet pressures in the vapor compression refrigeration cycle heat exchanger: 101.3 kPa and 100 kPa, respectively (vacuum condition considered);
• Captured CO₂ composition: 100% [19,21];
• Captured gas pressure and temperature: 150 kPa, 40 °C [19,21];
• Storage pressure and temperature: 1500 kPa, −27.71 °C [29];
• Sea water temperature: 30 °C [29].

2.3. Design of CO₂ Liquefaction Systems

The simulation results of the two systems are summarized in Table 2 and Table 3. The corresponding stream numbers are indicated in Figure 1 and Figure 2.

Table 2. Steady-state simulation result of the Linde–Hampson refrigeration system.

Stream Number	1	2	3	4	5	6
Vapor fraction	1.000	1.000	1.000	1.000	1.000	0.000
Pressure (kPa)	150	1550	1500	1500	9950	9900
Temperature (°C)	40.00	116.3	35.00	33.63	128.7	35.00
Flow rate (kg/h)	27,970	27,970	27,970	51,403	51,403	51,403
Stream Number	7	8	9	10	11	-
Vapor fraction	0.000	0.456	0.000	1.000	1.000	-
Pressure (kPa)	9850	1500	1500	1500	1500	-
Temperature (°C)	28.58	−27.71	−27.71	−27.71	32.00	-
Flow rate (kg/h)	51,403	51,403	27,970	23,433	23,433	-

Table 3. Steady-state simulation result of the vapor compression refrigeration system.

Stream Number	1	2	3	4	5
Vapor fraction	1.000	1.000	1.000	1.000	1.000
Pressure (kPa)	150	358.9	308.9	739.3	689.3
Temperature (°C)	40.00	123.4	35.00	117.7	35.00
Flow rate (kg/h)	27,970	27,970	27,970	27,970	27,970
Stream Number	6	7	8	9	10
Vapor fraction	1.000	1.000	0.000	0.000	1.000
Pressure (kPa)	1650	1600	1550	1500	1500
Temperature (°C)	118.3	35.00	−27.70	−27.71	−27.71
Flow rate (kg/h)	27,970	27,970	27,970	27,970	0.000
Stream Number	11	12	13	14	15
Vapor fraction	0.000	1.000	1.000	1.000	1.000
Pressure (kPa)	1500	100	266.3	216.3	576
Temperature (°C)	−27.71	32.00	132.2	35.00	136.1
Flow rate (kg/h)	27,970	8531	8531	8531	8531
Stream Number	16	17	18	19	-
Vapor fraction	1.000	1.000	0.000	0.233	-
Pressure (kPa)	526	1400	1350	101.3
Temperature (°C)	35.00	136.7	35.00	−33.26	-
Flow rate (kg/h)	8531	8531	8531	8531	-

In the Linde–Hampson refrigeration cycle system, the captured CO₂ gas is supplied at 150 kPa and 40 °C. After three stages of low-pressure compression, the gas reaches 1550 kPa and 116.3 °C, with intercooling to 35 °C after each stage. After two stages of high-pressure compression, the pressure and temperature rise to 9950 kPa and 128.7 °C, after which the gas is cooled to 35 °C to form a saturated liquid at 9900 kPa. It is then subcooled to 28.58 °C in the heat exchanger and expanded through the Joule–Thomson valve, yielding a vapor–liquid equilibrium state. The gas and liquid are separated in the separator. The separated gas exchanges heat with the compressed gas and is recycled to the high-pressure compressor inlet, while the liquid is stored in a saturated state at 1500 kPa and −27.71 °C.

For the vapor compression refrigeration cycle, the captured CO₂ enters under the same inlet conditions. After undergoing three stages of compression, the pressure and temperature rise to 1650 kPa and 118.3 °C, with each stage followed by cooling to 35 °C. The compressed gas is subsequently subcooled in the heat exchanger and expanded through the valve, producing liquefied CO₂ in a saturated state at 1500 kPa and −27.71 °C. The refrigerant loop in this system operates independently of the CO₂ stream. Ammonia, serving as the refrigerant, is compressed in three stages, reaching 1400 kPa and 136.7 °C. At the downstream of the final compressor, the refrigerant is condensed in a cooler to form a high-pressure liquid at 1350 kPa and 35 °C. Expansion through the Joule–Thomson valve reduces its pressure to 101.3 kPa and temperature −33.26 °C, reaching a vapor–liquid equilibrium state. After exchanging heat with the captured CO₂, the refrigerant returns to the cycle as a gaseous state at 100 kPa and 32 °C.

2.4. Thermodynamic Performance Indicators

We evaluated the two systems by using two performance indicators derived from the first law of thermodynamics: the COP and SEC.

2.4.1. Specific Energy Consumption (SEC)

For a liquefaction process, where the product is a liquefied mass of gas, the most direct and practical metric for energy efficiency is the SEC. It is the standard indicator for assessing liquefaction systems [22,32], as it clearly represents the energy cost required to produce a unit mass of the desired product. It is defined as

$$\mathrm{S}\mathrm{E}\mathrm{C}={\displaystyle \frac{W_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}{{\dot{m}}_{{\mathrm{C}\mathrm{O}}_2}}},$$

(1)

where $W_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ is the total power consumption of all the compressors, and ${\dot{m}}_{{\mathrm{C}\mathrm{O}}_2}$ is the mass flow rate of the liquefied CO₂.

2.4.2. Establishing a Common Thermodynamic Framework: The Coefficient of Performance (COP)

The COP is a key indicator of a refrigeration system’s efficiency, representing how effectively heat is removed relative to the energy input [19,21]. It is defined as the ratio of the heat removed (${\dot{Q}}_{\mathrm{L}}$) to the total energy supplied to the system ($W_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$), as expressed in Equation (2):

$$\mathrm{C}\mathrm{O}\mathrm{P}={\displaystyle \frac{{\dot{Q}}_{\mathrm{L}}}{W_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}}$$

(2)

While COP is clearly defined for the closed-loop vapor compression cycle, its application to the open-loop Linde–Hampson cycle is not straightforward. This difficulty arises because the system does not use a separate refrigerant with a distinct evaporator load that defines ${\dot{Q}}_{\mathrm{L}}$; instead, the refrigeration effect is distributed throughout the process.

However, the primary goal of this study is to establish a consistent thermodynamic framework to compare the fundamentally different open-loop Linde–Hampson and closed-loop vapor compression cycles. While SEC is a product-based metric that quantifies the overall energy cost per unit of liquefied gas, COP functions as a mechanism-based metric. It compares the internal thermodynamic efficiencies of the thermodynamic process: the conversion of input work into a useful heat removal effect. By establishing a system-level definition of ${\dot{Q}}_{\mathrm{L}}$ for the Linde–Hampson cycle that is conceptually analogous to the evaporator load in the vapor compression cycle, we can directly compare how efficiently each system’s machinery performs this core task. Therefore, developing and validating this metric is essential for a robust comparative analysis.

2.4.3. Defining and Validating a System-Level ${\dot{Q}}_{\mathrm{L}}$ for the Linde–Hampson Cycle

To determine an appropriate definition of ${\dot{Q}}_{\mathrm{L}}$ for the Linde–Hampson cycle, we considered three alternatives based on the heat removed by different system boundaries: (1) the aftercooler, (2) the heat exchanger, and (3) the overall system. Unlike conventional refrigeration systems with a single evaporator, the Linde–Hampson cycle achieves its cooling effect through a distributed process involving intercoolers, aftercoolers, and the Joule–Thomson expansion. Consequently, defining ${\dot{Q}}_{\mathrm{L}}$ based on any single component would be inherently arbitrary and incomplete, as it would neglect the contributions of other stages and thus fail to capture the total thermodynamic effort. Therefore, defining ${\dot{Q}}_{\mathrm{L}}$ as the total heat removed from the overall system provides the most physically consistent representation of the system’s total useful cooling effect.

The validity of this approach was subsequently confirmed by demonstrating its thermodynamic consistency with the primary performance metric, the SEC. The analysis in Section 3.1 shows that the pressure yielding the maximum COP under this definition is identical to the pressure yielding the minimum SEC. This correspondence validates our choice and confirms that defining ${\dot{Q}}_{\mathrm{L}}$ based on the overall system is the most appropriate method for performance evaluation.

2.4.4. Complementary Insights from SEC and COP

The SEC and the system-level COP are complementary indicators that offer different perspectives on system performance. SEC is a product-based metric ($W_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}/{\dot{m}}_{{\mathrm{C}\mathrm{O}}_2}$), quantifying the overall cost per unit mass of liquefied CO₂, thereby assessing the overall practical outcome. In contrast, COP is a mechanism-based metric (${\dot{Q}}_{\mathrm{L}}/W_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$), which evaluates the intrinsic efficiency of the underlying thermodynamic machinery responsible for heat removal.

A fair comparison between two different architectures, such as an open-loop and a closed-loop system, necessitates making this distinction. The final product output measured by SEC is influenced by multiple factors, not just the cycle efficiency. Using both metrics allows for a more in-depth analysis: COP reveals the fundamental efficiency of the heat removal machinery itself, while SEC captures the all-encompassing result. This is crucial because it helps identify the true sources of performance advantages or disadvantages—whether they lie within the core thermodynamic cycle or elsewhere in the process design. Therefore, this approach enables a more robust and complete comparison than could be achieved with either metric in isolation.

3. Results and Discussion

3.1. Validation of the COP Evaluation Method for the Linde–Hampson Cycle

To apply the proposed COP evaluation method, the COP and SEC were evaluated across a Joule–Thomson inlet pressure range from 7950 kPa to 11,450 kPa in 100 kPa increments. Figure 3, Figure 4 and Figure 5 illustrate the COP values obtained from each definition of ${\dot{Q}}_{\mathrm{L}}$, alongside the corresponding SEC.

Figure 3. COP and SEC vs. Joule–Thomson valve inlet pressure (aftercooler-based ${\dot{Q}}_{\mathrm{L}}$).

Figure 4. COP and SEC vs. Joule–Thomson valve inlet pressure (heat exchanger-based ${\dot{Q}}_{\mathrm{L}}$).

Figure 5. COP and SEC vs. Joule–Thomson valve inlet pressure (overall system-based ${\dot{Q}}_{\mathrm{L}}$).

As shown in Figure 3 and Figure 4, when ${\dot{Q}}_{\mathrm{L}}$ is defined by the heat removed in the aftercooler or the heat exchanger, the pressure maximizing the COP does not match the pressure minimizing the SEC. By contrast, Figure 5 demonstrates that when ${\dot{Q}}_{\mathrm{L}}$ is defined as the heat removed from the overall system, the COP maximum coincides with the SEC minimum.

These results indicate that defining ${\dot{Q}}_{\mathrm{L}}$ as the total heat removal from the overall system is the most reasonable approach for COP evaluation in liquefaction systems without external refrigerants, such as the Linde–Hampson refrigeration cycle.

3.2. Comparison of the Two CO₂ Liquefaction System Performance

In this section, the performance of the two CO₂ liquefaction systems is presented and discussed in terms of the COP and SEC. To ensure a rational comparison, the optimal inlet pressure of the Joule–Thomson valve in the refrigerant cycle was also determined for the vapor compression system. The COP and SEC were evaluated over an inlet pressure range of 1350 kPa to 1800 kPa in 25 kPa increments. At pressures below 1350 kPa, the cooling capacity of the valve was insufficient to achieve complete liquefaction of the refrigerant. Consequently, the cooling effect of the CO₂ side Joule–Thomson valve decreased, and the optimization range was set at 1350 kPa or higher. The optimal operating point of the vapor compression refrigeration cycle is presented in Figure 6.

Figure 6. COP and SEC vs. Joule–Thomson valve inlet pressure of the refrigerant side (vapor compression refrigeration cycle).

As shown in Figure 6, for the vapor compression cycle, the COP maximum and SEC minimum coincide at a refrigerant-side Joule–Thomson valve inlet pressure of 1350 kPa.

The Linde–Hampson and vapor compression refrigeration cycles required 3677 kW and 3232 kW of power, respectively, with their Joule–Thomson valve inlet pressures set to the optimal values (Figure 7 and Figure 8). The higher power demand of the Linde–Hampson system arises from the larger flow rates handled by the high-pressure compressors. With COP and SEC values of 0.814 and 0.131, respectively, for the Linde–Hampson cycle and 0.882 and 0.116, respectively, for the vapor compression cycle, the latter demonstrated superior efficiency, achieving an 8.35% higher COP and an 11.45% lower SEC under identical boundary conditions (Figure 9 and Table 4).

Figure 7. Compressor energy consumption (Linde–Hampson refrigeration cycle).

Figure 8. Compressor energy consumption (vapor compression refrigeration cycle).

Figure 9. COP and SEC comparison of the two CO₂ liquefaction systems.

Table 4. COP, SEC, and relative difference for the two different CO₂ liquefaction systems.

Item	Linde–Hampson Refrigeration Cycle	Vapor Compression Refrigeration Cycle	Relative Difference (%)
COP	0.814	0.882	8.35
SEC (kWh/kg)	0.131	0.116	11.45

4. Conclusions

This study investigated two CO₂ liquefaction systems for OCCS in a 174,000 m³ LNG carrier: the Linde–Hampson and the vapor compression refrigeration cycle. Their performance was evaluated using the COP and SEC. Our comparative analysis demonstrated that the vapor compression cycle is the more energy-efficient option. Under optimized conditions, the vapor compression cycle achieved an 8.35% higher COP and an 11.34% lower SEC than the Linde–Hampson cycle.

A key contribution of this work is the methodological framework that reconciles the concepts of COP and SEC for comparing open- and closed-loop liquefaction systems. By defining heat removal (${\dot{Q}}_L$) based on the overall system and demonstrating the optimal points for maximizing COP and minimizing SEC align, this study establishes a robust and consistent basis for performance analysis. This validated methodology not only underpins the findings of this specific OCCS comparison but also provides a reliable tool for future assessments of diverse refrigeration and liquefaction technologies. Future research will build upon this validated foundation, extending the analysis to exergy-based methods to further refine system for CO₂ liquefaction systems.