Nomenclature
ATCI:
Annualized total cost index
ATOC:
Annualized total operation cost
CEPCIρ:
Chemical engineering plant cost index
COP:
Coefficient of performance
EOS:
Equation of state
FG:
Flash gas
GCU:
Gas combustion unit
JT:
Joule–Thomson
L-HC:
Linde–Hampson cycle
LNG:
Liquified natural gas
MAPE:
Mean absolute percentage error
MHV:
Modified Huron-Vidal
MR:
Mixed refrigerant
MRC:
Mixed-refrigerant cycle
PR:
Peng–Robinson
PSO:
Particle swarm optimization
PT:
Pressure-Temperature
RBC:
Reverse Brayton cycle
SLNG:
Subcooled LNG
SPC:
Specific power consumption
TAC:
Total annualized cost
TCI:
Total capital investment
vdW:
van der Waals
VLE:
Vapor–liquid equilibrium
1. Introduction
The demand for natural gas is increasing continuously amid the global response to global warming and efforts for transition to a green society (Dudley, 2017). Since the industrial revolution, greenhouse gas (GHG) emissions (e.g., carbon dioxide) from the use of fossil fuels have been highlighted as the main cause of global warming. Natural gas is a fossil fuel that emits GHGs during combustion; however, it serves as a transition fuel for carbon reduction owing to its relatively low carbon-dioxide emissions compared with coal and oil (Thomson et al., 2015). In particular, blue hydrogen, which is generated by applying carbon capture and storage technology to natural gas, is considered an intermediate step necessary for the transition to hydrogen economy; additionally, it is a major factor contributing to higher demands for natural gas (Al-Kuwari and Schönfisch, 2022; Lee et al., 2023; Simpa et al., 2024).
For mass transportation, natural gas is transported in the form of liquified natural gas (LNG) at a cryogenic temperature of approximately −162 °C under atmospheric pressure. During this process, the boil-off gas (BOG) generated must be effectively treated as it incurs safety risks. LNG is a natural gas liquefied to maximize long-distance transportation and storage efficiency, and its volume decreases to approximately 1/600 that in the gas state (Meza et al., 2021). LNG under cryogenic conditions, however, continuously vaporizes owing to heat inflow caused by temperature difference arising from the external environment. BOG increases the pressure inside the tank, thereby causing severe safety issues that may cause the allowable pressure to be exceeded or cargo spill (Chen et al., 2004). Hence, various cargo-handling systems are applied in LNG carriers, including a gas combustion unit (GCU) for burning excessive BOG, a vent system for releasing excessive BOG, and a reliquefaction system for reliquefying BOG and then returning it to the tank, in addition to LNG subcooling for subcooling LNG and injecting it into the tank. The GCU and vent system are structurally simple and favorable for instantaneous pressure control; however, they emit GHGs (e.g., methane and carbon dioxide) during the combustion or release of BOG (Balcombe et al., 2022; Chen et al., 2004; Fernández et al., 2017; Moon et al., 2005). Accordingly, a reliquefaction system that can retrieve BOG is typically adopted (Bian et al., 2022; D. Kim et al., 2019; Kim et al., 2020; Lee et al., 2023; Gómez et al., 2015; Tan et al., 2018).
The conventional reliquefaction system involves an increase in system load due to the generation of gas caused by system expansion. As shown in Fig. 1(a), the reliquefaction system compresses BOG to a high-pressure and high-temperature state and converts it into a high-pressure and low-temperature state through self-cooling or heat exchange with an external refrigerant before finally liquefying it into LNG through the Joule–Thomson expansion. This reliquefaction system does not significantly increase the cost of equipment investment because the fuel-supply compressor can be used unmodified; however, it requires the recirculation of flash gas (FG), which is generated during the expansion of high-pressure BOG. In particular, FG primarily comprises light components, such as nitrogen. This increases the circulation flow rate in the system and the loads of the compressor and heat exchanger, thereby increasing the overall energy consumption (Choi, 2018; Kim et al., 2019; Lee et al., 2023).
To overcome the limitations of the reliquefaction system, improved LNG subcooling processes that apply mixed refrigerants (MRs) to the existing subcooling system have been proposed. As shown in Fig. 1(b), the subcooling system cools LNG to less than −170 °C and sprays it from the top of the tank to condense BOG and inhibit additional BOG generation on the LNG surface. The most significant benefit of this system is that it can maintain the pressure in the tank without increasing the system load or causing performance degradation because FG is not generated, unlike the conventional reliquefaction method. The conventional subcooling system, however, utilizes a nitrogen-expansion cycle that uses a nitrogen refrigerant. In this case, only sensible heat is used during the cooling process, which implies that a significant amount of refrigerant circulation is required to obtain the same cooling effect, thereby increasing energy consumption (Lee et al., 2023; Yin and Ju, 2020). To overcome such limitations, subcooling systems that apply MRs composed of hydrocarbons with various boiling points instead of nitrogen refrigerants have been proposed. Since these systems affords high heat-exchange efficiencies compared with sensible heat-oriented nitrogen refrigerants, the energy efficiency of the system can be improved by decreasing the refrigerant flow rate and the volumetric flow rate of the compressor to achieve the same cooling performance (Lee et al., 2023). The application of MRs, however, may form liquid during refrigerant compression (Atmaca et al., 2020), thereby restricting compressor operation and limiting the scope of refrigerant composition.
This study aims to overcome the limitations of the existing subcooling system and propose a high-efficiency subcooling process system that considers refrigerant composition and liquid formation. Specifically, the process is designed by applying the concepts of vapor –liquid separation compression and dual expansion using Aspen HYSYS—a commercial software program. Additionally, the optimal MR composition and operating conditions are identified using an optimized algorithm in MATLAB—a numerical-analysis tool. To identify potential improvements in the designed process, the existing reliquefaction system and subcooling process are compared with the proposed process. Subsequently, economic evaluation is performed on the reliquefaction and subcooling processes to analyze whether the proposed subcooling process is economical compared with the conventional re-liquefaction process.
2. Backgrounds
2.1 Equation of State
The Peng–Robinson equation of state (PR EOS) is commonly used to calculate the thermodynamic properties of LNG (Peng and Robinson, 1976; Lin and Duan, 2005; Qyyum et al., 2019). It can predict the vapor–liquid equilibrium (VLE) of nonpolar or weakly polar mixtures with relatively high accuracy and has been widely used in various processes owing to its applicability and numerical stability in wide temperature and pressure ranges. The PR EOS is expressed as shown in Eqs. (1) to (5).
where R is the gas constant; TC and PC are the critical temperature and critical pressure, respectively; ω is the asymmetry factor of a pure substance; and Tr is the reduced temperature. The PR EOS is applied together with mixing rules to predict the thermodynamic properties of mixtures. The van der Waals (vdW) mixing rule is used as a representative mixing rule. However, the vdW mixing rule exhibits low accuracy in non-ideal mixing states, such as high-pressure regions and liquids (Schmid and Gmehling, 2010). Hence, mixing rules that can reflect non-ideality more precisely have been proposed. Among them, the modified Huron–Vidal (MHV) mixing rule can consider intermolecular interactions in a liquid mixture based on activity coefficient models (Maeta et al., 2015; Morrison et al., 1995). In particular, the MHV mixing rule provides enhanced predictive performance under multicomponent system, high-pressure, or non-ideal conditions. It has been applied in systems containing MRs or liquids. The MHV mixing rule is expressed as shown in Eq. (6).
where gE is the excess Gibbs energy, a is the interaction parameter, b is the excluded volume parameter, and q1 and q2 are energy parameters. In general, q1 = −0.4347 and q2= −0.003654 are used in the PR EOS (Huang and Sandler, 1993).
2.2 Performance index
The coefficient of performance (COP), which represents the efficiency of the refrigeration cycle, can be used as a representative index to quantitatively evaluate the performance of the liquefaction process. The COP is defined as the ratio of the amount of heat removed per unit energy consumption and can be calculated using Eqs. (7) to (9).
where ṁLNG is the rate of LNG flow into the subcooling cycle; hLNG and hSLNG are the enthalpies of LNG before and after subcooling, respectively; Q̇R is the amount of heat to be removed for LNG subcooling; ẆP and ẆC are the power consumptions of the pump and compressor, respectively; and ẆT is the total power consumption. In addition to the COP, the specific power consumption (SPC), which represents power consumption for unit mass, is used as a process performance index. It is suitable for evaluations that involve the retrieval and utilization of BOG. Performance analysis through SPC, however, is limited under conditions where BOG is not directly converted into LNG. In this case, the COP serves as an appropriate criterion for evaluating the performance of the refrigeration cycle. Because the COP reflects only the thermodynamic efficiency of the refrigeration cycle, it may differ from the energy efficiency of the entire process.
2.3 Exergy Efficiency
Exergy efficiency can be used as an index to quantitatively evaluate heat-exchange efficiency in the liquefaction process. Exergy efficiency is defined as the ratio of useful exergy utilized in a system or device to the total exergy input. It is particularly useful for comparing the performance of components, such as heat exchangers (Bian et al., 2022; Marmolejo-Correa and Gundersen, 2012). Exergy efficiency in a heat-exchanger unit can be calculated using Eq. (10).
where ṁHXi,in and ṁHX i,out are the mass flow rates at the inlet and outlet of heat-exchanger unit i, respectively; eHX i,in and eHX i,out are the exergy per unit mass at the inlet and outlet, respectively; and n is the total number of heat exchangers. Eq. (10) is used to evaluate the degree of exergy conservation in the entire system based on the exergy flow rates at the inlet and outlet of each heat exchanger. It is used as a criterion for determining the effectiveness of process improvements from the perspective of minimizing thermodynamic losses.
2.4 Previous Studies
Fig. 2 shows the configurations of the Linde–Hampson cycle (L-HC), reverse Brayton cycle (RBC), and mixed-refrigerant cycle (MRC), which are representative BOG reliquefaction systems. Fig. 2(a) shows an L-HC system that reliquefies BOG through the self-heat exchange of BOG with a temperature of approximately −120 °C and its expansion in a high-pressure and low-temperature state (Choi, 2018; Kim et al., 2019; Lee et al., 2023). Fig. 2(b) shows an RBC system that reliquefies BOG through the reverse Brayton refrigeration cycle using nitrogen as a refrigerant (Lee et al., 2023; Shin and Lee, 2009). Fig. 2(c) shows an MRC process involving an MR that reliquefies BOG with reduced temperature through cooling via Joule–Thomson expansion (Lee et al., 2023; Tan et al., 2018). Fig. 3 shows the subcooling systems. Two types of systems were proposed: a subcooling system that applies the RBC (reverse Brayton cycle–subcooled LNG, RBC-SLNG; Fig. 3(a)) and a subcooling system that applies an MR (mixed refrigerant–subcooled LNG, MR-SLNG; Fig. 3(b)). Table 1 shows a comparison of the COP of each liquefaction process. As shown, the MR-SLNG that used an MR exhibited the highest COP value.
2.5 Particle Swarm Optimization (PSO) Algorithm
The optimal combination of process parameters that satisfies a specified objective function can be derived by applying the PSO algorithm, which is an optimization method for deriving the optimal operating conditions of a process. The PSO algorithm explores the optimal solution while each particle shares information with one another. It tends to converge to the globally optimal solution at the group level even if individual particles fall into locally optimal solutions (Al-Smadi et al., 2023; Kennedy and Eberhart, 1995; Wang et al., 2018). The flow of the algorithm is shown in Fig. 4. Setting constraints within the algorithm will prevent solutions that hinder them from being selected during the exploration process by assigning penalty terms to the objective function.
2.6 Economic Evaluation
The total annualized cost (TAC) can be calculated to quantitatively evaluate the economic feasibility of the designed process (Kim et al., 2019; Turton et al., 2018). It is the sum of the annualized total cost index (ATCI) and annualized total operation cost (ATOC), and the detailed calculation process for each item is shown in Fig. 5.
Cp represents the purchased-equipment cost and can be calculated using Eq. (11).
where
C P , j 0
Here, B1 and B2 are modularization coefficients, which are assigned fixed values based on the equipment type; FM is the material adjustment factor, which varies depending on the type of internal material; and FP is the pressure adjustment factor, which is determined by the operating pressure and equipment type (Turton et al., 2018). The total capital investment (TCI) indicates the total capital investment required for the entire process. It is calculated by adding CBM for each piece of equipment and multiplying it by the extension factor FEtt (plant cost adjustment factor), as shown in Eq. (13). Subsequently, the ATCI is calculated by converting the TCI on an annual basis based on the equipment service life, as shown in Eq. (14). Finally, the ATOC is calculated by including maintenance and utility costs (e.g., electricity and cooling water), as shown in Eq. (15).
Here, i is the annual interest rate; n is the operation period of the equipment (years); FCTO is the maintenance and overhead factor; PTotal is the total power consumption; Ccw is the amount of cooling water used; and Ce and Ccw are the unit electricity charge and unit cooling-water cost, respectively.
3. Modeling & Simulation
3.1 EOS Validation
The applicability of the EOS and mixing rules was examined to predict the characteristics of the MR used in the cooling process more accurately. The PRMHV2 model used in the subcooling process design was the PR EOS that applied the MHV mixing rule. Three EOS models were selected for comparison, including the PR, SRK, and GERG-2008 models that applied the vdW mixing rule. To verify the predictive accuracy of each model, a refrigerant composition similar to the MR composition considered in this study was assumed, as shown in Table 2. Subsequently, a pressure-temperature (PT) diagram was constructed, and the computational accuracy and consistency of the PRMHV2 and comparison models were analyzed. Additionally, simulation was performed based on experimental data for mixtures composed of methane (CH4) and ethane (C2H6) (Ioannidis and Knox, 1999) to evaluate the VLE prediction performance of the PRMHV2 model. The calculation based on the PR EOS that applied the vdW mixing rule was compared as well. The mean absolute percentage error (MAPE) between the predicted values of each model and the experimental values was calculated to evaluate the predictive accuracy of the EOS model under the application of the MHV mixing rule.
3.2 Process Specifications
A large LNG carrier measuring 174K m3 with the specifications listed in Table 3 was selected as the target vessel of this study (Kim et al., 2019; Kim et al., 2020; Lee et al., 2023). The initial composition of the stored LNG was assumed as shown in Table 4. In this instance, the amount of BOG generated can be estimated using the evaporation rate (rBOR), total volume of the cargo tank (VTank), average water level of the tank (LvTank), and LNG density (ρLNG), as shown in Eq. (16). The heat inflow into the tank (Q̇Tank) can be estimated using Eq. (17) based on the calculated BOG flow rate and the latent heat of evaporation of LNG (ΔHLNG) (Lee et al., 2023; Romero Gómez et al., 2015). The calculated heat inflow into the cargo tank is 0.72 MW, which is the minimum cold duty to be removed from the tank via subcooling.
3.3 Process Modeling and Simulation
In this study, process design and simulation were performed for four cases. Case 1 (Fig. 6(a)) and Case 2 (Fig. 6(b)) are reference processes to be compared, which involve a BOG reliquefaction system that uses a nitrogen refrigerant (Shin and Lee, 2009) and a conventional MR subcooling system (Lee et al., 2023), respectively. Case 3 (Fig. 6(c)) and Case 4 (Fig. 6(d)) are systems that improve the subcooling system based on Case 2. Case 3 (Fig. 6(c)) applies the concept of vapor–liquid separation compression, which prevents damage to the compressor in the presence of liquid in the MR and reduces energy consumption by reducing the volumetric flow rate. After separating the refrigerant into vapor and liquid using a phase separator, vapor and liquid can be compressed through the compressor and pump, respectively, to ensure operational stability and reduce the compressor load (Atmaca et al., 2020). In Case 4 (Fig. 6(d)), the concept of dual expansion is applied, where the compressed MR is separated into vapor and liquid and then expanded separately to utilize them as refrigerants with different compositions. In this process, light components (e.g., nitrogen and methane) are separated as vapor while heavy components (e.g., propane and butane) are separated as liquid. This can result in a gentler temperature gradient by the heat exchangers and improve the heat-exchange efficiency (Ha and Lee, 2014; Lee et al., 2011). Table 5 shows the process parameters for simulation, which were equally applied to each case. The BOG flow rate and the cold duty of the cooling process were estimated based on Table 3 and Eqs. (16) and (17).
3.4 Process Optimization
To derive the optimal operating conditions for each case and conduct a comparative evaluation based on the subsequent COP, process optimization was performed using the PSO algorithm. The COP was selected as the objective function for optimization. Since higher COP values indicate higher process efficiency, the process optimization was designed to identify points that maximize the COP value through the optimization algorithm. Next, the constraints listed in Table 6 were applied to prevent simulation results that hinder them from being selected as optimal values by applying penalties to the objective-function results.
The optimization variables for each case are summarized in Table 7. In both Case 1 (Fig. 6(a)) and Case 2 (Fig. 6(b)), the compression ratio of each compressor and the temperature and pressure of the refrigerant before compression were set as optimization variables. In Case 2, the molar flow was included as an optimization variable to determine the flow rate and composition simultaneously. In Case 3 (Fig. 6(c)), the temperature and pressure of the refrigerant before compression, the vapor fraction of the refrigerant before the Joule–Thomson expansion, the compression ratio of each compressor, and the MR composition were set as optimization variables. The refrigerant composition was based on the molar flow, thus enabling the flow rate and composition to be determined simultaneously. In Case 4 (Fig. 6(d)), the compression ratio of each compressor, the temperature and pressure of the refrigerant before compression, and the vapor fraction of the stream into the heat exchanger were set as optimization variables in a manner similar to Case 3.
3.5 Economic Evaluation
Economic evaluation was performed to examine the economic feasibility of the proposed processes for Cases 3 and 4. Economic evaluation was estimated using Eqs. (11) to (16). Since the reference standard for the equipment price is 2001 (Turton et al., 2018), the price was converted into monetary value in 2024 using the CEPCI. The annual interest rate (i) was set to 10% and the equipment operation period (n) to 20 years, considering the replacement cycle of the vessel (Kim et al., 2019; Son et al., 2022). As for the heat-exchanger type, plate and U-tube heat exchangers were assumed for the main and intermediate cooling heat exchangers, respectively, to calculate the value of variable U (Son et al., 2022). Other parameters used in the economic evaluation, such as FEXT, FCTO, and FBM, are summarized in Table 8.
4. Result & Discussion
4.1 EOS Validation Result
The calculation accuracy of the EOS models and mixing rules used in this study was verified. Fig. 7 shows the results based on the PT diagram of each model for the mixture with the composition listed in Table 2. Whereas the PRMHV2 model exhibited thermodynamic consistency, the PR, SRK, and GERG-2008 models utilizing the vdW mixing rule showed missing calculations for the MR under the design process conditions. Based on an examination of the calculation accuracy of the PRMHV2 model through VLE calculations using experimental data, the simulation values indicated MAPEs of 4.28% and 8.76% compared with the experimental values under the application of the MHV and vdW mixing rules, respectively (see Fig. 8,), thus demonstrating the high calculation accuracy of the MHV mixing rule. Thus, PRMHV2 is confirmed to be an appropriate model for calculating the thermodynamic properties during subcooling process design.
4.2 Optimization Results
Table 9 shows the optimization results for each case. The COP of Case 1—a nitrogen refrigerant reliquefaction system—was 0.131, which represents the lowest process efficiency. The COP of Case 2—an existing subcooling process that applies an MR—was 0.206. In Case 3, which incorporated the concept of vapor–liquid separation compression presented in this study, the COP was slightly higher at 0.210. In Case 4, which incorporated the concepts of vapor–liquid separation compression and dual expansion, a COP value of 0.220 was indicated, which was 68% and 6.8% higher than those of Cases 1 and 2, respectively.
4.3 Discussion
The proposed processes (Cases 3 and 4) afforded COP improvements owing to the following reasons: First, as shown in Fig. 10, liquid is present in the refrigerant during the intermediate cooling process after a three-stage compression if vapor–liquid separation compression is not applied (Case 2). When this liquid is introduced into the compressor, the compressor can be damaged; thus, the cooling effect of cooling water cannot be fully exploited. Fig. 11(a) shows the compression process after vapor–liquid separation (Case 3) based on a PH diagram. The cooling effect of cooling water can be exploited more effectively by compressing the vapor and liquid through the compressor and pump, respectively. Fig. 11(b) shows the energy consumption of Case 3 with vapor–liquid separation compression compared with the compression energy consumption of Case 2 without vapor–liquid separation. As shown, the separation compression is favorable in terms of the energy required for compression.
Second, enhancing the heat-exchanger efficiency through dual expansion resulted in a significant improvement. After vapor–liquid separation compression was performed, the vapor and liquid of the MR were used for cooling the refrigerant and the LNG subcooling process, respectively, via dual expansion. During this process, the heat-transfer efficiency can be improved by minimizing the temperature difference between the heat-exchange curves for each heat exchanger. In particular, whereas the minimum access temperatures of the self-cooling and subcooling heat exchangers were 3.6 °C and 3.4 °C, respectively, in Case 3 (Fig. 12(a)), they decreased to 3. 1 °C and 3.0 °C, respectively, in Case 4 (Fig. 12(b)), thus confirming an improvement in heat-exchanger performance.
To quantitatively examine the heat-exchange efficiency improvement, the exergy efficiency was analyzed as shown in Table 10. For pre-cooling, the exergy efficiency was 0.92 in Case 3, whereas it increased to 0.97 in Case 4 with dual-expansion heat exchange. This appears to be caused by a decrease in the irreversible loss in the heat exchanger due to the optimization of the refrigerant flow through dual expansion. In the case of the LNG subcooling heat exchanger, an increase in temperature difference between the refrigerants slightly decreased the exergy efficiency from 0.99 (Case 3) to 0.98 (Case 4), whereas the COP of Case 4 was higher because the increase in exergy efficiency from pre-cooling exerted a more prominent effect.
4.4 Economic-Evaluation Result
Economic evaluation was performed based on the TAC, and the results are summarized in Table 11. Case 1, which involves a reliquefaction system that uses a nitrogen refrigerant, exhibited the highest TAC, followed by Cases 2, 3, and 4 (Fig. 13). In Case 1, the compressor investment cost was extremely high due to the multistage compressor; similarly, the operating cost was high owing to high power consumption, which significantly increased the total cost. In Case 2, the initial investment cost decreased because no separate BOG compressor was required. Similarly, the operating cost decreased due to a relatively lower power consumption compared with Case 1, thus resulting in a lower total cost. Cases 3 and 4, which are the proposed processes, indicated low investment and operating costs owing to the lower compressor proportion and higher efficiency. Case 4 exhibited the lowest TAC value among all cases. These results confirmed that Case 4, which is the subcooling process designed in this study, is highly competitive in terms of economic feasibility compared with the conventional reliquefaction system (Case 1) and the existing subcooling system (Case 2).
5. Conclusion
This study proposed a new process configuration for increasing energy efficiency to improve the existing LNG subcooling system. The concepts of vapor–liquid separation compression and dual expansion were applied to the proposed processes. Subsequently, the optimal operating conditions of each process were derived using an optimization algorithm. The improvement effect of the design was quantitatively analyzed in terms of process efficiency based on the COP—a performance index. First, the multiphase compression problem was prevented and compression energy was saved through the subcooling process that applied the concept of vapor–liquid separation compression (Case 3). Consequently, a COP of 0.210 was achieved, which was 60% higher than that of the reliquefaction process (Case 1) and 2% higher than that of the existing MR subcooling process (Case 2). The minimum access temperatures of the self-cooling and subcooling heat exchangers, however, were 3.6 °C and 3.4 °C, respectively, thus indicating potential improvement in the heat-transfer efficiency. Thus, the concept of dual expansion was additionally introduced in Case 4. The temperature gradient in the heat exchangers was mitigated and the heat-transfer efficiency was improved by separating the MR into vapor and liquid and then expanding them separately. Consequently, the minimum access temperatures of the heat exchangers decreased to 3.1 °C and 3.0 °C. The COP was 0.220, which was 68% higher than that of the reliquefaction process (Case 1) and approximately 6.8% higher than that of the existing MR subcooling process (Case 2). Additionally, the TAC was calculated based on the ATCI and ATOC for economic evaluation. Based on the evaluation results, the conventional nitrogen-refrigerant BOG reliquefaction process (Case 1) and MR subcooling process (Case 2) showed TAC values of 5.20 and 3.13 Million USD/year, respectively, whereas the proposed Case 4 recorded the lowest TAC of 2.95 Million USD/year. In particular, the low ATOC arising from reduced energy consumption contributed significantly to the improved economic feasibility. In general, the proposed subcooling system (Case 4) was demonstrated to be more competitive than the existing processes in terms of economic feasibility and process efficiency. Thus, the system is expected to be a promising alternative for LNG reliquefaction system design.
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