Thermal Efficiency and Economics of a Boil-Off Hydrogen Re-Liquefaction System Considering the Energy Efficiency Design Index for Liquid Hydrogen Carriers

This study analyzes the thermodynamic, economic, and regulatory aspects of boil-off hydrogen (BOH) in liquid hydrogen (LH2) carriers that can be re-liquefied using a proposed re-liquefaction system or used as fuel in a fuel cell stack. Five LH2 carriers sailing between two designated ports are considered in a case study. The specific energy consumption of the proposed re-liquefaction system varies from 8.22 to 10.80 kWh/kg as the re-liquefaction-to-generation fraction (R/G fraction) is varied. The economic evaluation results show that the cost of re-liquefaction decreases as the re-liquefied flow rate increases and converges to 1.5 $/kg at an adequately large flow rate. Three energy efficient design index (EEDI) candidates are proposed to determine feasible R/G fractions: an EEDI equivalent to that of LNG carriers, an EEDI that considers the energy density of LH2, and no EEDI restrictions. The first EEDI candidate is so strict that the majority of the BOH should be used as fuel. In the case of the second EEDI candidate, the permittable R/G fraction is between 25% and 33%. If the EEDI is not applied for LH2 carriers, as in the third candidate, the specific life-cycle cost decreases to 67% compared with the first EEDI regulation.


Introduction
Due to the current global attention concerning the reduction of carbon dioxide (CO 2 ) emissions, which is the largest contributor to global warming [1], the demand for renewable energy is increasing. A large portion of CO 2 emissions is attributed to the combustion of the fossil fuels, which provide approximately 80% of the total world energy supply [2]. From 2009 to 2018, global CO 2 emissions increased by 16% [3]. To reduce CO 2 emissions, power generation using renewable energy, which is not accompanied by CO2 emissions, has been increasing. According to the International Energy Agency, power generation achieved using renewable energy has increased by 57% from 2010 to 2018 [4]. The portion of renewable energy used for electricity generation has been projected to consistently increase in the future [5].
Although renewable energy can be used to reduce CO 2 emissions, its production varies from region to region. This uneven distribution of renewable energy requires the use of energy carriers that can transport surplus renewable energy. Hydrogen is regarded as a potential energy carrier candidate for storing and transporting surplus renewable energy over long distances [6]. The delivered hydrogen generates energy from an oxidation process in fuel cells, which produces no CO 2 and only pure water [7]. Hydrogen also has other principal advantages as an energy carrier, as noted by Rosen et al. [8]. It is tion cycles were compared in terms of their energy consumption. Considering the required energy for the liquefaction process described in their paper, the SEC for the most efficient configuration was calculated as 17.37 kWh/kg, which includes the energy consumed for ortho-para conversion. Yuksel et al. also proposed a hydrogen liquefaction system with four serial helium turbo expanders and analyzed this system [27]. These previous studies showed that the SECs of hydrogen liquefaction systems vary with the configuration of the system and the inlet conditions of the hydrogen.
BOH re-liquefaction systems, however, differ from liquefaction systems for hydrogen at ambient temperatures. The temperature of BOH is much lower than the ambient temperature. Additionally, such a system does not require an ortho-para conversion process because the LH 2 in the cargo tank has already been converted into para-hydrogen. Lee et al. proposed a partial BOH re-liquefaction system for use on an LH 2 carrier [28]. In their study, some of the BOH from the LH 2 cargo tank was used as a fuel in a protonexchange membrane fuel cell (PEMFC). The remainder was precompressed to 40 bar using a cold compressor with an inlet temperature of 120 K. This compressed BOH was cooled down using helium in a reverse Brayton cycle and re-liquefied by expansion. This BOH re-liquefaction system exhibited an SEC of 3.30 kWh/kg and exergy efficiency of 74.9%.
Previous studies of BOH re-liquefaction systems lacked an investigation of the economic feasibility of these systems that considered the installation and operation costs. A comparison with the production costs of LH 2 can be used to investigate the economic feasibility of BOH re-liquefaction systems. Moreover, considering that existing LNG carriers vary in terms of their capacity, economic case studies of BOH re-liquefaction systems with varying capacities are required.
Another critical factor to consider in the design and operation of the BOH re-liquefaction system is the energy efficiency design index (EEDI) regulation of LH 2 carriers. The EEDI is the design indicator regulated by the International Maritime Organization (IMO), which restricts the CO 2 emissions of ships during the design process. Ship of certain types as indicated by the IMO must obey this index to operate. The EEDI also affects the electricity generation of BOH re-liquefaction systems. However, such a regulation for LH 2 carriers has not yet been established. LH 2 is similar to conventional liquefied gases such as LNG and liquefied petroleum gas (LPG) in that it is liquefied. However, liquid hydrogen differs from other conventional liquefied gases because it is an extremely low-density liquefied gas that is free from CO 2 emissions. Consequently, the establishment of EEDI regulations for LH 2 carriers is difficult in comparison with that of other liquefied gases.
The objective of this study is to investigate the thermodynamic, economic, and regulatory aspects of BOH in LH 2 carriers in which the BOH can be either re-liquefied using the proposed re-liquefaction system or used as fuel for the fuel cells. A case study is conducted that considers five LH 2 carriers sailing between two designated ports. A thermodynamic analysis is carried out, followed by an economic assessment considering the re-liquefactionto-generation (R/G) fraction. As these evaluations are meaningful in terms of the allowable EEDI, three EEDI candidates are proposed for estimating a feasible R/G fraction. Figure 1 shows a process flow diagram of the proposed system. The system consists of a re-liquefaction cycle and PEMFC stack. The proposed re-liquefaction cycle is modified from a reverse Brayton cycle to utilize the cold energy of BOH heading to the PEMFC stack. The BOH to be utilized in the PEMFC stacks is first heated to the operating temperature of the PEMFC system. HX 1 and HX 3 are introduced to transfer the cold energy of the BOH to the helium refrigerant and increase the BOH temperature to the ambient temperature. Stream 101 indicates the BOH generation from the cargo tank. This stream is divided into two streams, which are labelled as 102 and 106. Stream 102 is cooled down and re-liquefied to a subcooled liquid state. Stream 106 cools the helium refrigerant and is utilized for propulsion. Stream 201 indicates the low-pressure helium stream. This stream is pressurized to a high pressure through Comp 1 and Comp 2. After AC 1, the helium is cooled down along with the BOH heading to the PEMFC system. After the helium is compressed, it is cooled down using the cold helium in HX 4. It is then primarily expanded to an intermediate pressure via EXP 1 and cooled down via HX 5. After passing through HX 5, the helium is expanded to a low pressure through EXP 2 and the BOH is liquefied in HX 6. After the BOH has been re-liquefied, this cold helium then cools down the hot helium and hydrogen. Aspen Hysys V11 was used to simulate the proposed system. The modified Benedict-Webb-Rubin equation was applied for the states of ortho-and para-hydrogen. The Aspen properties (RefProp) were used for helium. Table 1 shows the boundary conditions for the process simulation. The following assumptions were made for this simulation:

Proposed Boil-Off Hydrogen Re-Liquefaction System Combined with Fuel Cells
• The dead-state temperature and pressure are 298 K and 1.01 bar, respectively.

•
The temperature at the exit of the aftercooler is 313 K.

•
The minimum temperature at the inlet of the compressor is 240 K.

•
The high and low pressures of the helium cycle are 10 and 1.2 bar, respectively.

•
The adiabatic efficiencies of the compressors are 75%.

•
The adiabatic efficiencies of the expanders are 75%.

•
The pressure drop in the heat exchangers is negligible.

•
In the heat exchangers, the minimum temperature difference is larger than 1% of the hottest stream temperature. If the temperature of the hottest stream in the heat exchanger is greater than 300 K, the minimum temperature difference is 3 K [23,26].

Energy and Exergy Efficiency
The total energy required to re-liquefy BOH is calculated using Equation ( The R/G fraction, which is the ratio of the re-liquefied flow rate to the BOH generation flow rate, is estimated using Equation (2). The SEC is defined by Equation (3) to evaluate the energy required to re-liquefy the 1 kg of BOH. Because the re-liquefaction system utilizes the cold energy of the hydrogen, the SEC varies with the R/G fraction. In thermodynamics, physical flow exergy refers to the maximum useful work delivered to an external user as the stream reaches the dead state [30]. Considering refrigeration systems, it refers to the reversible and minimum work required for refrigeration to occur at a certain state. The physical flow exergy of stream can be estimated using Equation (4) [31]. In Equation (4), subscripts S and 0 refer to present state of the stream and dead state, respectively. Subscript ** means state that has same temperature with the dead state and same pressure with the present state. The first two terms in Equation (4) corresponds to thermal exergy, which is the physical exergy from the temperature difference of the stream with the dead state. The last two terms represent mechanical exergy, which is the physical exergy from pressure difference of the stream with the dead state. During re-liquefaction, the irreversibility between processes causes exergy loss. To calculate this exergy loss, the physical exergy difference between inlets and outlets of a component can be used [32]. This exergy loss makes the system less efficient and require more work than an ideal system. From this point of view, the system exergy efficiency can be estimated using the numerical indicator η ex via Equation (5).

Economics
CAPEX is defined as the initial investment required to construct a plant [33], and it consists of the direct project expenses, indirect project expenses, contingency and fee as depicted in Figure 2. The direct expenses encompass the equipment costs, material costs, and labor costs required to install the equipment. The indirect project expenses include the freight costs, insurance, and taxes. They also include the overhead costs required to construct the plant. The contingency is the cost that covers unforeseen circumstances, while the fee is related to the contractors. Among these costs, the sum of the direct and indirect costs is called the bare module cost. The contingency and fee are assumed as 15% and 3% of the bare module cost, respectively. The bare module cost for each component is estimated using the Aspen Capital Cost Estimator V11. OPEX is defined as the costs associated with the day-to-day operations of a plant [33]. OPEX consists of direct manufacturing costs, fixed manufacturing costs, and general manufacturing expenses as depicted in Figure 3. The direct manufacturing costs are the operating expenses, which vary with the production rate. They include raw materials costs, utilities costs, and operational labor. The fixed costs are independent of changes in the production rate. They include taxes and insurance. The general expenses are overhead costs that are necessary to carry out business functions. They include administration, distribution and selling costs, as well as costs for research and development. Equation (6) [33] is used to estimate OPEX. Table 2 shows the specific values used to estimate CAPEX and OPEX.
C OL : Cost of the operator salary C UT : Cost of utilities C WT : Cost of the cooling water  The life cycle cost (LCC) is defined as the total costs required to install and operate the system during the life cycle [33]. It is estimated using Equation (7). The specific life cycle cost (SLCC) is defined as the LCC required for 1 kg of BOH, which is estimated using Equation (8). Additionally, the cost difference is defined as the difference between the LH 2 production cost and SLCC, as expressed by Equation (9).

Restrictions on CO 2 Emissions from LH 2 Carriers
The attained EEDI indicates the CO 2 emissions per unit of deadweight divided by the ship speed, which is calculated using Equation (10) for each ship [36].
P ME : Power of the main engine P AE : Power of the auxiliary engine C ME : Conversion factor of the main engine between the fuel consumption and CO 2 emissions C AE : Conversion factor of the auxiliary engine between the fuel consumption and CO 2 emissions SFC ME : Specific fuel consumption of the main engine SFC AE : Specific fuel consumption of the auxiliary engine DWT: Deadweight of the ship V ref : Speed of the ship A diesel electric propulsion obtained using LNG is assumed for LH 2 carriers. Specific fuel consumption is assumed as 175 g/kWh. The conversion factor between the fuel consumption and CO 2 emissions is 2.75 [37]. According to the Marine Environment Protection Committee (MEPC) issued by the IMO, the power of the main engine for diesel electric propulsion is calculated using Equation (11). The parameter η is taken as 91.3 %, which indicates the product of the electrical efficiencies of the generators, transformers, converters and motors. Considering ships whose rated output of the motor is larger than 10,000 kW, the power of the auxiliary engine is calculated using Equation (12) [36].
MPP motor : Rated output of the motor η: Product of the electrical efficiencies of the generator, transformer, converter, and motor The PEMFC system uses the BOH to generate electricity, which is then utilized for propulsion in conjunction with the electricity from the main engine. Therefore, the required power of the main engine is calculated using Equation (13). In this study, the efficiency of the PEMFC system is assumed to be 42% compared with lower heating value of hydrogen. In the case of LNG carriers with a BOG re-liquefaction system, the power required for the BOG re-liquefaction is added to the auxiliary engine power, as shown in Equation (14).
P PEMFC : Electricity generated from the PEMFC P re−liq : Power required for re-liquefaction The required EEDI indicates the criteria that the ship under EEDI regulations must satisfy. Equations (15)-(17) show the methodology for calculating the required EEDI [36]. The parameters a and c in the required EEDI equation are determined based on the type of ships. The variable b is the deadweight of the ship. X, which is between 0 and 1, is a reduction factor that indicates the reinforcement of the regulations over time. The time factor (referred to as the 'phase') represents the reinforcement of the regulations over time, which is determined using the value of X. For example, phase 3 indicates the year after 2025 and the factor X in this time is 0.3.
Because the EEDI regulations for LH 2 carriers have not yet been designated, various perspectives should be considered before determining the final designation. This study considers the following EEDI candidates: The concept behind EEDI candidate 1 is to utilize the required EEDI of LNG carriers for LH 2 carriers. Table 3 shows the parameters used for the evaluation of the required EEDI of LNG carriers. In this EEDI candidate, the parameters in Table 3 and the deadweight of the LH 2 carrier are used to calculate the required EEDI for LH 2 carriers. Therefore, the required EEDI of an LNG carrier with the same deadweight as the LH 2 carrier is calculated and compared with the attained EEDI for the LH 2 carrier. EEDI candidate 2 considers the energy density difference between LH 2 and LNG. As shown in Table 4, the density of LH2 is 16% of that of LNG. This low density of LH 2 makes the attained EEDI of an LH 2 carrier calculated using Equation (10) smaller than that of an LNG carrier with the same volumetric capacity. Conversely, LH 2 has a heating value that is 2.58 times that of LNG. This indicates that LH 2 can carry more energy within the same mass as LNG. EEDI candidate 2, therefore, considers this energy density factor. The energy density is used to introduce the "re-scaled deadweight" concept shown in Equation (19) in place of the mass density. Using this rescaled deadweight, Equation (20) defines the "energy-based EEDI", which applies the energy density concept to the attained EEDI. In EEDI candidate 2, it is compared with the required EEDI of LNG carriers with the same volumetric capacity.
EEDI energy−based = P ME ·C ME ·SFC ME  EEDI candidate 3 refers to the case in which LH 2 carriers have no restrictions regarding their CO 2 emissions provided that conventional clean fuels such as LNG are used. Unlike other gas carriers that carry CO 2 -rich fuels, such as LPG and LNG, LH 2 carriers are used to transport CO 2 -free hydrogen. The strong regulations on CO 2 emissions from LH 2 carriers, such as those considered in EEDI candidates 1 and 2, may thereby be impartial to liquid hydrogen, ultimately preventing the shipping of this clean fuel. It would therefore be fair to impose no restrictions on CO 2 emissions if these ships utilize relatively clean fuels such as LPG or LNG. In this case, the practicality of BOH re-liquefaction can be determined purely on an economic basis.

Target Ship Descriptions
LH 2 carriers with five different sizes are considered for the subsequent case studies. The data of LNG carriers from the Clarksons database is used to assume the cargo capacity, rated output of motors for propulsion, and deadweight of LH 2 carriers [38]. The deadweight of an LH 2 carrier is assumed to be sum of the LH 2 cargo weight and the deadweight of an LNG carrier without cargo and with the same capacity. The rated output of the motor (MPP) is calculated to have the same propulsion power of an LNG carrier with the same capacity. Table 5 shows the specifications of the LH 2 carriers based on these assumptions.

Voyage Conditions
The LH 2 export terminal is assumed to located be at Darwin, Australia, while the import terminal is assumed to located be at Pyeongtaek, South Korea. The boil-off rate for a laden voyage is assumed to be 0.2%/day [29]. The BOH generation for a ballast voyage is assumed to be 40% of that of the laden voyage. Table 6 shows the voyage conditions between Darwin and Pyeongtaek. Table 7 shows the BOH generation rates for the laden and ballast voyages. Table 8 shows the total amounts of BOH generated during one-way trips.

Liquid Hydrogen Production Cost
An LH 2 production cost is assumed for comparison with the LCC of the BOH reliquefaction system. The Fuel Cells Program Records from the Department of Energy provides the costs for hydrogen production and liquefaction. These documents also provide the terminal cost of LH 2 [39,40]. As a result, the total cost for LH 2 production and shipping is assumed to be 6.5 $/kg as described in Table 9. Table 9. LH 2 production cost assumption.

Item Unit Value
LH 2 production cost $/kg 6.50 Figure 4 shows the SEC of the proposed BOH re-liquefaction system, which varies from 8.22 to 10.80 kWh/kg as the R/G fraction varies from 10% to 100%. The BOH that is diverted to the PEMFC cools down the helium refrigerant through HX 1 and HX 3. As the temperature of the helium at the inlet of the compressors decreases, the specific volume of the helium also decreases. The compressor work required to achieve a specific pressure ratio decreases as this specific volume decreases. In the 100% re-liquefaction case, the temperature of the helium increases from 311 to 486 K during compression from 1.20 to 2.89 bar in Comp 1. In this case, a specific compressor work of 907.94 kJ/kg is required. Conversely, in the 10% re-liquefaction case, the cold BOH heading to the PEMFC stacks cools down the helium refrigerant in HX 3. The inlet temperature of Comp 1 is 240 K and increases to 375 K during compression from 1.20 to 2.89 bar in Comp 1. In this case, the specific compressor work is 700.91 kJ/kg. By comparing the 100% to the 10% R/G fraction, the cold energy from BOH reduces 23% of the required compressor work. As noted for the compression at Comp 1, the cold energy from the BOH reduces the compressor work of Comp 2. In the 100% re-liquefaction case, the inlet and outlet temperatures are 313 and 582 K at Comp 2, respectively, where the helium refrigerant is compressed from 2.89 to 10 bar via 1396.85 kJ/kg of specific compressor work. Similarly, the BOH cools down the helium in the 10% re-liquefaction case. The inlet and outlet temperatures are 240 and 446 K, respectively, with same pressure ratio in the 10% re-liquefaction case, and the specific compressor work is 1071.37 kJ/kg. By comparing the effects of 100% and 10% R/G fractions at Comp 2, the cold energy from the BOH reduces 23% of the required compressor work.  Figure 5 shows the exergy efficiency of the BOH re-liquefaction system with varied R/G fractions. The exergy efficiency increases from 0.209 to 0.258 as the R/G fraction increases from 10% to 30%, and it then converges after an R/G fraction of 30%. Figure 6 shows the exergy loss at each component in the re-liquefaction system. The exergy loss in the expanders and compressors is caused by mechanical irreversibility. The exergy loss in the after-coolers and heat exchangers is caused by the heat transfer between a finite temperature difference. It should be mentioned that the exergy loss due to heat transfer decreases as the R/G fraction increases from 10% to 30%, while it converges after 30%. When the R/G fraction is lower than 30%, the excess cold energy is provided by the BOH heading to the PEMFC. The excess cold energy enlarges the temperature difference between the helium and BOH heading to the PEMFC, and this large temperature difference causes a large amount of exergy loss.  In the process flow diagram depicted in Figure 1, Stream 108 indicates the BOH diverted to the PEMFC stacks. This stream provided cold energy through HX 3 and HX 1 and is designed to be 310 K, which is the ambient temperature. However, in the cases of 10% and 20% re-liquefaction, the excess cold energy is not fully utilized, and the temperature of Stream 108 is lower than 310 K. Because of this low temperature of Stream 108, the temperature differences in HX 1 and HX 2 are larger than those in the higher R/G fraction cases. As a result, increased exergy losses of 58% and 15% are generated by the heat transfer at the 10% and 20% R/G fractions, respectively, compared to the other R/G fraction cases. Figure 7 shows the structures of the LCCs for the BOH re-liquefaction systems. It is indicated that OPEX, which includes the operation and maintenance expenses, more influences the LCC than CAPEX, which contains the initial investment of the system. It is obvious that the total LCC increases with the increasing LH 2 capacity of the ship. However, the SLCC, which is the LCC per 1 kg of BOH to be re-liquefied, decreases because the increase of the LCC is lower than the increase of the mass of the re-liquefied BOH. Figure 8a shows the SLCC of the BOH re-liquefaction system as it varies with the capacity of the ship and R/G fraction. It is indicated that at the same R/G fraction, the SLCC decreases as the capacity of the ship increases. Moreover, the SLCC decreases as the R/G fraction increases for the same ship. It can be deduced that as the mass of BOH re-liquefaction increases, the SLCC of the BOH re-liquefaction system decreases. Figure 8b shows the SLCC results with the varied mass of the re-liquefied BOH. It is indicated that as the re-liquefied mass increases, the specific LCC decreases. The slope of the graph in Figure 8b decreases as the re-liquefied mass increases. After the re-liquefied mass is greater than 7.2 ton/day, the SLCC converges at 1.5 $/kg.  Compared to the LH 2 production cost of 6.50 $/kg (as mentioned in Section 4.3), the BOH re-liquefaction system is considered to be beneficial for 20% to 100% R/G fractions. The production cost and SLCC can be used to estimate the economic benefit obtained by using such a system. During the voyage from Darwin to Pyeongtaek described in Section 4.2, the cost difference between the LH 2 production cost and SLCC for a round-trip is estimated in Figure 9.   Figure 10 shows the attained EEDI results of the ships with varied R/G fractions. Each graph includes the required EEDI phase 3 line of the LNG carrier with the same volumetric capacity. As shown in Equation (10), the calculation results obtained using the same R/G fraction for each ship tend to decrease as the volume capacity of the ships increase. This indicates that as the volumetric capacity of the ship increases, the attained EEDI of the LH 2 carriers tends to decrease and becomes more similar to EEDI candidate 1. As the R/G fraction increases, the BOH utilized in the PEMFC decreases and the required power from the main engine increases. The more power the main engine generates using the LNG fuel, the more CO 2 the ship emits. Table 10 shows the permittable R/G fractions according to EEDI candidate 1, indicating that only a small amount of BOH is permittable for re-liquefaction. In the cases of Ships #1 and #2, whose capacity is relatively smaller than the other LH 2 carriers, additional hydrogen is required to satisfy the EEDI candidate 1. Additionally, in the cases of Ships #3 to #5 with larger capacities, less than 15% of the generated BOH is permittable for re-liquefaction.    Figure 11 shows the energy-based EEDI calculation results defined for EEDI candidate 2. Each graph for Ships #1 to #5 presents the results of this energy-based EEDI with varied R/G fractions. The graphs also exhibit the required EEDI phase 3 for LNG carriers with the same rescaled deadweight as each LH 2 carrier. Similar to the attained EEDI shown in Figure 10, as the R/G fraction increases, the energy-based EEDI increases. Moreover, the energy-based EEDI tends to decrease as the volumetric capacity of the ships increases. However, unlike the attained EEDI results shown in Figure 10, every ship is able to reliquefy a ratio of BOH between 25% and 33% such that the energy-based EEDI is less than the required EEDI phase 3 of LNG carriers. These results were obtained due to the rescaled deadweight that was increased from the original deadweight considering the differing heating values of LH 2 and LNG. Table 11 shows the permittable R/G fractions of Ships #1 to #5. The permittable R/G fraction tends to increase as the volumetric capacity of the ships increases. The differences between Tables 10 and 11 indicate how the mass and energy densities of LH 2 differ from those of LNG. Because LH 2 has a lower density but larger heating value than LNG, the permittable R/G fraction is larger in EEDI candidate 2 than in EEDI candidate 1. The cargo of the currently used energy carriers under EEDI regulations is mainly hydrocarbon materials such as oil and LNG. These materials have different densities and heating values compared to hydrogen. The existing EEDI regulation for energy carriers, which is calculated using the mass-based deadweight, is used due to the properties of these hydrocarbons. Therefore, the application of this regulation directly to LH 2 carriers without considering the properties of LH 2 is inappropriate. The large heating value of hydrogen should be reflected in these regulations such that the energy carrier may carry energy efficiently.

EEDI Candidate 3
EEDI candidate 3 exempts the LH 2 carriers from the EEDI regulations. The LH 2 carriers deliver LH 2 cargo, which emits no CO 2 , unlike other fuels. In addition, it is highly likely that only CO 2 -free LH 2 will be allowed for international trading. Therefore, although regulations on CO 2 emissions may not be imposed on LH 2 carriers, LH 2 is far less CO 2intensive than other liquefied cargos such as LNG and LPG considering the entire supply chain.
In this case, the BOH R/G fraction is determined mainly via economic motivations. As discussed in Section 5.2, the SLCC of the BOH re-liquefaction system decreases as the R/G fraction increases. Consequently, all BOH may be re-liquefied considering the economic results obtained using EEDI candidate 3. Table 12 shows the SLCCs for the permittable R/G fractions obtained using each EEDI candidate. As described in Section 5.3.1, the permittable R/G fraction indicates the amount satisfying the EEDI restrictions for each candidate. In the case of EEDI candidate 3, this ratio is 100% because there is no EEDI restriction. Compared with EEDI candidate 1, the SLCC for the permittable R/G fraction decreases from 50% to 68% depending on the capacity of the LH 2 carriers in EEDI candidate 3. Likewise, the SLCC decreases from 18% to 48% compared to the EEDI candidate 2. These results indicate the economic advantages that may be obtained when LH 2 carriers are not subjected to EEDI restrictions. Considering this advantage and the CO 2 -free characteristic of LH 2 , the EEDI-free regulation of LH 2 carriers can be considered, which exempts LH 2 carriers with LNG fuels from the CO 2 emissions restrictions.

Conclusions
This study proposed a partial BOH re-liquefaction system based on the reverse Brayton helium cycles. This system divides the generated BOH into two streams, one of which is to be re-liquefied and the other is utilized to generate electricity in PEMFC stacks. Various evaluations for the system were performed based on an assumed voyage route, five different LH 2 carrier specifications, and an assumed LH 2 production cost.
The SEC increased from 8.22 to 10.80 kWh/kg as the R/G fraction increased from 10% to 100%. The exergy efficiency was increased from 0.209 to 0.258 as the R/G fraction increased from 10% to 30%, and it converged to 0.258 when the R/G fraction was larger than 30%. The exergy loss in heat transfer occupied the largest portion of all. Due to the excessive cold energy of the BOH heading to the PEMFC stacks, compared to other R/G fraction cases, 58% and 15% more exergy loss occurred in 10% and 20% cases, respectively.
The system economics indicated that the re-liquefied mass of BOH is inversely proportional to the SLCC. The gradient of this decrease became smoother as the re-liquefied mass of BOH increased. When the re-liquefied mass of BOH was larger than 7200 kg/day, the SLCC was almost unchanged from 1.5 $/kg; this value is much lower than 6.50 $/kg, which is the assumed LH 2 production cost.
Considering EEDI candidate 1, the attained EEDI demonstrated that most of the BOH should not be re-liquefied when the required EEDI was evaluated based on the parameters of the LNG carrier for the required EEDI phase 3 with the same volumetric capacity. However, for EEDI candidate 2, it was shown that the permittable R/G fraction was between 25% and 33% considering energy-based EEDI and required EEDI phase 3. Finally, for EEDI candidate 3, the EEDI-free regulation of LH 2 carriers was discussed considering the CO 2 -free characteristic of LH 2 . If the EEDI regulation is not used for LH 2 carriers, the SLCC of the BOH re-liquefaction system decreases up to 68% compared to LNG carriers with equivalent EEDI regulations.

Conflicts of Interest:
The authors declare no conflict of interest. Attained EEDI (g/ton-mile) P ME Power of the main engine (kW) P AE Power of the auxiliary engine (kW) C ME Conversion factor of the main engine between fuel consumption and CO 2 emissions C AE Conversion factor of the auxiliary engine between fuel consumption and CO 2 emissions SFC ME Specific fuel consumption of the main engine (g/kWh) SFC AE Specific fuel consumption of the auxiliary engine (g/kWh) DWT Deadweight of the ship (ton) V re f Speed of the ship (knot) MPP motor Rated output of the motor (kW)