**1. Introduction**

Due to the current global attention concerning the reduction of carbon dioxide (CO2) emissions, which is the largest contributor to global warming [1], the demand for renewable energy is increasing. A large portion of CO2 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 CO2 emissions increased by 16% [3]. To reduce CO2 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 CO2 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 CO2 and only pure water [7]. Hydrogen also has other principal advantages as an energy carrier, as noted by Rosen et al. [8]. It is

**Citation:** Choi, M.; Jung, W.; Lee, S.; Joung, T.; Chang, D. Thermal Efficiency and Economics of a Boil-Off Hydrogen Re-Liquefaction System Considering the Energy Efficiency Design Index for Liquid Hydrogen Carriers. *Energies* **2021**, *14*, 4566. https://doi.org/10.3390/ en14154566

Academic Editor: Bahman Shabani

Received: 21 June 2021 Accepted: 20 July 2021 Published: 28 July 2021

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free from exhaustion because it can be obtained by electrolyzing water into oxygen and hydrogen. Additionally, unlike electricity itself, it can be stored in a variety of forms such as compressed gas, liquid, and in chemical compounds including ammonia and metal hydrides [9].

Considering the large-scale transportation of hydrogen, it is essential to develop liquid hydrogen (LH2) carriers. LH2 has a density of 70 kg/m3, which is higher than the density of compressed hydrogen (39 kg/m3) at 70 MPa [10]. Compared to ammonia, LH2 is safer, as it is nontoxic. Moreover, because it is a pure substance that is not combined with other elements, it does not require any additional energy or processes to break its chemical bonds.

The main challenge concerning the transportation of hydrogen in a liquid state is its cryogenic boiling temperature, which is 20 K at atmospheric pressure. Although LH2 storage tanks on land are heavily equipped with an insulation layer, heat ingress is inevitable [11], resulting in the generation of boil-off hydrogen (BOH) and increase in the pressure of the storage tank if no preventative measures are used. This issue also exists for LH2 cargo tanks used in LH2 carriers.

In the case of relatively large-scale liquefied natural gas (LNG) carriers, whose cargo temperature is around 110 K, a boil-off gas (BOG) re-liquefaction system is usually installed. This system extracts the BOG from the cargo tanks, re-liquefies it using a refrigeration cycle, and returns the re-liquefied BOG to the cargo tank. Many studies have been conducted concerning this BOG re-liquefaction system [12–15]. Romero et al. analyzed and evaluated the conditions, parameters, and energy consumption of a reverse Brayton cycle-based BOG re-liquefaction system [16]. Kwak et al. investigated a small-scale BOG re-liquefaction system for use on LNG-fueled ships. They optimized the nitrogen reverse Brayton cycle using a genetic algorithm and compared two cases with and without BOG compressors [17]. Yin et al. compared a reverse Brayton cycle-based BOG re-liquefaction system with two expanders to such a system with a single expander. They simulated two cycles using parallel and serial nitrogen expanders and compared them with the base case that possessed a single expander [18]. Sayyaadi et al. used a genetic algorithm to optimize the price of the BOG re-liquefaction system products [19]. In these previous studies of BOG re-liquefaction systems, the specific energy consumption (SEC), which indicates the energy required to re-liquify 1 kg of BOG, was found to be between 0.73 to 1.41 kWh/kg. This value varied depending on the inlet conditions of the BOG system. Moreover, the precooling and precompression processes affected the SEC. The reverse helium Brayton cycle for BOG re-liquefaction was preferred because it was easy to operate. Additionally, this cycle did not require high pressures and was more appropriate for onboard systems in terms of safety [17]. These studies can be utilized to design appropriate BOH re-liquefaction systems.

Many studies have been conducted to liquefy hydrogen from ambient temperatures [20–22]. The main results of these investigations may also be applied towards designing BOH re-liquefaction systems. Chang et al. analyzed and compared various figures of hydrogen liquefaction systems in terms of exergy efficiency [23]. In their study, the reverse Brayton cycle with two expanders showed an exergy efficiency of 24.2%, while the Claude cycle had an exergy efficiency of 27.2%. Asadnia et al. proposed a hydrogen liquefaction system using combined mixed refrigerants [24]. They separated the cycles into two sections, in which the first section was used for precooling and the second was used for cryogenic liquefaction. In the precooling section, 11 materials including hydrocarbons were used as a mixed refrigerant. In the cryogenic section, hydrogen, helium and neon were used as mixed refrigerants. The simulation results showed an SEC of 7.69 kWh/kg. Sadaghiani et al. also proposed a hydrogen liquefaction system that used mixed refrigerants [25]. The proposed system was composed of two cycles, one of which used a mixture of hydrocarbons while the other used a mixture of hydrogen, neon and helium as a mixed refrigerant. This system demonstrated an SEC of 4.41 kWh/kg. Chang et al. proposed a hydrogen liquefaction system that utilized the cold energy of LNG [26]. In that study, the LNG precooled the hydrogen and was vaporized after precooling. Following the design of a hydrogen liquefaction system using LNG precooling, three configurations of the liquefaction 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 LH2 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 LH2 carrier [28]. In their study, some of the BOH from the LH2 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 LH2 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 LH2 carriers. The EEDI is the design indicator regulated by the International Maritime Organization (IMO), which restricts the CO2 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 LH2 carriers has not yet been established. LH2 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 CO2 emissions. Consequently, the establishment of EEDI regulations for LH2 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 LH2 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 LH2 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.

### **2. Proposed Boil-Off Hydrogen Re-Liquefaction System Combined with Fuel Cells**

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.

**Figure 1.** Process flow diagram of the proposed system.

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.

**Table 1.** Boundary conditions of the BOH re-liquefaction cycle.


The following assumptions were made for this simulation:

