1. 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 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 (LH
2) carriers. LH
2 has a density of 70 kg/m
3, which is higher than the density of compressed hydrogen (39 kg/m
3) at 70 MPa [
10]. Compared to ammonia, LH
2 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 LH
2 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 LH
2 cargo tanks used in LH
2 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,
13,
14,
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,
21,
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 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 proton-exchange 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-liquefaction-to-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.
6. 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 LH2 carrier specifications, and an assumed LH2 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 LH2 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 LH2 carriers was discussed considering the CO2-free characteristic of LH2. If the EEDI regulation is not used for LH2 carriers, the SLCC of the BOH re-liquefaction system decreases up to 68% compared to LNG carriers with equivalent EEDI regulations.