*5.3. Consequences of the EEDI*

#### 5.3.1. EEDI Candidate 1

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 LH2 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 CO2 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 LH2 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.

**Table 10.** Permittable R/G fractions of the LH2 carriers according to EEDI candidate 1.

**Figure 10.** *Cont*.

**Figure 10.** Attained EEDIs for (**a**) Ship #1, (**b**) Ship #2, (**c**) Ship #3, (**d**) Ship #4, and (**e**) Ship #5 using EEDI candidate 1.

#### 5.3.2. EEDI Candidate 2

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 LH2 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 LH2 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.

**Table 11.** Permittable R/G fractions of the LH2 carriers according to EEDI candidate 2.


The differences between Tables 10 and 11 indicate how the mass and energy densities of LH2 differ from those of LNG. Because LH2 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 LH2 carriers without considering the properties of LH2 is inappropriate. The large heating value of hydrogen should be reflected in these regulations such that the energy carrier may carry energy efficiently.

**Figure 11.** *Cont*.

**Figure 11.** Energy-based EEDIs for (**a**) Ship #1, (**b**) Ship #2, (**c**) Ship #3, (**d**) Ship #4, and (**e**) Ship #5 using EEDI candidate 2.

#### 5.3.3. EEDI Candidate 3

EEDI candidate 3 exempts the LH2 carriers from the EEDI regulations. The LH2 carriers deliver LH2 cargo, which emits no CO2, unlike other fuels. In addition, it is highly likely that only CO2-free LH2 will be allowed for international trading. Therefore, although regulations on CO2 emissions may not be imposed on LH2 carriers, LH2 is far less CO2 intensive 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 LH2 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 LH2 carriers are not subjected to EEDI restrictions. Considering this advantage and the CO2-free characteristic of LH2, the EEDI-free regulation of LH2 carriers can be considered, which exempts LH2 carriers with LNG fuels from the CO2 emissions restrictions.


**Table 12.** SLCCs for the permittable R/G fractions obtained using each EEDI candidate.

#### **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.

**Author Contributions:** Conceptualization, M.C., W.J. and S.L.; methodology, W.J. and T.J.; software, M.C.; validation, M.C. and W.J.; formal analysis, M.C.; investigation, M.C.; resources, T.J.; data curation, M.C.; writing—original draft preparation, M.C.; writing—review and editing, W.J.; visualization, M.C.; supervision, W.J. and D.C.; project administration, D.C.; funding acquisition, D.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was a part of the project titled 'Development of Safety and Control Standards for Hydrogen Ships: Cargo Handling and Fuel Gas Supply Systems' (Grant number: 20200456), funded by the Ministry of Oceans and Fisheries, Korea.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


