**5. Results and Discussion**

#### *5.1. Energy and Exergy Efficiency Results*

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 4.** SEC with varying R/G fraction.

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.

**Figure 5.** Exergy efficiency with varied R/G fractions.

**Figure 6.** Specific exergy loss with varied R/G fractions.

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.

### *5.2. Economic Evaluation Results*

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 LH2 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.

**Figure 7.** Life cycle cost structures of (**a**) Ship #1, (**b**) Ship #2, (**c**) Ship #3, (**d**) Ship #4, and (**e**) Ship #5.

**Figure 8.** SLCC for each ship with varied (**a**) R/G fractions and (**b**) re-liquefied masses.

Compared to the LH2 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 LH2 production cost and SLCC for a round-trip is estimated in Figure 9.

**Figure 9.** Cost difference with varied R/G fractions during the voyage.
