## 3 Results  
### Base Case  
To verify the performance of the PSO algorithm, the performance of three different optimization algorithms are compared and results are shown in Figure 6. The performance comparison between the pattern search (PS), the genetic algorithm (GA), and the PSO algorithm was investigated for the base case. Also, the execution time of each algorithm for the base case is  
The base case adopts the lean natural gas and the optimized results of each process are summarized in Table 14(6); Figure 7 shows exergy efficiency and TAC of each case. As shown in Figure 6, SMR has the highest exergy efficiency (38.85%) and the lowest TAC (0.888 MM USD/year). In contrast, propane pre-cooled self-refrigeration has the lowest exergy efficiency (13.65%) and the highest TAC (2.179 MM USD/year). The details of TAC are summarized in Table 6 and Figure 8 shows total equipment cost (TEC) breakdown of each process. As shown in Table 6, TAC of SMR (0.888 MM USD/year) is considerably lower than that of the others because of the low direct cost contributed by the simple process layout. According to Figure 8, the compressor costs comprises a significant portion of the TEC regardless of the process, and therefore, Wnet and the number of compressors is the most important factors in the cost analysis. Further, Wnet affects the variable cost because the energy cost comprises a large portion of the variable cost. The proportion of the makeup system in TEC of SMR is about 38.98%, which is remarkably higher than that of other processes because of mixed refrigerant. In contrast, the proportion of the makeup system in propane pre-cooled self-refrigeration does not seem to be significant (3.39%) because of the single (propane) refrigerant. The product cost for propane pre-cooled self-refrigeration (10,213.5 USD/tpa) has the highest value, followed by that for dual nitrogen expansion (5645.4 USD/tpa) and SMR (4162.5 USD/tpa). According to the Oxford institute for energy studies [59], a capital expenditure (CAPEX) of small-scale movable LNG liquefaction usually ranges between 200-1600 USD/tpa. The CAPEX can be calculated by dividing TCC by the annual LNG production rate. The CAPEX for SMR, dual nitrogen expansion, and propane pre-cooled self-refrigeration investigated in this paper are 858.5 USD/tpa, 1069.9 USD/tpa, and 2064.9 USD/tpa, respectively. Therefore, the results of the CAPEX for the three processes are approximately in the range of 200-1600 USD/tpa, the economic analysis in this study appears reliable. \begin{table}
\begin{tabular}{c c} \hline \hline
**Optimization Algorithm** & **Execution Time (Min.)** \\ \hline \hline \
\begin{tabular}{c} Patter search \\ Genetic algorithm \\ Particle swarm optimization \\ \end{tabular} &
\begin{tabular}{c} 241.8 \\ 533.2 \\ 132.2 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Execution time comparison of optimization algorithms for the base case. Figure 7: Exergy efficiency and the total annualized cost for each process. Figure 9 shows the compassion of TAC differences between the case with and without the refrigerant leakage consideration. As shown in Figure 8, TOC and TCC differences between both cases in SMR are significant because of the complex refrigerant make-up system. In contrast, TOC and TCC differences between both cases in other processes are not significant because of the simple make-up system.