## 1 Introduction
Further, [PERSON] and [PERSON] [16] investigated the performance of the two different refrigerants (R410a and propane) for pre-cooling the nitrogen expansion cycle. They optimized three different processes using specific energy consumption as the objective function and proved that nitrogen expansion with the R410a pre-cooling cycle is better than that with or without the propane pre-cooling cycle. [PERSON] et al. [17] proposed a novel small-scale liquefaction that uses single nitrogen expansion with a carbon dioxide pre-cooling cycle. They compared the energy consumption of the proposed process with three different small-scale LNG liquefaction cycles such as a propane pre-cooling MR cycle, an N\({}_{2}\)-CH\({}_{4}\) expander cycle, and a modified mixed refrigerant cycle (MRC). They concluded that the proposed cycle achieved the lowest energy consumption (9.90 kWh/kmol) among all compared processes and insisted on the advantages of considerable stability and simple capability of their process. [PERSON] et al. [18] proposed the closed-loop self-cooling recuperative N\({}_{2}\) expander cycle, wherein they added a recuperator to the single nitrogen expansion cycle to reduce exergy losses. In addition, after performing optimization configurations of the proposed process, they concluded that a configuration with a natural gas feed expander can save up to 22.2% of the required energy compared to the base case. Self-refrigeration LNG liquefaction based on the Linde-Hampson cycle is another improvement in the natural gas liquid (NGL) recovery process [19]. The gas from the separator is partially vaporized, and this vapor is then used as the refrigerant in the cycle to cool the inlet gas. This process is called self-refrigeration, and it can reduce the refrigeration duty of the cooling cycle and the required amount of refrigerants [19]. Unfortunately, there have been few studies regarding the self-refrigeration process. The LNG production and transportation company Galileo Technologies developed a small-scale movable LNG liquefaction plant by applying the self-refrigeration technology to their product called Cryobox; this is an actual commercialized movable LNG production plant [20]. Although various studies developed the LNG liquefaction process, only a few studies focus on the leakage problem on the compressors. Previous studies focused on developing new processes with high energy or energy efficiency, performing optimizations to increase efficiency, or varying the composition of the refrigerant. [PERSON] et al. [21] pointed out that the potential problem of LNG liquefaction plants is the refrigerant leak from the compressors. Further, the leakage problem can cause considerable problems for entire system, especially in small-scale LNG liquefaction systems where the compressors and seal systems are not leak-tight [22]. Consequently, the sustainability of the LNG liquefaction plants can be improved by solving this leakage problem. The refrigerant leakage problem can be resolved using a makeup system. Although it is easy for large-scale LNG plants to compensate for the leaked refrigerant using an NGL fractionation unit; this is not an economical option for small-scale LNG plants [23]. Therefore, small-scale LNG plants or movable LNG plants need to consider extra external makeup facilities for the leaked refrigerant or to use less leaking compressors [22]. In this study, three LNG liquefaction processes for a small-scale movable LNG liquefaction plant: SMR, dual nitrogen expansion, and propane pre-cooled self-refrigeration are investigated considering compressor leakage. To analyze the thermodynamics and economics, exergy efficiency, and product cost of all three processes are calculated in this study. The product cost of a small-scale movable LNG plant is not very economically favored compared to medium to large-scale businesses. However, small-scale movable LNG plant can be considered the first alternative for businesses that require a lower CAPEX and relatively simple on-site infrastructure [24].