Liquid air energy storage (LAES) processes have been extensively analyzed due to their low constraints and capability for large-scale storage. However, the efficiency and storage flexibility of conventional LAES are significantly constrained by the air purification process. To improve the continuous storage capacity and economic viability of LAES, this paper proposes two enhanced processes, dual-compression LAES and mediumpressure expansion LAES, utilizing the backflow gas as purified purge gas. The design and operating parameters of liquefaction process were optimized using a genetic algorithm. The round-trip efficiency, system exergy efficiency, dynamic payback period, and levelized cost of electricity for the dual-compression LAES are 58.98 %, 65.9 %, 11 years, and 120.4 $/MWh, respectively, while those for the medium-pressure expansion LAES are 62.15 %, 68.17 %, 9 years, and 114.4 $/MWh, respectively. Additionally, the economic benefits of mediumpressure expansion LAES become more significant with higher off-peak electricity costs and a lower peakvalley electricity price ratio. The proposed processes are characterized by high efficiency and economic viability, without storage time constraints. The dual-compression process is simple to retrofit but has limited upgrade potential, making it suitable for existing LAES, whereas the medium-pressure expansion process offers more significant upgrades but requires extensive retrofitting, making it suitable for new LAES.