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Notes

40-50% efficiency of air storage, compared to 70-90% for batteries.
Pumping and air engines are 60-70% efficient.
Scroll Compressor is nearly 100% efficient, but expensive.
Highest ESOI of any energy source - [2]
Conclusion of Reference [7] - The sizing of storage tanks for a SHS-CAES has been determine by modeling all the components downstream of the storage tank. To operate the system with SHS load of 29.65W for 12 hours requires a tank size of 18 m3, with an initial pressure of 8 bar and regulator setting 3.511 bar.
8 bar system operates at around 60% roundtrip efficiency - that is impressive.
P. 60 of thesis [3] shows the size of tank required for 3kWhr storage - 65 cubic meter.