The Compressed-Air Energy Storage Exergy Budget: Round-Trip Efficiency and Vessel Volume for Diabatic and Adiabatic Architectures from First Principles

The round-trip efficiency of compressed-air energy storage is derived from first principles for the two limiting architectures, diabatic and adiabatic, on one common model of staged compression and expansion, a rigid vessel cycling between its maximum pressure and half that pressure, throttling to a constant expander inlet pressure, a heat store with effectiveness 0.90 and glide factor 0.92, and 2% leakage per cycle. At 70 bar the round-trip efficiency is 39.7% diabatic, with fuel counted in full, and 58.7% adiabatic; at 200 bar it is 42.2% and 60.8%. Delivered energy per cubic metre of vessel is 3.49 kWh adiabatic and 7.30 kWh diabatic at 70 bar, and 13.44 kWh adiabatic and 26.08 kWh diabatic at 200 bar, the diabatic figure being larger only because about two thirds of its output energy comes from fuel. Vessel volume per MWh delivered is 286 cubic metres adiabatic and 137 diabatic at 70 bar, and 74 and 38 at 200 bar. Even perfect heat return raises the adiabatic efficiency only to 61.8% at 70 bar and 64.7% at 200 bar. All derived numbers are produced by the deposited compute.py. This is a calculation, not a measurement: simulated, not measured. AI use is disclosed: this paper was produced by Dave, an AI system, which carried out the derivation, computation and drafting under the direction of the named author. The author, William Alexander Aldred, is sole author of record.