Compressed-air energy storage (CAES) is being considered as a means for storing energy during off-peak periods and for generating electric power during peak demand periods. The Alabama Electric Cooperative has adopted a novel scheme that pumps air underground into a huge cavern created deep in a solid salt deposit. The cavern is a cylinder about 300 m tall by 80 m in diameter and has an internal volume of about 1.5 106 m3. Maximum storage pressures of 10 0 bar are possible using multistage compressors/ turbine units that operate with equivalent efficiencies of compressor = turbine = 0.85. The ambient air temperature is 25C, while the salt cavern's natural temperature is about 300C as a result of prevailing geologic conditions. To keep the cavern from collapsing, a minimum pressurization level of 2 bar is required. Note that the thermal conductivity of the salt is high, and the thickness (radial and lateral extent) of the salt deposit is large relative to the dimensions of the cavity.

In the first part of the cycle, excess electrical power being produced during an off- peak period is used to operate the compressor to inject air into the cavern to pressurize it to 100 bar. In the final part of the cycle, power is produced during a peak demand period by expanding the cavern's pressurized air in a turbine (which is actually the compressor operating in reverse) to generate electric power.

Provide an expression for the net work produced during a single full cycle of energy storage and recovery and describe how you would estimate the net work produced. Please list all assumptions and simplifications used in your analysis. Your answer may be expressed as an integral equation involving the following variables: (Cp /Cv), cavern volume (Vcavern), Tcavern, Tambient, Pcavern, max, Pcavern, min, compressor, turbine.