Adiabatic compressed air energy storage (A-CAES) represents a valuable and environmentally friendly option for massive energy storage. Existing examples of CAES refer to underground storage at medium pressure level. But for widespread utilization, independent from the availability of underground storage volumes, artificial reservoirs would be required. This requires rather high air pressure within the storage, which in turn will demand a carefully optimized recovery of the thermal energy released in the compression phase. Starting from a detailed thermodynamic analysis of the relevant design parameters and their influence on the system efficiency, we propose a comprehensive set of criteria for the design of the system, with particular attention to heat transfer devices.