The compression process in a piston cylinder device in a Compressed Air Energy Storage (CAES) system is studied computationally. Twelve different cases featuring four different compression space length-To-radius aspect ratios and three different Reynolds numbers are studied computationally using the commercial CFD code ANSYS FLUENT. The solutions show that for compression with a constant velocity, the compression can be approximated by a polytropic pressure vs. volume relation. The polytropic exponent, n, characterizes the heat transfer and temperature rise of the air being compressed. For the cases computed, it varies from 1.124 to 1.305 and is found to be more affected by Reynolds number and less by the length-To-radius ratio. Since the efficiency and storage power of the compressor depend on pressure vs. volume trajectory during compression, they are written as functions of the pressure rise ratio and the polytropic exponent, n. The efficiency is high at the beginning of the compression process, and decreases as the compression proceeds. The effect of temperature rise or heat transfer on efficiency and storage power is shown by comparing the efficiency and storage power vs. volume curves having different n values. Smaller temperature rise always results in higher efficiency but lower dimensionless storage power for the same compression pressure ratio. The storage power is used in this study to distinguish the compression process effect (n effect) and the compressor's size effect on the storage power. The likelihood of flow transitioning into turbulent flow is discussed. A k- Reynolds Averaged Navier Stokes (RANS) turbulence model is used to calculate one of the larger Reynolds number cases. The calculated polytropic exponent was only 0.02 different from that of the laminar flow solution. The CFD results show also that during compression, complex vorticity patterns develop, which help mix the cold fluid near the wall with the hot fluid in the inner region, beneficial to achieving a higher efficiency.