In the Compressed Air Energy Storage (CAES) approach, air is compressed to high pressure, stored, and expanded to output work when needed. The temperature of air tends to rise during compression, and the rise in the air internal energy is wasted during the later storage period as the compressed air cools back to ambient temperature. The present study focuses on designing an interrupted-plate heat exchanger used in a liquid-piston compression chamber for CAES. The exchanger features layers of thin plates stacked in an interrupted pattern. Twenty-seven exchangers featuring different combinations of shape parameters are analyzed. The exchangers are modeled as porous media. As such, for each exchanger shape, a Representative Elementary Volume (REV), which represents a unit cell of the exchanger, is developed. The flow through the REV is simulated with periodic velocity and thermal boundary conditions, using the commercial CFD software ANSYS FLUENT. Simulations of the REVs for the various exchangers characterize the various shape parameter effects on values of pressure drop and heat transfer coefficient between solid surfaces and fluid. For an experimental validation of the numerical solution, two different exchanger models made by rapid prototyping, are tested for pressure drop and heat transfer. Good agreement is found between numerical and experimental results. Nusselt number vs. Reynolds number relations are developed on the basis of pore size and on hydraulic diameter. To analyze performance of exchangers with different shapes, a simplified zero-dimensional thermodynamic model for the compression chamber with the inserted heat exchange elements is developed. This model, valuable for system optimization and control simulations, is a set of ordinary differential equations. They are solved numerically for each exchanger insert shape to determine the geometries of best compression efficiency.