Heat exchangers (HEXs) are among the key components of adiabatic compressed air energy storage (A-CAES) systems. However, the existing HEX models applied in the A-CAES systems are overly simplistic, limiting research regarding design and operational simulation. For the first time, this study incorporates a comprehensive HEX model, including calculations for geometric dimensioning, heat transfer, and pressure drop, into the A-CAES system model; in addition, a novel layered, interactive system design and operational simulation algorithms are developed. The developed models and algorithms can facilitate the design process and yield reasonable operational simulation results with only basic parameters. The design algorithm can determine all key parameters of the system and assess the effect of the HEX pressure drop and heat transfer area on the system performance. The operational simulation algorithm considers the performance of all key equipment under off-design conditions. The design exergy efficiency and daily net income of the system are 73.15 % and $26,998, respectively; however, these values decrease during operation to 72.15 % and $25,034, respectively. A comprehensive analysis of the key parameters during operation revealed that the primary causes for the degradation were the sliding pressure in the energy storage process and variations in the air storage tank parameters.