Porous media compressed air energy storage (PM-CAES) is a viable option to compensate intermittent renewable sources in future energy systems with a 100 % share of renewables. However, the design and evaluation of operational conditions for a PM-CAES requires an efficient coupled power plant - geostorage model. In this study, therefore, a novel semi-analytical solution for the geostorage model is developed and evaluated with respect to three realistic energy system scenarios. The developed model is able to simulate the typical storage operation processes charging, discharging and storage, taking into account facility and technical constraints, physical properties of the stored gas and storage well configurations. We validate the model using two realistic energy system scenarios and demonstrate that it provides a consistent approximation, yielding storage pressure, rates, and capacity within 98 % of the full-scale geostorage model. Two scenario studies show that the designed PM-CAES plant delivers a continuous energy discharge of 3.0 GWh - 6.7 GWh at a power rate of 50 MW with a storage efficiency of 53 %. The model presented in this study provides a reliable and efficient approximation of the full-scale numerical geostorage model for PM-CAES systems. Moreover, the use of a simplified reservoir model and semi-analytical solutions for the boreholes yields a reduction of runtime by a factor of about 20 compared to numerical solutions. Therefore, this approach enables fast site assessment and various scenario simulations during site selection or planning for PM-CAES, making it a valuable tool for optimising the design and evaluation of operational conditions for renewable energy storage applications.