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In the upgrade project of the Beijing Electron Positron Collider (BEPCII), three superconducting magnets are employed to realize the goal of two orders of magnitude higher luminosity. A cryogenic system with a total capacity of 0.5 kW at 4.5 K was built at the Institute of High Energy Physics (IHEP) to support the operations of these superconducting devices. For preparing the commissioning of the system, the refrigeration process was simulated and analyzed numerically. The numerical model was based on the latest engineering progress and focused on the normal operation mode. The pressure and temperature profiles of the cryogenic system are achieved with the simulation. The influence of the helium mass flow rates to cool superconducting magnets on the thermodynamic parameters of their normal operation is also studied and discussed in this paper.