The pipeline transportation of CO₂ plays a crucial role in carbon capture, utilization, and storage (CCUS) systems as an intermediate link. Leakage is the primary risk in CO₂ pipeline transportation process, with the leakage rate being a key indicator for assessing pipeline leakage incidents. Due to the significant variations in pressure and thermophysical properties during the leakage process, simulation methods often face convergence difficulties. Moreover, the classical small-orifice leakage model fails to meet the accuracy requirements for CO₂ pipeline leakage calculations. To address this issue, a mathematical model based on isentropic expansion and choked flow effects was proposed. The effect of vena contracta on leakage was considered, and the flow area at the leakage orifice was modified. This model allows for accurate calculation of the temperature, pressure, and leakage rate at the CO₂ pipeline leak, with the predicted results aligning well with experimental leakage data, demonstrating high computational accuracy and stability, significantly outperforming classical small-orifice leakage models. This model can provide leakage source strength data for research on far-field leakage dispersion, thereby offering a valuable reference for decision-making in CO₂ pipeline transportation safety engineering.