The objective is to address the issue of gas-carrying particles generated by erosion wear problems in the transportation process of gas storage reservoir pipelines. In accordance with the principles of the multiphase flow theory, the particle discrete phase model, high temperature, high pressure, water volume fraction, and other pertinent factors, this paper presents a three-phase gas-liquid-solid erosion mathematical model of a three-way gas storage reservoir. The effects of temperature, pressure, water content volume fraction, gas extraction, particle mass flow rate, and particle size on the tee's erosion location and erosion rate were investigated based on this model. The findings indicate that, as the pressure and temperature decline, the maximum erosion rate of the tee exhibits a decreasing trend. Gas storage reservoir water production is relatively low, and its maximum erosion rate of the tee exerts a negligible influence. Conversely, the maximum erosion rate of the tee is significantly influenced by the gas extraction rate, exhibiting an exponential relationship with the maximum erosion rate and the rate of gas extraction. It was observed that, when the volume of gas extracted exceeded 70 x 104 m3/d, the maximum erosion rate of the tee exceeded the critical erosion rate of 0.076 mm/a. The maximum erosion rate of the tee caused by the sand mass flow rate remained relatively constant. However, the maximum erosion rate of the tee exhibited a linear correlation with the salt mass flow rate and the maximum erosion rate. The maximum erosion rate of the tee is greater than the critical erosion rate of 0.076 mm/a when the gas extraction volume is greater than 37.3 x 104 m3/d and the salt mass flow rate is greater than approximately 25 kg/d. As the sand and salt particle sizes increase, the maximum erosion rate of the tee initially rises, then declines, and finally stabilizes. The findings of this study offer valuable insights into the mechanisms governing tee erosion under elevated temperatures and pressures within storage reservoirs.