In order to facilitate the treatment of associated gas in the Liaohe Oilfield, the numerical simulation of the periodic operation process of the three-canister regenerative thermal oxidizer (RTO) was carried out. This work established a three-dimensional physical model and an unsteady mathematical model for the three-canister RTO. Multiple unsteady simulations were performed to analyze the RTO operation process within one switching period, considering different switching times, regenerator heights, and inlet volume flow rates. The variations in purification efficiency, thermal efficiency, and outlet temperature of the regenerator were investigated under different operating conditions of the RTO. The results showed that the thermal efficiency and outlet temperature on the exothermic side gradually decreased with operation time during the three stages of the valve switching period. A balance between higher thermal efficiency and better economic benefits could be achieved under the operating condition of a regenerator height of 1.2 m and a valve switching period of 180 s. Additionally, higher inlet volume flow rates led to increased thermal efficiency and higher outlet temperatures on the exothermic side of the regenerator during each switching period. The purification efficiency of various volatile organic components remained consistently above 99% in the oxygen-rich environment of this type of RTO.