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Abstract: The study considers gas compression properties, gas slippage, back pressure (BP), phase transition (PT), well depth, and differences in gas-liquid physical properties. A new temperature model for multiphase flow is proposed by considering phase transition in the drilling process. The mathematical model of multiphase flow is solved using the finite difference method with annulus mesh division for grid nodes, and a module for multiphase flow calculation and analysis is developed. Numerical results indicate that the temperature varies along the annulus with the variation of gas influx at the bottom of the well. During the process of controlled pressure drilling, as gas slips along the annulus to the wellhead, its volume continuously expands, leading to an increase in the gas content within the annulus, and consequently, an increase in the pressure drop caused by gas slippage. The temperature increases with the increase in BP and decreases in gas influx rate and wellbore diameter. During gas influx, the thermal conductivity coefficient for the gas-drilling mud two phases is significantly weakened, resulting in a considerable change in temperature along the annulus. In the context of MPD, the method of slightly changing the temperature along the annulus by controlling the back pressure is feasible.