Wellbore temperature distribution during circulation stage when well-kick occurs in a continuous formation from the bottom-hole

In the exploration and development of deep reservoir resources, the occurrence of well kick will have a very important impact on wellbore temperature distribution during circulation. This study aims to investigate the wellbore temperature distribution during circulation when well kick occurs in a continuous formation from the bottom-hole. A transient temperature model was established by the first law of thermodynamics. The finite volume method was used to discretize the model and the under-relaxation iterative method was used for numerical calculation. The validity of the model has been verified by the previous typical models and actual measured temperatures. The calculation results showed that the highest temperature of annulus fluid was at the bottom-hole and annulus fluid temperature increased as the formation high-temperature fluid continuously enters the annulus when well kick occurred. The occurrence of well kick led to a significant increase in outlet fluid temperature and bottom-hole fluid temperature. The occurrence of well kick changed the formation radial temperature distribution and the temperature difference distribution between the annulus fluid and the drilling fluid inside the drill string. The flow rate of the well kick and the location of the well kick occurred also had an important impact on wellbore temperature distribution.