Prediction of wellbore and formation temperatures during circulation and shut-in stages under kick conditions

• The transient heat transfer models under well kick condition were developed.
• The kick had a great effect on the heat transfers of wellbore and formation.
• The Temperature distributions were changed during circulation and shut-in stages.
• This model fitted actual field data better than other heat transfer models.

As the kick occurred during the drilling process is a key factor for effecting the temperature distributions of wellbore and formation, the transient heat exchange mechanisms for the radical and axial directions of wellbore and formation under kick conditions were investigated. Two operation stages, namely circulation and shut-in, were taken into consideration. Based on the first law of thermodynamics, a set of transient heat transfer models were developed to accurately predict temperature profiles of wellbore and formation. The models were solved using the fully implicit finite difference method, coupled with clustering method. The results indicated that the depth of kick and casing program could alter the heat exchange efficiency of wellbore and formation, and therefore affect the temperature distribution of wellbore and formation. Additionally, circulation and shut-in stages as well as the initial and boundary conditions for each region of wellbore and formation could also affect the heat transfer mechanism, leading to the variation of distribution distance of the initial formation temperature in the surrounding wellbore. More importantly, this model fitted actual field data better than other heat transfer models. These findings could provide theoretical insights into the temperature distribution of wellbore-formation system in drilling under kick conditions.