Transient heat transfer models of wellbore and formation systems during the drilling process under well kick conditions in the bottom-hole

The temperature distributions in wellbore and formation systems significantly influence the fluid property and pressure control in a well under well kick conditions. Based on mass and energy conservation principles, numerical models were developed for different thermal regions in wellbore and formation systems and were situated inside the pipe, the drilling pipe wall, the annulus and the surrounding formation. In this study, the models were designed to calculate two-dimensional transient heat transfer during circulation and shut-in stages under well kick conditions in the bottom-hole. Moreover, the mathematical models also determined transient convective heat transfer of the rock surrounding a well. A fully implicit finite difference method was applied to solve the partial differential equations of heat transfer mechanism. The results indicated that the amount of well kick at bottom-hole and casing program had significant effects on the temperature distributions of wellbore and formation. During the drilling process, the disturbance distance of the formation temperature during the shut-in stage was longer than that of the circulation stage. The numerical model's validity was verified by both measured and calculated data. Based on the results, a comparative perfection theoretical basis of temperature distribution in wellbore and formation systems during deep well drilling was developed.