Dynamics of temperature in the wellbore at local induction heating in a casing

New analytical solutions for the calculation temperature changes in the liquid flow and in the metal casing string due to induction heating of the string section. The solutions are based on a one-dimensional analytical model, in which convective heat transfer by fluid flow is taken into account, heat transfer between the liquid and the casing string, heat generation in the metal column when the inductor is turned on and losses in cement and rock due to thermal conductivity. To obtain a solution, the integral method was used. Laplace transform in time, inverse transform carried out using the numerical Stefest algorithm. Features explored temperature field during heating and after shutdown inductor, it is shown that the rate of decrease in temperature anomalies increases with increasing liquid flow in the column. Comparison of the results of calculations by the analytical model with numerical simulation results in the Ansys software package Fluent, as well as with experimental data. It is shown that the received analytical solutions can be used in forecasting temperature anomalies caused by induction heating of the casing columns.