Numerical transient and steady state analytical modeling of the wellbore temperature during drilling fluid circulation

Abstract

In this paper, a transient model that describes the heat transfer processes in the wellbore during circulation is presented. A simulation of the transient effect on these heat transfer processes was achieved by using a numerical approach to solve the thermal balance equations that describe the heat flow in that system. The present model can be applied for both laminar and turbulent flow regimes through the convective heat transfer coefficient (CHTC). The run time of the present model is relatively short, hence it can be applied for real-time simulation applications. This was achieved by simplifying the model and reducing the calculation complexity. Moreover, the present model has gone through different validation processes. First, the present model is reduced to a steady state condition and solved analytically. This solution was used as a reference to verify the results of the numerical model. Additionally, a grid sensitivity analysis was performed. Second, the analytical solution was validated through a comparison with the known literature. Finally, the assumptions that were made to simplify the model were verified by comparing the results with the comprehensive version of the model. The effect of the flow rate and the flow regime on the wellbore temperature profile are examined. The results showed a reverse effect of the flow rate on the bottom hole temperature within each flow regime. However, a significant increase in the bottom hole temperature is observed as the flow regime changed from laminar flow to turbulent flow. Changing the flow regime from laminar to turbulent will affect the value of the CHTC leading to a significant increase in wellbore fluid temperature. It is also shown that the maximum temperature at the annulus is located where the rate of heat exchange between the annulus and the pipe and the heat from the formation to the annulus is equal.