## Summary

The advent of deviated, horizontal, and extended-reach drilling has led to increased frictional forces acting between the drillstring and the wellbore wall. Wellbore mechanical friction attributable to pipe rotation or to torque and drag plays a significant role in drilling operations and is considered to influence the downhole temperatures of the drilling fluid. An analytical model to estimate the influence of this pipe friction will help in providing a better physical insight to understand the downhole borehole conditions as well as in realizing the effect of its underlying parameters.

This study aims to develop a simple mathematical model to analyze the heat generated downhole from the drillstring and borehole contact and then predict its influence on the temperature of the drilling fluid during a drilling operation at any depth in the well. The model presents a steady-state solution for heat transfer between the drillstring and the fluids in the drillpipe and annulus, as well as for heat transfer between the annular fluid and the formation. The heat generated from friction has been modeled by use of the torque acting on the drillstring as a result of contact forces. A linear temperature gradient for the formation and a constant borehole-wall temperature has been assumed to simplify the model. Frictional pressure losses in the drillpipe, in the annulus, and across the bit have been incorporated in the model because they contribute to the heat generated downhole. The temperature profile of the drilling fluid has been estimated both in the annulus and inside the drillpipe for the entire well profile under consideration.

This paper will present the derivations of the generalized heat-transfer model and its validation by use of two practical drilling scenarios. Two different field cases, one for a deviated well and the other for a horizontal well, have been presented, and the estimated temperature profile by use of the model is compared with the actual temperature measured downhole by use of measurement-while-drilling (MWD) tools. The increase in temperature for a particular depth in the well for the entire bit run has also been presented as another successful application of this model. The impact of drilling parameters on temperatures has also been analyzed and can be used effectively to maintain a better check on undesired temperatures.

This simple analytical model can be suitably applied to field cases on the basis of the well profile and can be effectively used to predict the maximal temperatures to be encountered downhole while drilling ahead as planned. An accurate estimation of maximal temperatures will help us prevent severe downhole friction heating in the future.