Abstract: Accurate prediction of annular frictional pressure drop is the key to ensuring the accuracy of bottomhole pressure prediction during deep well drilling. The flow rate of the drilling fluid, drillpipe rotation speed, and the annular eccentricity are important factors affecting the annular frictional pressure drop. To investigate the change in annular frictional pressure drop with the combined effects of various factors, a drilling fluid flow model in the annulus of a horizontal well was developed, and the flow characteristics of power-law fluids under laminar and turbulent flow conditions were numerically investigated. The results show that: 1) under the laminar flow condition, annular frictional pressure drop decreases when the eccentricity or the drillpipe rotation speed increases separately. However, when these two parameters increase simultaneously, the annular frictional pressure drop increases first and then decreases as eccentricity increases. This is due to the destruction of helical flow by the inertia effect in the eccentric annulus. 2) Under the turbulent flow condition, drillpipe rotation speed has almost no effects on the frictional pressure drop in the concentric annulus. In the eccentric annulus, with the drillpipe rotation speed increasing, the frictional pressure drop under different eccentricities increases gradually and converges to the frictional pressure drop in the concentric annulus. Based on the numerical simulation data, the prediction model for annular frictional coefficient with the combined effects of drillpipe rotation speed and eccentricity under laminar and turbulent flow conditions are developed. The maximum fitting error of the model to the simulated data is 9.18%, and the prediction error for experimental data is no more than 8.33%. The results of this study could provide reference for wellbore pressure control and hydraulic parameter optimization during deep well drilling.