Semi-analytical model of the axial movements of an oil-well drillstring in deviated wellbores

The lumped element model of the axial movement in a drillstring that was developed in Ref. [1], is extended to apply for deviated wellbores. This extension involves taking into account the Coulomb friction forces that are present in the curved boreholes. The Coulomb friction forces are proportional to the normal forces, which are dependent on the distributed mass of the drillstring and the curvature of the hole. We consider a constant rotation speed and since the Coulomb friction forces are opposing the movements, the axial friction components are proportional to the axial velocities divided by the constant rotation speed. We outline a methodology for predicting when the Coulomb friction forces are dominating the viscous friction forces in deviated wellbores. As in Ref. [1], the model is simply a convolution of the topside movement and a semi-analytical expression. The model is therefore suitable for a real-time implementation and the model is also an asset for finding reasonable physical approximations and to benchmark other models.