Stress–Based Torque and Drag Model

Abstract

The models used currently in industry have shown a considerable discrepancy between theoretical data and actual data observed in the field. The birth of torque and drag (T&D) modeling was in 1984 in Exxon Production Research Company, and was published by C.A Johancsik. It provided the first mechanical model as well as an illustration of the origin of torque and drag forces. Johancsik’s paper stated that these resisting forces originate from the friction of the drill string against the wellbore and depend on the drill string weight supported by the borehole. Many subsequent models adopted the same concept including some improvements.

In this work, a new approach of torque and drag calculation is proposed. It consists of taking the forces acting on the drill string and converting them into resulting stresses on the pipe body, and transferring the stress tensor from one segment to the next using continuum mechanics geometrical transformations. The stress tensors are accumulated to yield the resulting stress acting on an element of the drill string in a given depth of the well. The back calculation from stress to forces allows deriving the cumulative traction and compression forces, and thus drag and torque. This approach has two main advantages over the discrete method proposed by Johancsik. First, when a force is applied on a body it propagates through the body, therefore, even if the force is axial, a portion of it is going to act normally and vice versa. Consequently, the axial force Johancsik is calculating does not fully act in the same axis, and the same can be said about the forces in the other directions. In this case, it is more physically representative to base the analysis on stress and not forces. Second, continuum mechanics provides a sound tool in handling geometries through stress tensor transformation matrices used in our model, instead of the angular approximations for inclination and azimuth used in Johancsik's equations.

A comparison between the two models for a real field case is included to show the relative under-prediction of the old model compared to the proposed model and actual data.