Torque and Drag in Directional Wells-Prediction and Measurement
Authors: Johancsik C.A. , Friesen D.B. , Dawson Rapier 
Published: December 2007

Summary
A computer model has been developed to predict drillstring torque and drag, and a versatile rotary torque meter has been built to use in calibrating the model. The principle of the predictive model is that torque and drag forces in a directional wellbore are primarily caused by sliding friction. Sliding friction force is calculated by multiplying the sidewall contact force by a friction coefficient. Realistic sliding friction coefficients were determined from field data by using the same predictive computer model. These field data were gathered using novel torque and hookload indicators that are accurate, portable, and easily installed. Good agreement between friction coefficients calculated from different loads in the same well, as well as agreement between those for different wells, indicates the validity of the predictive drillstring model. Sliding friction is concluded to be the major source of torque and drag in directional wells. For water base mud systems, typical friction coefficients range from 0.25 to 0.40.

Introduction
Drill string drag is the incremental force required to move the pipe up or down in the hole; torque is the moment required to rotate the pipe. Drag forces usually are given relative to the string weight measured with the string rotating but not reciprocating. Measured from the rotating string weight, the pickup drag usually is slightly greater than the slack-off drag. The magnitudes of torque and drag are related in any particular well; high drag forces and excessive torque loads normally occur together. There are a number of causes for excessive torque and drag, including tight hole conditions, sloughing hole, key seats, differential sticking, cuttings buildup caused by poor hole cleaning, and sliding wellbore friction. With the exception of sliding friction, these causes are associated with problem conditions in the wellbore. Conversely, in wells with good hole conditions, the primary source of torque and drag is sliding friction. Torque and drag from any source tend to be more troublesome in directional holes. In very deep, highly deviated wells overcoming torque and drag can be critical to the successful well completion. The capability to predict frictional loads on drillpipe has two main benefits. First, deep, highly deviated wells can be planned to minimize torque and drag. Use of torque and drag as criteria to select the most appropriate well path will help ensure successful drilling operations to total depth. Second, more complete knowledge of drill string loading allows use of improved drill string design techniques. Drill string components can be chosen by using a systematic approach that considers the extra forces involved.

Torque and Drag Prediction Technique
Mathematical Model. A lumped-parameter model provides the basis for the prediction of torque and drag. Both torque and drag are assumed to be caused entirely by sliding friction forces that result from contact of the drill string with the wellbore. Other less important sources of torque and drag are not considered in this model. Two factors affect sliding wellbore friction-the normal contact force and the coefficient of friction between the contact surfaces. The product of these two factors represents the magnitude of the sliding friction force. The normal contact force between the pipe and hole wall depends on several factors. This paper considers only two contributions to nominal force-the effects of gravity on the pipe and the effects of tension acting through curvatures in the wellbore. These forces, and their contributions to normal force, are shown schematically in Fig. 1. Other factors such as pipe bending may contribute small normal forces but are not considered here. The sliding friction coefficient is the ratio of the friction force to the normal contact force. In reality, this value depends on specific contacting materials and on the degree of lubrication at various places in the wellbore. However, in this paper all these effects are expressed as a single characteristic friction coefficient representing average conditions in a particular wellbore. Determination of this lumped-parameter coefficient is fundamental to practical application of this model.
Computer Calculations. The following paragraphs describe the calculation of torque and/or drag forces when the sliding friction coefficient is given. This calculation is made directly. The reverse calculation, where a friction coefficient is determined from given torque or drag data, is done by assuming a friction coefficient and iterating to match the data. In either case, drill string description and wellbore survey data are required.