Engineers’ Trilemma: Use and Limitation of Torque and Drag Models

Different methods to calculate torque and drag have been used by the oil industry for years. Various assumptions are used in formulating these models. Opinions have often varied as to which model is better and whether the assumptions are valid. This paper discusses the trilemma considerations for an engineer 1. Soft string model vs stiff string model 2. Survey calculation method based on minimum curvature 3. Appearing and vanishing tortuosities after the casings have been run. Because of various underlying assumptions, the friction factor calibration is done often to match the calculated results with the actual results. This results in a wrong conclusion due to the change in the drag forces but on the contrary, it may be due to the exacerbation of the assumptions. The paper presents the pitfalls of the drillstring models, borehole curvature, appearing and vanishing tortuosities and their relationship with related well engineering calculations. Mathematical underpinnings are provided for all the trilemma considerations. Results demonstrate that a string with a large-size section can be very soft in a straight wellbore, and a string with small-size section can be very stiff in a wellbore with severe tortuosity, which is better fit for a stiff string model. Results also confirm that the soft string model is a better choice when the string is slimmer, the wellbore is in a lower curvature shape, and the clearance is larger. It has been observed that the absence or the discontinuity of bending moment results in the underestimate of forces, torque, and stresses when the minimum curvature method is used. This vanishing tortuosity alters the apparent wellpath and the new tortuosity representative of the cased hole path may present new appearing tortuosity and results in over and under estimation of the torque and drag calculations. To accurately estimate the drag force, the stiffness, as well as the wellbore shape and its clearance, should be considered.