Sensitivity of drill string drag forces to geometrical imperfections of curvilinear well bore trajectory

Abstract

Based on the theory of flexible curvilinear rods, direct and inverse problems of elastic bending of a drill string in a curvilinear well bore have been defined. A procedure for solving the problems has been proposed. Sensitivity of the drill string drag forces to additional geometrical imperfections of the well centerline is studied.Introduction. Nowadays, based on economic considerations, hydrocarbons field conditions, and available process facilities of oil-and gas-producing companies, the wells to be drilled can be vertical, controlled directional, or horizontal ones, running to various depths. Experience of the last decades suggests that the well yield and hydrocarbons withdrawal efficiency can be significantly improved by choosing an appropriate well centerline trajectory; therefore, the current tendency is to give preference to directional and horizontal well bores.The practical implementation of deep-well drilling with a complex spatial orientation of the well trajectory necessitates theoretical modeling of mechanical phenomena encountered during the well operation in order to predict possible critical states [1, 2]. One of the important aspects of these efforts is to simulate the deep drill string (DS) behavior in curvilinear well bores at the running and pulling stages. Considering that the cost of well bore laying-out, in view of increasing well depth and distance, has already exceeded US$ 50 million [3] and, according to statistics, one in three wells experiences an accident [4], it becomes clear how important the problem of theoretical prediction of DS critical states is and how much a mistake in such predictions would cost.In our earlier publications, we addressed the stability of a deep-well vertical drill string [5], the problem of self-excitation of torsional oscillations [6], defined and solved the problem of initiation of critical states in directional wells [7,8]. In the present work, we have set and solved the problem of elastic bending of a drill string in a curvilinear well bore with geometrical imperfections.1. State of the Subject. The currently available methods of physical and mathematical modeling of mechanics of DS in curvilinear wells generally represent a DS as an absolutely flexible inextensible string [9,10]. Such a model can be justified during tentative calculations at a predesigning stage, where the well trajectory is preset in the form of a smooth curve of the simplest outline with large radii of curvature [11]. However, in the course of drilling, especially for a deep well, the designed idealized geometry of the well can not be achieved and there arise local geometrical distortions along the well centerline due to process or tectonic perturbations. These distortions act as imperfections. They can have a form of small-scale three-dimensional spirals of variable diameter and step, plane harmonic waves or rounded bends. Since the curvatures of the well centerline grow sharply at these sections, the DS is subjected to elastic bending there and, consequently, the forces of contact ...