Mechanical model of the casing sidetracking tool system considering weight on bit and axial displacement

Abstract

It is of practical interesting to investigate the mechanical behaviors of sidetracking tool system and describe the sidetracking window profile with its influencing factors, because it can provide an important basis for optimizing the sidetracking tool system and controlling the shape of sidetracking window effectively. A load-displacement equation of sidetracking tool system, which describes the force-displacement relation of grinding shoes, is established using the piecewise rigidization method. Stress equations of sidetracking tool system are derived to describe the stress distribution characteristics and their influencing factors more effectively, in which the weight on bit (WOB) is considered. An axial displacement function of flexible joint is obtained through numerical simulation and data fitting, and then a profile equation of sidetracking window is established to express the influences of axial displacement. It should be emphasized that the established profile equation can predict the casing sidetracking window shape more accurately because the influence of the axial displacement of the flexible joint is considered. The load-displacement equation, stress equations, axial displacement function and window profile equation, which have been mentioned above, compose a mechanical model of sidetracking tool system. Using the mechanical model, the influence laws of flexible joint length and thickness and construction WOB on window shape are calculated and analyzed, and then the operation parameters of sidetracking window are optimized. Some useful findings are as follows. The sidetracking window profile resembles an inverted tear drop shape. The window width is mainly affected by the size of casing and grinding shoe, while the window length is mainly affected by the angle of whipstock and the combined deformation of sidetracking tool. The adjustable range of window width is less than that of the window length. The length of the window increases with the reduced length of the flexible joint, or the increased thickness of the flexible joint, or the increased WOB. This work can become a theoretical basis and calculation tool for designing a sidetracking tool system which produces the sidetracking window shape more effectively and accurately.