MODEL OF INTERACTION WITH THE INNER SURFACE OF AN ORIENTED WELLBORE EQUIPPED WITH AN AXIAL OSCILLATION TOOL
DOI:
https://doi.org/10.31471/1993-9868-2024-2(42)-61-70Keywords:
directional drilling, friction forces, layout of the bottom of the drill string, generator of axial oscilla-tions, mathematical model, Lagrange’s equation.Abstract
Today, due to advancements in scientific and technical fields, drilling inclined wells has become increasingly popular. A crucial factor in ensuring wells' safe and efficient construction is the selection of the optimal layout for the bottom of the drill string. This layout should provide the necessary control over the well trajectory while also achieving high technical and economic performance in the well construction process. The choice of the drill string layout depends on the available technological equipment, as well as the technical and geological conditions of the drilling site. This choice must be well justified. One common method for justifying the drill string bottom's layout selection is modeling the well drilling process. This work focuses on a mathematical model that addresses the interaction of a specialized two-support layout of the drill string, which is equipped with an axial oscillation generator, and the walls of the well. We analyzed various drill string layouts used in drilling directional well sections and developed a mechanical and mathematical model based on these layouts to achieve this. In our simulation, we assumed that friction exists between the well walls and the drill string, described by the Coulomb model while neglecting the influence of the flushing fluid flow. The mathematical model was derived using the second-order Lagrange equation, employing a method that introduces fictitious degrees of freedom for the drill string. This approach allows us to determine the reactions of the elements using the principle of possible displacements. As a result, we obtained a system of differential equations, which reveals the forces of contact interaction between the supports of the drill string and the walls of the well. This proposed model enables us to assess the forces exerted by the drill string on the well walls, taking into account the kinematic characteristics of the drill string movement, the geometric parameters of the layout, the axial load on the bit, and the friction parameters.
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