An Analytical–Numerical Model for Determining “Drill String–Wellbore” Frictional Interaction Forces

Currently, drilling of directional oil and gas wells under complex technical-technological and mining-geological conditions requires the use of drill pipes made of various materials. In turn, to choose rational modes of strengthening drill pipes and drill string layouts, information on the contact forces and friction forces of the drill string pipes on boreholes is necessary. Drill pipe curved sections friction with boreholes and drill bit resistance moment changes are the main causes of uneven rotation of a drill string during rotary or combined drilling methods and the occurrence of parametric oscillations. To reduce the cost of mechanical energy for well wiring, it is necessary to take into account the “drill string–borehole rocks” force interaction to estimate the magnitude of the frictional forces and their influence on the technological parameters of the drilling process. To solve this problem, mathematical models of “conventionally vertical and inclined drill string sections–borehole” were built. Based on the industrial data, an analysis of the force interaction of a deformed drill string composed of pipes made of different materials (aluminum, titanium, steel) was carried out. Analytical dependences were obtained for determining the contact forces and friction of the pipes on boreholes. A numerical study of the change of these power factors depending on the depth of the well under conditions of intensive vibration loading was carried out. The amplitude values of these forces, the frequency of their change for good sections, as well as the places for the most rational installation of drill pipes in the layout of the drill string were estimated. It was established that the intensity of contact and friction forces for steel drill pipes is greater than for titanium or aluminum ones. It is shown that the greater impact of a solid steel string on contact forces and frictional forces compared to a layout with sections of titanium or aluminum pipes in the range of vibration frequencies of 8–22 Hz corresponds to a bit rotation frequency of 70–80 rpm. The practical application of the obtained research results will contribute to the improvement of technical and economic indicators of the well drilling process.