The article discusses the development of technology for directional drilling of oil and gas wells in the perspective of modeling downhole operations. The most significant mathematical models developed by Soviet and foreign scientists in the XX century are listed. An example of calculating the reaction on a bit based on the most widely used method of initial parameters is shown. In the process of a typical calculation of the deflecting force on the bit, it was possible to set the boundary conditions on the bottom hole assembly (BHA) supports in a natural form, using a well-known approach for calculating the deflection of the beam. The obtained results of calculations were applied in the construction of a simulation model for computer simulation based on a virtual program-simulator of the drilling directional wells. The simulating software allowed us to evaluate the effect of the Zenith angle of the well and the rigidity of the oriented layout on the deflecting force on the bit, the deflection of the turbo drill along the length from the bit to the nearest lower point of contact of the well wall.
Development of mathematical model of oil and gas wells drilling based on use of energy transmitted to bottom hole