exposed to the action of friction and contact forces, the forces of inertia from a washing fluid, etc. The listed phenomena exert a negative impact on the elements of a drill string, bits, downhole motors, and in general lead to a loss of energy and reduce the techno-economic indicators of drilling [1-4]. To refine the parameters of loading and the stressed-deformed state of a drill string, it is necessary to have a well-defined procedure for determining the moments of inertia of its curved sections. Therefore, it is a relevant task for the theory of dynamic stability of elastic systems to investigate the inertial properties of a curvilinear string of pipes at rotation. The solution to this problem is necessary in order to properly conduct a dynamic analysis of drill strings at rotor and rotor-turbine drilling techniques.

The purpose of the work is to increase the insulation work efficiency by using thermoplastic mixes based on polyethylene terephthalate. The tasks set were solved by a complex method of research, including the analysis and synthesis of the literary and patent sources, as well as conducting the analytical and experimental studies. The experimental data were processed on a PC using the methods of mathematical statistics. A method for insulating the absorbing horizons with thermoplastic materials has been developed and substantiated. To implement it, the following technological operations should be performed: supply of the thermoplastic materials to the borehole bottom, melting and squeezing of thermoplastic materials into absorption channels. For various geological and technical conditions of drilling, technological schemes of insulating the absorbing horizons with thermoplastic materials are proposed. The use of the household waste based on polyethylene terephthalate has been proposed as the plugging material to insulate the absorbing horizons of boreholes. For the first time, the possibility of using the household waste based on polyethylene terephthalate as the plugging thermoplastic material has been substantiated and proved. For the first time, a method for determining the efficient range of technology application for absorbing and unstable horizons insulation with thermoplastic materials through the use of bottom hole thermal sources has been substantiated analytically.

Purpose. To increase the stability of the wellbore during its construction in unstable rocks. Methodology. To solve the set tasks, an integrated approach is used in the work, which includes critical analysis and generalization of scientific and technical achievements in combination with theoretical and experimental research. Findings. Factors influencing the stability of the borehole walls in conditions prone to rock slides and rock falls are analyzed. Expediency of using baths for strengthening the walls of wells in deposits of clay rocks, including clay shales, has been established and substantiated. A formulation of a fuel-bituminous bath has been proposed, the installation of which in a well for 78 hours makes it possible to increase the initial compressive strength of rocks, which will ensure the integrity of the borehole walls. It is recommended to use corrugated casing pipes to cover the sections of the wellbore where there is intensive crumbling and collapse of rocks. Originality. For the first time, the main factors of wall destruction have been established and a method has been developed to prevent the destruction of walls of directional wells composed of rocks prone to loss of stability under the action of drill string loads. Practical value. To combat the collapse of the walls of the well composed of rocks, prone to loss of stability, the authors suggested setting up fuel-bituminous baths in the range of complications. In case when the collapse of the walls of the well can not be prevented with a fuel-bitumen bath, it is proposed to overlap the area of collapse with the casing using advanced corrugated casing pipes with the injection of adhesive into the rock mass in the near-wellbore zone. The use of an adhesive material increases the contact area of the metal shell with the rock, which collapses increasing the stability of the borehole walls.

In the period of shortage of gas supply, special attention is given to reducing the supply of gas to its consumers, that is, their complete and uninterrupted gas supply. Increasing gas losses associated with technological transportation costs, in particular caused by gas flow instability and frequent changes in gas transmission network operating modes. Considering losses due to unreliability of gas pumping is one of the important tasks of gas supply optimization. The purpose of the study is to develop an optimization mathematical model that will simultaneously take into account the factors of reliability and minimum lossesIn the general case, the optimization calculations of the modes of operation of the main gas pipelines are intended to solve three main problems: determining the maximum productivity, calculating the optimal mode with a given productivity and choosing the optimal strategy, the development of the pipeline. On the basis of approaches of simulation modeling of complex systems, a multi-parameter mathematical model of gas supply process optimization was developed. It is shown that a comparative analysis of the forecast and actual indicators of the operating modes of the plunger gas pumping unit shows their satisfactory convergence. The performance of the compressor operation period in the process of injection according to the forecast deviates from the actual value for the whole period of operation of the plunger gas pumping unit in 2016 by 2.98%. The optimization problem of gas pumping planning is considered, taking into account the expected losses, on the basis of which the transfer of the controlled system from the initial state to the final one is carried out by such a sequence of states that minimizes the total cost of the system evolution.

Purpose. Finding the cause and effect relationships between the parameters of nonstationary longitudinal and torsional vibra tions of a drilling tool and developing a mathematical model to study their properties.Methodology. The solution to this problem is based on one of the basic principles of analytical mechanics -the Lagrange principle. The equation of motion of the studied rod mechanical system with four degrees of freedom is made using the Lagrange equation of the second kind, which is one of the next stages of its dynamic analysis.findings. In the process of solving this problem on the basis of industrial data, the analysis of axial load functions, angular rota tion speed and torque of the drilling tool for their nonstationarity was carried out. The frequency of change in these nonstation ary drilling mode functions is set by rapid Fourier transform. originality. For the first time, analytical dependences were obtained to determine the forces of cutting and friction on the bit from the second derivatives of the independent generalized coordinates of the mechanical system over time, as well as the relation ship between the generalized accelerations of the translational and rotational motions of the bodies of the mechanical system.Practical value. The practical value of the work is the obtained equations of motion of the system, taking into account the re ceived frequency compositions of the mode parameters of drilling until their subsequent numerical solution. The results of this task will further facilitate the choice of optimal modes of dynamic loading of the drilling tool in order to improve its energy efficiency and reliability. Analysis of the frequency dependences of the change in nonstationary functions of the drilling mode parameters will allow evaluating the level of wear of the rock destruction tool, as well as to predict the durability of the drill string elements.