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Study of natural oscillations of oil in a vertical well

In the oil industry, an important aspect in the production of hydrocarbons is the control of the state of the well and the study of the near-wellbore zone adjacent to it. For this purpose, various geophysical well survey methods (GIS) are used. One of the methods of well logging is acoustic spectroscopy of wells, where the characteristics of the well and reservoir can be studied by means of excitation of natural oscillations of the fluid. In this paper, the problem of natural oscillations of a fluid in a vertical well, which arose as a result of a sharp opening or closing of the well, is investigated. To describe this process, a mathematical model of natural oscillations of the liquid column in the well, which communicates with the reservoir through the permeable walls of the open area, is constructed using the mass and momentum conservation equation in the well area, the mass conservation equation in the open area of ??the well, and the filtration equation in the reservoir. Taking into account the initial and boundary conditions, an analytical solution was found in the form of standing waves to determine the pressure and velocity of oil in the well. The dependences of the oscillation frequency, decrement and damping factor on the reservoir permeability are shown, the pressure dynamics in the well is given and the amplitude of the oscillations is considered. A comparative analysis of changes in such indicators as oscillation frequency, decrement and damping coefficient has been carried out. The influence of such parameters as the length of the bottomhole zone and the permeability coefficient on the nature of the change in the natural fluctuations of the fluid has been established.