Investigation of Fluid Column Oscillations in an Open Vertical Well
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DOI:
https://doi.org/10.32523/3007-0155/bulmathenu.2024/2.3Keywords:
собственные колебания, собственные частоты, гидроудар, скважина, фильтрация жидкости, затухающие колебания, гидроразрыв пластаAbstract
The natural oscillations of a liquid column in an oil well caused by a sudden stop of pumps (hydraulic hammer) are analyzed. It should be noted that the wave parameters of the oscillations depend on the rheological properties of the liquid, the reservoir characteristics of the bottomhole formation zone and the hydraulic fractures of the formation. Based on a mathematical model describing the movement of liquid in a well with an open upper end and the filtration flow in the bottomhole zone with hydraulic fracturing, taking into account the initial and boundary conditions, analytical solutions in the form of standing waves for the problem of natural damped oscillations of a liquid column in a well are found. Expressions are obtained for finding the pressure and velocity of the liquid in the well. A characteristic equation is obtained for finding the wave parameters of natural frequencies (frequency, period, damping coefficient and decrement). The influence of the permeability of the formation and the conductivity of the hydraulic fracture on the oscillation frequency, the damping coefficient and decrement of pressure oscillations is analyzed. The dynamics of pressure in the middle and at the bottom of the well are considered in cases of absence and presence of a hydraulic fracture of the formation. A comparison of these characteristics is made for liquids with different densities, namely for oil and water.
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