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DOI 10.21662
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Nasyrova D.A. Natural fluctuations of the liquid in vertical and horizontal wells. Multiphase Systems. 19 (2024) 3. 125–131 (in Russian).
2024. Vol. 19. Issue 3, Pp. 125–131
URL: http://mfs.uimech.org/mfs2024.3.018
DOI: 10.21662/mfs2024.3.018
Natural fluctuations of the liquid in vertical and horizontal wells
D.A. Nasyrova
Mavlyutov Institute of Mechanics UFRC RAS, Ufa

Abstract

Currently, hydraulic fracturing (FRACKING) technology is widely used in oil production. Cracks are created in the formation, fixed with propants to prevent them from closing. The paper considers the natural fluctuations of the liquid in a vertical oil well with a closed upper boundary and in a horizontal well with multiple fracturing. Based on a mathematical model describing the movement of a column of liquid in a well and filtration in a bottomhole zone exposed to hydraulic fracturing, solutions to the problem of intrinsic damping vibrations of a column of liquid in a well are obtained. We have obtained a characteristic equation for determining the natural frequencies of vibrations. The dependences of natural frequency, attenuation coefficient and attenuation decrement on crack conductivity and reservoir permeability are investigated.

Keywords

hydraulic fracturing,
oil well,
natural oscillations,
reservoir permeability,
attenuation coefficient

Article outline

Oil production is a complex and knowledge–intensive process that is continuously being modernized and improved, both in the practical and theoretical fields. Currently, one of the problems of the oil and gas industry is to maintain the level of oil production against the background of depletion of deposits with traditional reserves and involvement in the development of hard-to-recover hydrocarbon reserves. In these conditions, geological and technological measures to intensify oil production have been widely used, the most effective of them is considered to be hydraulic fracturing. Hydraulic fracturing (FRACKING) is a method of intensifying the operation of wells, leading to a drastic change in its flow rate. The formations that are being put into operation have low permeability, because of this, proven oil reserves are depleted. Thanks to hydraulic fracturing, it is possible to revive old wells and significantly increase the flow rate. Therefore, hydraulic fracturing technology is used in both production and injection wells and the tasks of determining the characteristics of hydraulic fracturing, the geometry of cracks and changes in reservoir characteristics appear. It is believed that an effective and convenient way from the point of view of technical implementation to determine the quality of perforation and fracture parameters of a hydraulic fracturing is a method based on the excitation of natural vibrations of a column of liquid in an oil well.

This study examines the natural fluctuations of the liquid column in a vertical oil well, which occur when the pumps of the well are abruptly closed or opened (water hammer), with the upper boundary open. A cased horizontal well of length is also considered, which communicates with the formation by means of radial fractures of hydraulic fracturing located evenly along the well. A transcendental equation is obtained from which complex natural frequencies are determined, according to which the oscillation frequency, attenuation coefficient, oscillation amplitude and other characteristics describing the natural vibrations of the liquid in a horizontal well with a system of cracks perpendicular to the wellbore are found. The dependences of the frequency and attenuation coefficient of pressure fluctuations in various sections of the well on the values of reservoir permeability and hydraulic fracturing parameters were studied. It is shown that acoustic diagnostics based on the analysis of natural vibrations in the well can serve as an effective tool for studying the bottomhole zone of the well.

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