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.
References
Economides M., Oligney R., Valk'o P. Unified fracture design : bridging the gap between theory and practice. Orsa Press, 2002. 200 p.
Khabibullin I.L., Khisamov A.A. K teorii bilineynogo rezhima fil'tratsii v plastakh s treshchinami gidrorazryva [On the theory of bilinear flow regime in the layers with hydraulic fracturing cracks], Vestnik Bashkirskogo universiteta [Bulletin of Bashkir University]. 2018. Vol. 23, No. 4. P. 958-96. [in Russian] DOI: https://doi.org/10.33184/bulletin-bsu-2018.4.3
Khabibullin I.L., Khisamov A.A. Unsteady flow through a porous stratum with hydraulic fracture, Fluid Dynamics. 2019. Vol. 54, No. 5. P. 594-602. https://doi.org/10.1134/S0015462819050057 DOI: https://doi.org/10.1134/S0015462819050057
Khabibullin I.L., Khisamov A.A. Modelirovaniye nestatsionarnoy fil'tratsii v sisteme plast - treshchina gidrorazryva [Modeling of unsteady filtration in a formation - hydraulic fracture system], Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika [Bulletin of Tomsk State University. Mathematics and Mechanics]. 2022. No. 77. P.~158-168. [in Russian] DOI: https://doi.org/10.17223/19988621/77/12
Nagaeva Z.M., Shagapov V.S. Elastic seepage in a fracture located in an oil or gas reservoir, Journal of Applied Mathematics and Mechanics. 2017. Vol. 81, No. 3. P. 214-222. https://doi.org/10.1016/j.jappmathmech.2017.08.013 DOI: https://doi.org/10.1016/j.jappmathmech.2017.08.013
Shagapov V.S., Nagaeva Z.M. Approximate solution of the problem on elastic-liquid filtration in a fracture formed in an oil stratum, Journal of Engineering Physics and Thermophysics. 2020. Vol. 93, No. 1. P. 201-209. https://doi.org/10.1007/s10891-020-02109-4 DOI: https://doi.org/10.1007/s10891-020-02109-4
Shagapov V.S., Khamidullin I.R., Nagaeva Z.M. Filtration to a vertical well from a broken-down formation in the case of short fractures, Journal of Engineering Physics and Thermophysics. 2020. Vol. 93, No. 6. P. 1363-1372. https://doi.org/10.1007/s10891-020-02241-1 DOI: https://doi.org/10.1007/s10891-020-02241-1
Carey M., Mondal S., Sharma M. Analysis of Water Hammer Signatures for Fracture Diagnos-tics, Annual Technical Conference and Exhibi-tion (Texas, USA). 2015. SPE-174866-MS. DOI: https://doi.org/10.2118/174866-MS
Iriarte J., Merritt J. Using Water Hammer Characteristics as a Fracture Treatment Diagnostic. SPE Oklahoma City Oil and Gas Symposium held in Oklahoma City, Oklahome (USA), 27-31 March 2017. DOI: https://doi.org/10.2118/185087-MS
Wuyi W., Wenrui H. Water hammer simulation of a series pipe system using the MacCormack time marching scheme, Acta Mechanica. 2018. Vol. 229. P. 3143-3160. DOI: https://doi.org/10.1007/s00707-018-2179-2
Wang X., Hovem K., Moos D., Quan Y. Water Hammer Effects on Water Injection Well Performance and Longevity, SPE International Sym-posium and Exhibitionon Formation Damage Control. 2008. SPE 112282. DOI: https://doi.org/10.2118/112282-MS
Yu S., Wei J., Shuanggui L., Yingjie Yu C. Wellbore annulus water hammer pressure prediction based on transient multiphase flow characteristics, Oil and Gas Science and Technology Rev. IFP Energies nouvelles. 2019. V. 74. P. 1-10. DOI: https://doi.org/10.2516/ogst/2019058
Lyudvinitskaya A.R., Shaidakov V.V. Pump dosing systems for difficult conditions of oil production, Oil and gas business. 2009. Vol. 7, No. 2. P. 71-79.
Shagapov V.Sh., Bashmakov R.A., Rafikova G.R., Mamaeva Z.Z. Zatukhayushchiye sobstvennyye kolebaniya zhidkosti v skvazhine, soobshchayushcheysya s plastom [Damped natural vibrations of fluid in a well interfaced with a reservoir], Prikladnaya mekhanika i tekhnicheskaya fizika [Applied Mechanics and Technical Physics]. 2020. Vol. 61, No. 4(362). P. 5-14. [in Russian] DOI: https://doi.org/10.1134/S002189442004001X
Mamaeva Z.Z., Rafikova G.R. Issledovaniye sobstvennykh kolebaniy nefti v vertikal'noy skvazhine [Study of natural oscillations of oil in a vertical well], Mnogofaznyye sistemy [Multiphase Systems]. 2021. Vol. 16, No. 3-4. P. 105-111. [in Russian] DOI: https://doi.org/10.21662/mfs2021.3.014