DAMPED NATURAL VIBRATIONS OF FLUID IN A WELL INTERFACED WITH A RESERVOIR
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DAMPED NATURAL VIBRATIONS OF FLUID IN A WELL INTERFACED WITH A RESERVOIR V. Sh. Shagapova,∗ , R. A. Bashmakovb ,
UDC 532.59
G. R. Rafikovaa , and Z. Z. Mamaevaa
Abstract: We study natural vibrations of the fluid column in a vertical oil well that occur during sudden shutdown or start-up of the well (water hammer). In this case, the period of vibration and the intensity of vibration damping are determined not only by the length and diameter of the fluid column in the well and the rheological properties of the fluid, but also by the reservoir characteristics of the bottomhole zone (in particular, permeability, the quality of well perforation, and the properties of the hydraulic fractures formed). Solutions to the problem of damped natural vibrations of the fluid column in the well are found using a mathematical model describing the movement of the fluid column in the well and filtration in the bottomhole zone. Characteristic equations for determining complex frequencies (frequency of vibration and the damping coefficient) are obtained. The dependences of the vibration frequency, damping coefficient, and damping decrement on reservoir permeability are studied, and the amplitudes of vibrations at different points of the well are obtained. Keywords: natural vibrations, natural frequencies, water hammer, well, fluid filtration, damped vibrations. DOI: 10.1134/S002189442004001X INTRODUCTION An important factor in the operation of oil wells is the supervisory control of the state of the bottomhole zone (especially after repair work and bottomhole treatment) aimed at improving the reservoir characteristics of this zone. A method for changing the well flow rate is hydraulic fracturing [1]. This method involves problems of determining the hydraulic fracture quality, fracture geometry, and the change in reservoir characteristics. An efficient and easy-to-implement method for determining the perforation quality and hydraulic fracture parameters is the method based on the excitation of natural vibrations of the fluid column in the well. In this case, the period of vibrations and the intensity of vibration damping are determined not only by the length and diameter of the fluid column in the well and the rheological properties of the fluid, but also by the reservoir characteristics of the bottomhole zone (in particular, permeability, the quality of well perforation, and the properties of the hydraulic fractures formed). Fluid vibrations in a well can be initiated by means of a water hammer in the wellbore. Field data obtained in such tests are presented in [2]. The type of pressure oscillograms taken in different regions of wells indicates that they correspond to natural vibrations of the well fluid column. The results of numerical solution of the
a
Mavlutov Institute of Mechanics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450054 Russia; ∗ [email protected]; rafikova [email protected]; [email protected]. b Bashkir State University, Ufa, 450000 Russia; Bashmakov [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya F
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