DAMPED NATURAL VIBRATIONS OF FLUID IN A WELL INTERFACED WITH A RESERVOIR

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.