On the Theory of Acoustic Sounding of Hydraulic-Fracturing Cracks Perpendicular to the Well

• Published in: Journal of engineering physics and thermophysics 2021-09, Vol.94 (5), p.1160-1169
• Main Authors: Shagapov, V. Sh, Galiakbarova, É. V., Khakimova, Z. R.
• Format: Article
• Language: English
• Subjects: Acoustic properties; Acoustic sounding; Acoustics; Attenuation coefficients; Boundary layers; Classical Mechanics; Complex Systems; Compressibility; Cracks; Engineering; Engineering Thermodynamics; Evolution; Fast Fourier transformations; Heat and Mass Transfer; Hydraulic fracturing; Hydraulics; Industrial Chemistry/Chemical Engineering; Mathematical models; Oil wells; Phase velocity; Pressure surges; Pressure transducers; Signal generators; Television receivers; Thermodynamics; Transducers; Wave propagation
• ISSN: 1062-0125; 1573-871X
• DOI: 10.1007/s10891-021-02396-5

Consideration has been given to the possibility of investigating the reservoir properties of hydraulic-fracturing cracks using an acoustic “television receiver,” which represents a cylindrical probe with a length of several meters and is equipped with a pulsed-signal generator and pressure transducers. It is assumed that the pulsed signal is produced in the liquid in the gap between the probe casing and the open well wall. The evolution of the signal, which is recorded by the pressure transducers in the form of the attenuation of its amplitude and the appearance of reflected pressure surges, permits assessing the state of the face zone, and also the presence and quality of hydraulic-fracturing cracks. It is agreed that the cracks initiated by hydraulic fracturing are perpendicular to the well. The well and the formation around it are filled with one and the same acoustically compressible liquid. A mathematical model has been adopted according to which the wavelength of the acoustic signal is smaller than the length of the probe but is larger than the size of the gap between the probe casing and the well. Furthermore, during the propagation of the wave in the gap, the influence of viscosity is manifested in a thin boundary layer near gap walls. The width of the hydraulic-fracturing crack is much smaller than the wavelength. Therefore, it is considered as a reflecting surface. On the basis of this model, dispersion expressions have been obtained for the phase velocity and the attenuation coefficient when the signal propagates in the gap, and also for the coefficient of reflection and transmission by the reflecting surface. The problem is solved numerically by the method of fast Fourier transformation. An analysis has been made of the influence of filtration characteristics of the cracks and the formation, and also the size of the gap on the evolution of harmonic waves and pulsed signals in the gap between the probe casing and the well wall.