ON THE THEORY OF ACOUSTIC SOUNDING OF HYDRAULIC-FRACTURING CRACKS PERPENDICULAR TO THE WELL

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 refl ected pressure surges, permits assessing the state of the face zone, and also the presence and quality of hydraulicfracturing cracks. It is agreed that the cracks initiated by hydraulic fracturing are perpendicular to the well. The well and the formation around it are fi lled 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 infl uence 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 refl ecting surface. On the basis of this model, dispersion expressions have been obtained for the phase velocity and the attenuation coeffi cient when the signal propagates in the gap, and also for the coeffi cient of refl ection and transmission by the refl ecting surface. The problem is solved numerically by the method of fast Fourier transformation. An analysis has been made of the infl uence of fi ltration 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
   
Author:  V. Sh. Shagapov, É. V. Galiakbarovaa, Z. R. Khakimova
Keywords:  well, probe, crack, hydraulic fracturing of the formation, harmonic pressure waves
Page:  1160