Multiscale wave dissipation characteristics of tight sandstone strata and a double-fractal structure model

Acoustic wave velocity dispersion and attenuation (anelasticity) can be adopted in estimating the pore structure and fluid content of underground in-situ rocks. However, there are actual differences between the measured data at different frequency bands since the measurements involve different spatial scales with sorts of heterogeneities. In this study, the measurements of ultrasonic tests (550 kHz), sonic logging (about 10 kHz) and seismic exploration (about 30 Hz) are performed on the tight reservoirs of the Chang 7 member of Yangchang Formation in Ordos Basin, west China. Ultrasonic tests are performed on the 38 tight sandstones, and the P-wave attenuation is estimated by the spectral-ratio method. The mineral composition and pore structure characteristics are obtained by the X-ray diffraction and casting thin section analyses. Sonic log data are collected from the six wells, including density, porosity, shale content and full-waveform signal data. Post-stack seismic gathers crossing the three wells are acquired. The sonic wave attenuation is estimated by the statistical average method on the basis of the full-waveform sonic-log data, while the seismic attenuation is obtained by an improved frequency-shift method. Moreover, P-wave velocities at different frequencies are obtained. The ultrasonic data results show that P-wave velocity increases while attenuation decreases as the confining pressure increases. The effect of porosity on P-wave attenuation decreases but that of the clay content increases with increasing confining pressure. This may be due to the gradual closure of the microcracks, weakening the effects of wave-induced fluid flow between the stiff pores and microcracks. At the different frequencies, the ultrasonic, sonic logging and seismic results exhibit the same variation trends with respect to the porosity or clay content, i.e., the velocity decreases and the attenuation increases with the increase of porosity or clay content. A comparative analysis shows that the medians of ultrasonic, sonic and seismic velocity data are 4883, 4521, and 4432 m/s, and the corresponding attenuation medians (1000/Q(p)) are 16.16, 17.97, and 25.56, respectively. P-wave velocity decreases more significantly when frequency decreases from ultrasonic to sonic ranges, with a median decline of 362 m/s, while the attenuation increases more significantly from sonic to seismic frequencies. Sonic logging and seismic velocity values are close and show similar normal distribution characteristics. To interpret the multiscale data, a double-fractal poroelasticity model by incorporating the self-similarity characteristics of crack systems and clay minerals is proposed. Numerical modeling is implemented through finite iterations, where a set of inclusions with the same scale are inserted into a porous host skeleton at each iteration. The simulations and observation results are in consistency, revealing the fractality of clay inclusions and crack systems. The attenuation at the seismic frequency band is mainly related to the wave-induced fluid flow mechanism occurring between the clay inclusions and intergranular pores, while the attenuation at the sonic and ultrasonic bands is caused by the joint effect of the two sets of fluid flow mechanisms associated with cracks and clay inclusions. The proposed model allows us to obtain the information about the characteristics (fractality) of fabric heterogeneities (cracks and clay) affecting wave anelasticity.