Slow P-Wave Attenuation Yielding From Berea Sandstone With Double Porosity

Double porosity model differentiates fluid pressure between contact of grains (COG) and the main pore space. This study is motivated by determining phase velocity (V_ps) and the quality factor (Q_ps) of slow P-wave for double porosity rock. The trick is the use of the compressibility matrices calibrated from (ultrasonic) fast P-wave data. Berea sandstone saturated with water is used for illustration. Double porosity models (with the real Darcy permeability k_D and assumed-zero k_D) are both capable of well regenerating the phase velocity (V_p) and quality factor (Q_p) of fast P-wave ultrasonically measured on the sandstone. However, the two double porosity models yield considerably different Q_p at frequencies exceeding 10⁷ Hz. In addition, Biot theory is used as a single porosity model for the calculation of V_ps and Q_ps. It is found that the double porosity model with the real k_D is substantially different from the single porosity model in the resulting V_ps at high frequencies. The results show that the behavior of slow P-wave at frequencies higher than 10⁵ Hz is governed by the double porosity model rather than the single porosity model.