An Alternative Approach to Acquiring Permeability from Ultrasonic S-Wave

Water interaction between fractures and rock matrix is one of the themes in hydrogeology. Accurate values of Darcy permeability (k_D) of the matrix are desired for better quantification of the water interaction. In contrast to the traditional method using seepage experiments to measure k_D of a rock, this study uses the technique of ultrasonic shear (S-) wave for determining k_D of the rock matrix. From the perspective of waves, Darcy seepage is driven by slow compressional (P-) wave at very low frequencies, and k_D is associated with slow P-wave in the regime of low frequency. Similarly, there is another permeability associated with S-wave, namely, S-wave permeability (k_s). The rock samples are Navajo sandstone and Berea sandstone. Data of the dry sandstones with water are entered into Biot theory for yielding saturated phase velocity (V_s) and the quality factor due to viscous fluid (Q_s). Then, ultrasonically measured V_s and Q_s are fitted with the use of the model output. For Navajo sandstone, low-frequency k_s appears to be 0.107-0.115 darcy, surprisingly close to k_D of 0.1 darcy. For Berea sandstone, low-frequency k_s turns out to be 0.081 darcy, also consistent with k_D of 0.075 darcy. The success robustly shows that Biot theory is applicable to S-wave in isotropic rock free of fractures. More importantly, the comparability between low-frequency k_s and k_D demonstrates that ultrasonic S-wave is an alternative approach to acquiring k_D of the matrix.