Monochromatic Wave of Fluid Pressure in a Porous Rock

From the perspective of rock mechanics, transmission of fluid pressure that drives groundwater flow is not instantaneous; instead it is a slow compressional (P) wave in porous rocks saturated with a fluid. In this paper, the approach of monochromatic wave is used to analyze the slow P-wave. Permeability is derived as a function of the frequency of the wave. The permeability appears to be a complex number which asymptotes to Darcy permeability at the low frequency end but tends to vanish at the high frequency end. With Biot theory, the permeability predicts phase velocity and the quality factor of the monochromatic wave. Using Berea sandstone as an illustrative example, the complex-number permeability can yield a lower phase velocity (within frequency of 10(5)-10(8) Hz) and a larger attenuation (for frequency above 10(6) Hz) than Darcy permeability does. This study extends the recent research of the low-frequency waves of fluid pressure to the regime of very high frequency.