High-frequency bulk moduli of fluid-saturated cracked porous rocks

Abstract

Many experimental data have confirmed velocity dispersion phenomena for body waves in fluid saturated porous rocks. Bulk modulus is a critical parameter for compressional wave velocity, so studing the high-frequency bulk modulus is of importance for ultrasonic compressional wave velocity measurement. Considering the soft pores such as cracks in rocks, Mavko and Jizba proposed a modified Gassmann equation to calculate the liquid saturated bulk modulus for high-frequency condition. However, the equation proposed by Mavko and Jizba is not derived through a rigorous derivation. And there is not an exact expression for high-frequency bulk modulus up to now. Upon above existing problems, we derive an exact expression of high-frequency bulk modulus for fluid saturated cracked porous rocks based on double-porosity model. The derived expression has the same form as Brown-Korringa equation. In the high-frequency limit, there is no time for fluid mass exchange between cracks and pores, and the fluid in cracks become a part of the host, so that the high-frequency effective solid bulk modulus is less than the pure solid bulk modulus. If fluid pressure in cracks has no effect on the fluid content variation in pores, the derived high-frequency drained bulk modulus reduces to Gurevichs result which derived from Sayers-Kachanov method. Numerical results show that the deviation of high-frequency saturated bulk modulus between Mavko-Jizbas equation and this derived expression increases as crack density increases. And, the high-frequency effective pore bulk modulus is always approximate to pure solid bulk modulus. In contrast, the high-frequency effective solid bulk modulus decreases obviously as crack density increases.