The Frequency Dependence of Poisson’s Ratio in Fluid-Saturated Rocks

Abstract

We investigated the frequency dependence of Poisson’s ratio $\nu$ in partially/fully fluid-saturated rocks. Based on one dominant fluid flow mechanism at each condition, we theoretically summarized that (1) when a rock is partially saturated or transits from drained state to undrained state at full saturation, $\nu$ increases monotonously with frequency, and the associated attenuation $\left(1/Q_{\nu }\right)$ is positive with one peak. (2) When the rock transits from undrained state to unrelaxed state at full saturation, there are three cases: 1) $\nu$ increases monotonously with frequency and has positive $1/Q_{\nu }$ with one peak, 2) $\nu$ keeps constant with frequency and has no attenuation, 3) and $\nu$ decreases monotonously with frequency and has negative $1/Q_{\nu }$ with one peak. In this condition, the dependence is influenced by the concentrations of stiff and soft pores, the aspect ratio of soft pores, and the pore fluid bulk modulus. (3) When it comes to the transition from drained state to unrelaxed state at full saturation, $\nu$ can exhibit two shapes with frequency: 1) step shape with two positive attenuation peaks and 2) bell shape with one positive attenuation peak and one negative attenuation peak. Then, we conducted a numerical example to indicate the effect of influence factors (the concentrations of stiff and soft pores, the aspect ratio of soft pores, and the pore fluid bulk modulus) on Poisson’s ratio from undrained state to unrelaxed state, and validated the theoretical analysis by the published experimental data. In addition, based on $1/Q_{\nu }$ , we reanalyzed and validated the relationship between different attenuation modes (i.e., bulk attenuation $1/Q_K$ , P-wave attenuation $1/Q_P$ , extensional attenuation $1/Q_E$ , and S-wave attenuation $1/Q_S$ ): (1) when $1/Q_{\nu }$ is positive, the relationship between them is $1/Q_K>1/Q_P>1/Q_E>1/Q_S$ ; when $1/Q_{\nu }$ is 0, the relationship between them is $1/Q_K=1/Q_P=1/Q_E=1/Q_S$ ; and when $1/Q_{\nu }$ is negative, the relationship between them is $1/Q_K<1/Q_P<1/Q_E<1/Q_S$ . The relationship between different attenuation modes does not depend on saturation state (partial or full saturation) or $\nu$ but on $1/Q_{\nu }$ . This research provides the frequency dependence of Poisson’s ratio in partially/fully saturated rocks, which helps better understand Poisson’s ratio at different frequencies and saturation states and can be used to improve the accuracy of geophysical data interpretation, such as lithology identification, hydrocarbon characterization in conventional reservoir, and brittleness evaluation of shale/tight sandstones in unconventional reservoir.