Variation in P-wave modulus with frequency and water saturation: Extension of dynamic-equivalent-medium approach

Abstract

We have developed a new modeling approach for the complex-valued P-wave modulus of a rock saturated with two-phase fluid accounting for the variation with frequency and water saturation. Our method is based on the dynamic-equivalent-medium approach theory, which predicts P-wave modulus dispersion due to mesoscopic-scale wave-induced fluid flow (WIFF). Although the application of the original theory was limited to small fluctuation media, we have extended it to also be applicable for high-fluctuation media such as partially saturated rock. Our modification and extension consists of two components. The first is introducing a scaling by the rigorous bounds for P-wave velocity dispersion by mesoscopic-scale WIFF. The second is to develop a model representing the effective patch size of stiffer fluid that controls the location of the dispersion curve. We have found that the spatial correlation length of heterogeneity of saturated rock used in the original theory does not appropriately capture the effective heterogeneity scale responsible for mesoscale pressure diffusion. Its variation with saturation can be properly accounted for by the proposed patch-sized variation model. The comparison of the theoretical prediction with the published laboratory velocity and attenuation measurements suggests that our approach predicts the wave properties for high-fluctuation media with reasonable accuracy. The effect of mesoscopic-scale pressure diffusion is significant and the amount of velocity dispersion and attenuation is large in high-fluctuation media; therefore, our extension will improve quantitative characterization of, for example, a [Formula: see text]-sequestrated reservoir either by P-wave velocity or attenuation.