Effects of pore water distributions on P-wave velocity–water saturation relations in partially saturated sandstones

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SUMMARY We have developed a new method for introducing the effects of pore water distribution into the interpretation of P-wave velocity (VP) dispersion in a partially saturated rock. Pore water in an unsaturated rock is distributed as patches, and mesoscopic-scale wave-induced fluid flow (WIFF) from saturated patches to empty patches is known as a key mechanism for interpreting P-wave dispersion. Mesoscopic WIFF depends on permeability and the scale of the saturated patch, thus evaluating their influences is important for estimating the relationship between water saturation (${S_{\rm{w}}}$) and VP. The simplest and conventional law for simulating the ${S_{\rm{w}}} - {V_{{P}}}$ relation considering the mesoscopic WIFF is White's model, which describes the patch size changes proportional to the saturation. However, White's model assumes homogeneity in the size and distribution of pores, and does not consider the effects of pore water distribution in a partially saturated rock. In the rock, pore water is distributed heterogeneously according to the pore radius, causing non-linear changes in the permeability and size of the saturated patches against the water saturation. In this study, we modified White's model by introducing relative permeability and a new coefficient describing the nonlinear change of the patch size into the conventional version, and applied the modified model to better interpret our experimental ${S_{\rm{w}}} - {V_{{P}}}$ relations, which were measured by an ultrasonic technique at 200 and 500 kHz for two types of Berea sandstone samples with different permeabilities as their water saturation was decreased by evaporative drying. The relative permeabilities were determined by applying the Mualem–van Genuchten model into the capillary pressure curves from mercury intrusion porosimetry. Furthermore, we proposed a calculation method for the new coefficient using tortuosity, which corresponds to the pore water connection. The modified White's model could reproduce the experimental ${S_{\rm{w}}} - {V_{{P}}}$ relations better than other conventional models. Consequently, our modification, considering the effect of pore water distribution, would be useful for more quantitative interpretation of P-wave velocity and attenuation under coexisting multifluid conditions.