A Partial Saturation Model Based on Squirt Flow Theory: Effects of Fluid Distribution on Seismic Wave Dispersion and Attenuation

The effect of fluid distribution on seismic-wave propagation is of great importance to oil and gas exploration. In rock-physics experiments, different saturation methods result in different fluid distributions. At the same saturation, the drainage process usually produces larger fluid patches, while imbibition results in a relatively homogeneous fluid distribution. In this paper, a partial-saturation model is developed based on squirt-flow theory and the mesoscopic fluid-flow equation for partially saturated media. The effects of different fluid distributions are also incorporated using a modified Brie equation. The proposed model is compared with published experimental results. Numerical analyses are then performed for different fluid distributions, fluid properties, and rock-frame moduli. The results show that the proposed model can predict bulk-modulus dispersion and attenuation more accurately than the White model under drainage conditions. Under imbibition conditions, however, the model can reproduce either the attenuation or the low-frequency bulk-modulus variation, but not both simultaneously. Macroscopic viscosity, saturation, and rock-frame properties jointly control the critical frequency. A larger fluid bulk-modulus contrast and a smaller pore aspect ratio produce stronger squirt-flow-induced dispersion and attenuation. The above results show that the predictions of the proposed model at low frequencies are close to the measured results and that the model can describe the effects of fluid and rock-frame properties on the elastic response. However, the model does not account for the high-frequency dispersion and attenuation that occur when the fluid is more homogeneously distributed.