In Biot theory, the relative velocity between fluid and solid and their relative acceleration, via Darcy permeability and the coupling factor, respectively, are used to quantify stress between the phases. In this paper, the relative velocity via variable permeability is used to improve the quantification of the stress. The modeling quantities are the S-wave velocity ratio of brine saturated Berea sandstone to the dry sandstone and the (viscous-flow-induced) attenuation. Although skeleton shear modulus depends on differential pressure (the confining pressure minus pore pressure), the two quantities are conservative at small differential pressures. The modeling results reveal that Berea sandstone has a permeability of 0.02–0.03 Darcy for S-wave at 1 MHz, much smaller than Darcy permeability (0.075 Darcy). The cause is that with the increase of frequency, the thinning of Stokes boundary layer decreases permeability. Moreover, the total porosity of 0.23 is better than the effective porosity of 0.20 in the simulation, because S-wave does not discriminate connected pores or occluded pores.

中文翻译：

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Berea砂岩中超声S波的速度和衰减

在比奥理论中，流体和固体之间的相对速度及其相对加速度（分别通过达西渗透率和耦合因子）用于量化相之间的应力。在本文中，通过可变渗透率的相对速度被用来改善应力的量化。建模量是盐水饱和的Berea砂岩与干砂岩的S波速比以及（由黏流引起的）衰减。尽管骨架的剪切模量取决于压差（围压减去孔隙压力），但在较小的压差下，这两个量是保守的。模拟结果表明，Berea砂岩在1 MHz时的S波渗透率为0.02–0.03 Darcy，远小于Darcy渗透率（0.075 Darcy）。原因是随着频率的增加，斯托克斯边界层的变薄降低了磁导率。此外，在模拟中，总孔隙度为0.23优于有效孔隙度为0.20，这是因为S波无法区分连通孔隙或封闭孔隙。