In double permeability models, the first and second porosities are represented by the main pores and fissures, respectively. The constitutional relation in the models suffers from a disadvantage that the compressibility matrix is symmetric which is incompatible with classic poroelasticity. This study aims to improving the double permeability models not only to well predict the measured velocity and attenuation at ultrasonic frequency, but also to yield the classic Gassmann velocity at the low frequency limit. The first porosity in this paper refers to the main pore space, while the second porosity refers to throat (between grains) and fissures. Our improvements in this paper include: (1) the compressibility matrix is unsymmetric for the model to automatically yield Gassmann velocity at the low frequency limit; (2) squirt coefficient is got from dimensional analysis; and (3) the compressibility coefficients are qualitatively constrained based on rock physics. For simplicity, permeabilities of the first and second porosities are set to zero because local squirt between them is dominant in P-wave attenuation. The wavenumber equation yields one fast P-wave and one slow P-wave (which has zero velocity due to vanishing permeabilities). Two core samples (Berea sandstone and Boise sandstone) with the measured data are used for illustration. The results show that the improved model successfully predicts both velocity and the quality factor of ultrasonic P-wave in the two sandstones, being superior to the previous models.

在双渗透率模型中，第一孔隙度和第二孔隙度分别由主要孔隙和裂缝表示。模型中的构造关系具有如下缺点：可压缩性矩阵是对称的，这与经典的多孔弹性不相容。这项研究旨在改善双渗透率模型，不仅可以很好地预测超声频率下测得的速度和衰减，还可以在低频范围内产生经典的加斯曼速度。本文中的第一个孔隙度是指主要孔隙空间，而第二个孔隙度是指喉咙（晶粒之间）和裂缝。我们在本文中所做的改进包括：（1）模型的可压缩性矩阵不对称，以便在低频极限时自动产生加斯曼速度；（2）喷水系数是通过尺寸分析得到的；（3）基于岩石物理学对可压缩系数进行定性约束。为简单起见，将第一孔隙率和第二孔隙率的渗透率设置为零，因为它们之间的局部喷射在P波衰减中占主导地位。波数方程产生一个快P波和一个慢P波（由于磁导率消失，速度为零）。带有测量数据的两个岩心样品（Berea砂岩和Boise砂岩）用于说明。结果表明，改进的模型成功地预测了两个砂岩中超声波P波的速度和品质因数，优于以前的模型。将第一和第二孔隙的渗透率设置为零，因为它们之间的局部喷射在P波衰减中占主导地位。波数方程产生一个快P波和一个慢P波（由于磁导率消失，速度为零）。带有测量数据的两个岩心样品（Berea砂岩和Boise砂岩）用于说明。结果表明，改进的模型成功地预测了两个砂岩中超声波P波的速度和品质因数，优于以前的模型。将第一和第二孔隙的渗透率设置为零，因为它们之间的局部喷射在P波衰减中占主导地位。波数方程产生一个快P波和一个慢P波（由于磁导率消失，速度为零）。带有测量数据的两个岩心样品（Berea砂岩和Boise砂岩）用于说明。结果表明，改进的模型成功地预测了两个砂岩中超声波P波的速度和品质因数，优于以前的模型。带有测量数据的两个岩心样品（Berea砂岩和Boise砂岩）用于说明。结果表明，改进的模型成功地预测了两个砂岩中超声波P波的速度和品质因数，优于以前的模型。带有测量数据的两个岩心样品（Berea砂岩和Boise砂岩）用于说明。结果表明，改进的模型成功地预测了两个砂岩中超声波P波的速度和品质因数，优于以前的模型。