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实验提出一种利用波速比求取致密砂岩基质矿物剪切模量的方法,具体步骤为:首先根据Biot-Gassmann理论方程得出致密砂岩波速比(Vp/Vs)与kma,μma及α的关系,然后利用孔隙度将α进行替换,得出波速比与岩石孔隙度之间的定量关系。利用由Gassmann流体替代方程推导而来的线性化方法求取kma,最终求取岩石μma。基于上述方法对所取深层致密砂岩样品进行物性及声学测试,结果表明,岩样(Vp/Vs)2与(1-Ф)-2间满足线性关系,相关系数R2=0.991;中间参数G取值为0.832。最终计算获得该砂岩的kma=72.85GPa,μma=54.64GPa,求算结果与岩石内部矿物成分、微观接触型式及应力状态相符,表明该方法的有效性。利用该方法能较有效的估算岩石基质矿物剪切模量,对测井、地震及岩石力学等方面更深入研究具有一定参考价值。
A method to calculate the shear modulus of tight sandstone matrix minerals by using the wave velocity ratio is proposed. The specific steps are as follows: First, the relationship between the velocities (Vp / Vs) and kma, μma and α of the tight sandstone is obtained based on the Biot-Gassmann theoretical equation , And then use the porosity to replace α, get the quantitative relationship between the velocity ratio and the rock porosity. Calculate kma using the linearization method derived from the Gassmann fluid substitution equation and finally determine the rock μma. Based on the above method, the physical and acoustic tests of the deep sandstone samples were carried out. The results show that the linear relationship between the rock sample (Vp / Vs) 2 and (1-Ф) -2 satisfies the correlation coefficient R2 = 0.991; The value is 0.832. Finally, the calculated kma = 72.85GPa and μma = 54.64GPa of the sandstone are calculated, and the calculated results are consistent with the mineral composition, micro-contact type and stress state of the rock, indicating the effectiveness of the method. The method can be used to estimate the shear modulus of rock matrix minerals effectively and has certain reference value for further research in well logging, earthquake and rock mechanics.