龙马溪组页岩数字岩芯超声响应数值模拟及散射特征分析

超高频（几百兆赫兹）超声数值模拟微米至纳米尺度的龙马溪组页岩数字岩芯及其强非均质性严重挑战数值模拟算法的精度和数值稳定性.本文利用图像阈值分割算法将龙马溪组页岩数字岩芯主要成分分解为石英类、黏土类、黄铁矿及孔隙四种类型，假定液相（油）均匀分布在整个介质模型中，根据岩芯的孔隙度、渗透率和各类矿物的岩石物理参数，建立了精细的非均质双相介质模型.采用基于Biot双相介质方程的不分裂卷积完全匹配层与高精度旋转交错网格有限差分方法精确模拟超声波在页岩岩芯中传播的散射衰减.通过精确控制匹配层吸收边界数来模拟边界反射量及其对尾波的干涉强度，并与超声实验尾波散射Q值进行比较，估算超声实验中的边界反射量及其对尾波的干涉强度.对不同超声子波主频的数值模拟试验，结合L/a-ka散射态式图分析表明：本文采用的龙马溪组页岩数字岩芯的非均质强度与600 MHz波长尺度相当，产生的散射衰减达到最大.开展页岩岩芯超声波散射数值模拟研究，据此评估页岩岩芯的非均质性，为页岩储层声学非均质预测提供依据.

The ultrasonic response of numerical simulation and analysis of scattering characteristics in digital core for shale reservoir

The precision and stability of the numerical algorithm is seriously challenged when applied to the modeling of strong heterogeneity on scales from micrometer to nanometer in the digital core of Longmaxi Formation shale at ultrahigh frequency. In this paper, we divide the major compositions in the digital core of Longmaxi Formation shale into four types, namely quartz, clay, pyrite and porosity. The liquid phase (oil) is assumed to be uniformly distributed throughout the medium. Based on the measured porosity and permeability of the digital core and the prior petrophysical parameters of minerals, a heterogeneous two-phase model is elaborately established. Then, the scattering attenuation of the ultrasonic wave propagating in the shale core is simulated by using the high-precision finite difference (FD) method with rotating staggered-grid and non-split convolution perfect matching layer (CMPL) based on Biot's two-phase media equation. The boundary-reflection energy and its effects on coda waves can be numerically modeled by precisely controlling the number of matching layers. By comparing with the coda Q values measured in the ultrasonic experiment, we quantify the boundary-reflection energy and its effects on coda waves in the experiment. The results of ultrasonic numerical tests at various central frequencies show that the scattering attenuation comes to maximum at frequency of 600 MHz. According to the scattering pattern analysis in the L/a-ka diagram, we infer that the heterogeneity length of the shale digital core is equivalent to the order of ultrasonic wavelength at 600 MHz. Based on the numerical simulation of the ultrasonic scattering in the shale digital core, the heterogeneity length of the core can be quantitatively evaluated, providing the basis for the prediction of acoustic heterogeneity in the shale reservoir.