龙马溪组页岩数字岩心动态法弹性等效数值建模

数字岩心是计算岩石弹性性质的一类常用方法.龙马溪组页岩具有多矿物构成、复杂微结构和强非均质等特征,常规岩石物理的弹性等效解析建模局限性较大,目前流行的静态数值等效建模方法的精度有限.本文基于高分辨率的页岩数字岩心数据,采用多阈值分割方法将数字岩心分解为黏土、石英、孔隙、TOC、长石类、黄铁矿类等六种矿物类型;利用矿物组分等效模量法计算各类矿物的弹性模量;采用二元函数分水岭方法表征不同压力下的岩石孔隙变形和颗粒接触关系变化;通过取向分布函数(ODF)定量分析矿物颗粒展布造成的各向异性特征.最后基于Biot孔弹方程,采用不分裂卷积完全匹配层(CPML)旋转交错网格有限差分法模拟不同压力下弹性波在数字岩心中的传播.以未加压的数字岩心为参考模型,计算不同压力下弹性波走时的平均时间差,进而估算各压力点的数字岩心等效速度.与该岩心样品的超声实验测量速度比较,动态法数值计算结果略偏高,据此校正数值计算过程中表征岩石微结构及颗粒接触关系随压力变化的二元函数,有效改善动态法弹性等效数值建模精度.

Elastic equivalent numerical modeling based on the dynamic method of Longmaxi Formation shale digital core

It is a widespread method to analyze rock elastic properties based on digital cores. As the result of many minerals, complex microstructures and strong heterogeneity in Longmaxi Formation shale, the accuracy of elastic equivalent analysis modeling by conventional rock physics method is limited, and the current popular static numerical equivalent modeling method also has strong limitations. We apply multi-threshold segmentation method to divide the high-resolution digital core images of shale into six types including pore, TOC, clay, quartz, feldspar and pyrite, whose elastic modulus were calculated by the mineral components equivalent modulus method. The changes of pore deformation and grain-to-grain contact in rock mass under different pressures were characterized by binary function watershed method. And we use orientation distribution function (ODF) to quantitatively characterize the anisotropy of mineral grain distribution. Finally, Biot poroelastic equation, applying the rotated staggered grid finite-difference technique with unsplit convolution perfectly matched layer (CPML), is used to simulate the propagation of elastic waves in digital core models under different pressures. Taking the uncompressed digital core model as the criterion, the average time delay of elastic wave propagation under different pressures is calculated, which contributes to estimate the equivalent velocity of the digital core models in each pressure. The numerical equivalent velocity is slightly higher than the velocity measured by ultrasonic experiment on the same core, so the binary function characterizing change of the rock mass microstructure and grain-to-grain contact dependent-pressure can be corrected to effectively improve the accuracy of dynamic elastic equivalent numerical modeling.