We have developed a method to estimate the dry frame elastic moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium theory (EMT) model. The existing EMT models often are used to predict the effective dry frame elastic moduli of granular aggregates as a function of porosity, average number of contacts per grain, grain radius, contact radius, and contact stiffnesses of an elastic two-grain combination. But, it is almost impossible to measure the number of contacts per grain, contact radius distribution, or contact stiffness distribution in complex rocks. Therefore, explicit assumptions based on simplified microstructural geometries often are made to predict these contact properties in granular aggregates. As a result, the predictions of dry frame elastic moduli using EMT models may fail to match the observed properties because of numerous simplified assumptions, which can be violated in complex rocks. Our method uses the morphological contact properties (i.e., the grain-to-grain contact radius distribution, grain radius distribution, and coordination number distribution) directly extracted from 3D digital rock images to improve the prediction accuracy of dry frame elastic moduli using the EMT models. With integration of digital rocks technology, there is no longer a need to assume the size and shape of the grains, contact size, and number of contacts. The prediction accuracy of our method is validated on high-resolution 3D micro-CT digital rock images of miniplugs extracted from plugs with ultrasonic velocity measurements under dry conditions at different confining pressures. Image-computed dry frame elastic moduli using the EMT model are consistent with laboratory-measured moduli extrapolated to ambient conditions.

中文翻译：

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使用基于接触力学的有效介质方法估算高分辨率3D数字岩石图像的干岩框架模量

我们已经开发出一种使用基于接触力学的有效介质理论（EMT）模型来估算高分辨率3D数字岩石图像的干框弹性模量的方法。现有的EMT模型通常被用来预测颗粒状骨料的有效干框弹性模量，该模量是孔隙率，平均每个晶粒的平均接触数，晶粒半径，接触半径和弹性两粒组合的接触刚度的函数。但是，几乎不可能测量复杂岩石中每个晶粒的接触数量，接触半径分布或接触刚度分布。因此，通常基于简化的微结构几何形状做出明确的假设，以预测颗粒状聚集体中的这些接触特性。结果是，由于许多简化的假设，使用EMT模型进行的干框架弹性模量的预测可能无法与观察到的特性相匹配，这在复杂的岩石中可能会被违反。我们的方法使用直接从3D数字岩石图像中提取的形态接触特性（即晶粒间接触半径分布，晶粒半径分布和配位数分布）来提高使用EMT模型预测干框弹性模量的准确性。随着数字岩石技术的集成，不再需要假设晶粒的大小和形状，触点尺寸以及触点数量。我们的方法的预测精度已在从干塞中提取的微型干塞的高分辨率3D micro-CT数字岩石图像上得到验证，并在干燥条件下，不同围压下通过超声波速度测量。使用EMT模型进行图像计算的干框弹性模量与外推至环境条件的实验室测得的模量一致。