Elastic properties predictions of rocks using numerical simulations are generally overestimated compared to laboratory measurements regardless of the algorithms used. This overestimation is prevalent among sandstones as well as carbonate rock types but the degree of the mismatch between the two results is much higher for carbonates due to the complex pore structures and heterogeneity at the pore scales. One key reason attributed towards the systematic overestimation is imaging system’s limitation to resolve pore structures below its threshold resolution at representative volumes. To study the effect of this limitation, we developed a multi-scale imaging approach and “up-scaling” framework to improve the numerical predictions of the linear, isotropic elastic properties of a standard dolomite rock using the Digital Rock Physics approach. We defined up-scaling as the process of integrating information from high resolution images (obtained at micro scale) to improve prediction using the lower resolution images obtained at full-plug scale covering a larger representative volume. A combination of multi-resolution (40, 13, 5 and $1\mathrm{\mu }\mathrm{m}$) X-ray micro computer tomography and Focus Ion Beam combined with Scanning Electron Microscope (FIB/SEM) images for the dolomite rock were then utilized. We compared numerically simulated linear elastic and isotropic moduli to in-house laboratory acoustic velocity test results performed on the same dolomite carbonate sample that was used for imaging. Results showed a reduction of the overestimation from 8.9% to 4.5% for predicted P-wave velocity and from 11.9% to 7.8% for predicted S-wave velocity when the multi-scale imaging approach was used.

不管使用哪种算法，与实验室测量值相比，使用数值模拟对岩石的弹性特性预测通常都高估了。这种高估在砂岩以及碳酸​​盐岩类型中普遍存在，但是由于碳酸盐岩的复杂孔隙结构和孔隙尺度的非均质性，两种结果之间的失配程度对于碳酸盐而言要高得多。归因于系统高估的一个关键原因是成像系统在有代表性的体积上无法分辨低于其阈值分辨率的孔结构。为了研究这种局限性的影响，我们开发了一种多尺度成像方法和“放大”框架，以改进使用“数字岩石物理学”方法对标准白云岩岩石的线性，各向同性弹性特性进行数值预测的能力。我们将放大定义为整合来自高分辨率图像（以微尺度获得）的信息以使用覆盖较大代表体积的全插头尺度获得的较低分辨率图像改善预测的过程。多分辨率组合（40、13、5和$\mathrm{1个}\mathrm{\mu }\mathrm{米}$然后利用X射线微型计算机断层扫描和聚焦离子束结合扫描电子显微镜（FIB / SEM）图像获得白云石岩石。我们将数值模拟的线性弹性模量和各向同性模量与在用于成像的同一白云石碳酸盐样品上进行的室内实验室声速测试结果进行了比较。结果表明，使用多尺度成像方法时，预测的P波速度的高估从8.9％减少到4.5％，预测的S波速度的估计过高从11.9％减少到7.8％。