基于Curvelet变换与POCS方法的三维数字岩心重建

随着页岩气勘探与开发的深入,研究页岩裂隙的三维空间展布成为页岩岩石物理研究的必要步骤之一.但由于仪器的限制,页岩切片在深度上具有不连续性,以及数字岩心纵向上成像最小间隔与横向分辨率的不一致成为影响裂隙表征和数字岩石物理模拟精度提高的重要因素.为了更好的研究裂隙在三维的空间展布,本文将curvelet稀疏变换与凸集投影(POCS)迭代算法有效结合,实现三维数字岩心重建.首先对X射线扫描砂岩得到的三维数据体进行隔片抽稀,利用本文方法实现三维数据体重建,重建结果与完整数据体具有很好的一致性,且优于现有方法(spgl1),验证了新方法的有效性与先进性.其次对聚焦离子束扫描电镜(FIB-SEM)得到的纳米级页岩二维切片在深度上进行了加密重建,获得纵向上成像最小间隔与横向分辨率基本一致的三维数字岩心,由于仪器限制引起的页岩切片深度上的不连续性得到减弱,裂隙展布更加清晰.砂岩CT图像以及页岩FIB-SEM成像数据的重建结果验证了本文方法的有效性与先进性.

Curvelet-based 3D reconstruction of digital cores using the POCS method

With the development of shale-gas exploration and exploitation, it is necessary to study the 3D spatial distribution of shale-gas fractures for research on shale rock physics. Because of the limitation of instruments, accurate shale slice is discontinuous in depth, and the minimum interval between adjacent slices is inconsistent with horizontal resolution of digital cores. These are the main factors which hamper accuracy improvement of fracture representation and physical modeling for digital cores. In order to study the 3D spatial distribution of fractures, we doubled the vertical slices increasing the vertical resolution to make it consistent with the horizontal resolution.The curvelet transform and projection onto convex sets (POCS) method are used to achieve the reconstruction of 3D digital cores. The curvelet transform is a sparse transform which has been widely used in seismic data denoising and interpolation and image denoising. The POCS method is an efficient method for seismic data interpolation and can be used in the reconstruction of 3D digital cores. This method is applied on each vertical slice and the 3D digital cores can be obtained after all the vertical slices are processed. Besides, the proposed method is superior to the spgl1 method.With the proposed method, we achieve the 3D digital cores from the cores which were sampled one per two slices in depth for the 3D volume of sandstone obtained by X ray scanner. The reconstruction result is consistent with the original one and superior to the spgl1 method, which proves the validity and superiority of the proposed method. Then the proposed method is applied to the shale cores, of which the 2D horizontal slices are obtained using focused ion beam scanning electron microscopy (FIB-SEM). Because of instrumental limitations, the vertical resolution is almost halved compared with the horizontal resolution. With the proposed method, we can double the horizontal slice in depth, which can help improve the vertical resolution to make it consistent with the horizontal one, weakening the discontinuity of shale slices in depth caused by the instrument limitation, resulting in a clearer fracture distribution.3D digital cores are reconstructed from the 2D shale slices based on the projection onto convex sets (POCS) method in the curvelet domain. The sand reconstruction test of 3D digital cores demonstrates that the proposed method is more suitable for rock slice reconstruction with high efficiency and accuracy compared with the popular spgl1 method. The shale reconstruction test of 3D digital cores from nano-scale shale slices obtained by FIB-SEM indicates that vertical spatial distribution of fractures is more clear and the minimum interval between adjacent vertical slices is basically consistent with the horizontal resolution after reconstruction, which can lay the foundation for the subsequent data processing and related simulation analysis of shale digital cores. 3D digital cores reconstruction numerical tests on 2D sand and shale slices demonstrate the validity of the proposed method. The methods based on direct 3D datasets and efficient sparse transform will be developed in future work.