一种新的三维欧式距离变换方法及在数字岩心中的应用

A new method of fast distance transform 3D image based on “neighborhood between voxels in space” theory

针对目前距离变换方法在三维数字岩心中应用时,搜索方向多、计算数据量大、耗费时间多、占用内存大等问题,提出一种基于几何拓扑学理论中空间邻居关系的新的距离化搜索算法.根据岩石内部孔隙结构与二维平面欧式距离求解方法,引入一个三维空间距离游标进行辅助计算.相比现有方法,新的算法简化了邻居域欧式距离值的比较规则,避免了复杂的欧式距离结构体带来的大量运算,且算法复杂度低,可以被更好地理解和应用.本文详细叙述了算法的具体实现过程,并将该方法推广到具有缝洞特征碳酸盐岩数字岩心的孔隙空间分割工作中.结果表明该方法准确高效,对于油气藏孔隙级微观描述具有现实意义.

Digital core technology is a new type of tool for analyzing and explaining the flow characteristics and fluid distribution of reservoir. Digital core technology has been widely used in recent years to describe features of pose space and simulate the process of fluid flow. As the basement of segmentation of pore space and reconstruction of pore network, the improvement of distance transform method has great impact on the development of digital core analysis technology. The accuracy and computation speed of distance transform method can directly affect the size of digital data and the detailedness of pore network model. Euclidean distance transform is the most precise one among all the distance transform methods, which means it is suitable for processing digital core data and calculating distance map. For traditional Euclidean distance transform method application in three-dimensional space data, there exist problems, such as too many search directions, large amount of data, and time-consuming. Large-scale data of digital core is hard to be transformed by this method. Therefore, a new theory of space based geometric topology neighbor relationship distance search algorithm was proposed in this paper. By introducing theory of neighborhood in 3D space, the relationship between 3×3×3 neighborhood with whole core data can be constructed, the computational area is greatly narrowed so that computation speed can be improved markedly Then, instead of calculating every distance between pore voxels and skeleton voxels, the Euclidean distance of a pore voxel can be obtained by scanning the distance value of its 3×3×3 neighborhood. Exact Euclidean distance map of digital core data includes large-scale data showed after only two-scans. Noteworthily, due to the disturbing of boundary points which out the range of data size, special treatment is needed to process the pore voxels which near boundary of digital core data. Compared to existing methods, according to the interior of the rock pore structure characteristics, we simplified the comparison rules of the neighbor domain Euclidean distance value so that we can significantly improve computing capacity and computation speed of the Euclidean distance transform method. By this way, a large number of operations by the complex Euclidean distance structure can be avoided. And the complexity of the algorithm is better understood and applied. This article describes the process of the algorithm in detail and the method is extended to characterize pore space segmentation work of digital cores. Fractured-cave digital core, fractured digital core and kinds of digital core data were transformed by the new method, the results show that the method is more accurate and efficient for the segmentation and reconstruction of pore space model. On this basis, pore structure characteristics of pore space can be extracted and analyzed by digital core technology, and more parameters like permeability, formation factor, and so on, can be simulated. This paper created a new distance transform method on digital rock identification and extraction, which laid a theoretical foundation for the efficient development of microscopic description of oil and gas reservoirs, especially for fractured and vuggy reservoirs.