Abstract：
Organic matter and its pore distribution are closely related to the adsorbed gas content of shale and the microscopic
gas flow mechanism. Studies have shown that the organic matter distribution in shale has anisotropic characteristics at the pore
scale. However, the existing digital core reconstruction algorithms for shale cannot effectively describe this feature. Aiming at
the anisotropic characteristics of organic matter distribution in shale samples, this paper introduced a two-point cluster function
as a statistical indicator to characterize the continuity of organic matter distribution based on the traditional simulated numerical
annealing reconstruction method for digital cores. Although the two-point cluster function belongs to the two-point probability
function, it contains high-order structural information. Therefore, the two-point cluster function is a statistical indicator that is
more sensitive to structural changes than the two-point correlation function. This paper presented the mathematical model of the
simulated annealing method coupled with a two-point cluster function. Meanwhile, taking the shale core sample of the Longmaxi
Formation of the Lower Silurian in the Sichuan Basin as an example, the systematic method flow of "sample imaging⸺image
processing⸺function extraction⸺reconstruction calculation" was discussed in detail. Through field emission scanning electron
microscopy (FESEM) and focused ion beam-field emission scanning electron microscopy (FIB-SEM) and image processing, the
shale organic matter and its pore distribution at the pore scale were obtained, and the statistical correlation of core samples in
three orthogonal directions was extracted. Functions include a single-point correlation function, two-point correlation function,
linear path function and a two-point cluster function. The paper established an effective method for three-dimensional recon
struction of organic matter aggregates, and applied the above statistical correlation functions to the reconstruction process of the
Dual-Region simulated annealing method to obtain reconstruction models of organic matter, organic matter pores and matrix
pores respectively. Combining the three coupled regions produces the final digital core 3D reconstruction model of the shale
sample. The reconstruction of the two-point cluster function distribution curve in three orthogonal directions of the shale digital
core shows that the organic matter has obvious anisotropy. By comparing organic matter equivalent volume radius distribution,
organic matter area, organic matter elongation and other parameter distributions of real shale samples and reconstructed shale
digital cores, the validity of the two-point cluster function method to characterize the anisotropic distribution of shale organic
matter has been proved. This method can be applied to related research work on shale digital core reconstruction.
Key words：shale; digital core; organic matter; two-point cluster function; anisotropy; simulated annealing method
Corresponding Authors：suiweibo@cup.edu.cn
Cite this article：SUI Weibo, YOU Yuan, CHENG Si, ZHENG Yizhen. Reconstructing and characterizing the anisotropy of shale organic matter with a two-point cluster function and a simulated annealing method. Petroleum Science Bulletin, 2021, 01: 46-57.
