A Multi-Dimensional Quantitative Analysis of Reconstructed Digital Core Based on Fractal and Topological Features

Accurate three-dimensional (3D) reconstruction of digital rocks from limited data remains a significant challenge in digital rock physics. While Multiple-Point Geostatistics (MPS) offers a powerful solution, its multi-scale performance, particularly regarding extrapolation from small training images to larger domains, lacks a comprehensive evaluation framework that connects structural fidelity to functional equivalence. This study proposes an integrative multi-dimensional quantitative evaluation system that incorporates macroscopic statistics, microscopic topology, complex morphology, and seepage properties. Utilizing an improved Single Normal Equation Simulation (SNESIM) algorithm and a 60 × 60 × 60 voxel sandstone Training Image, 3D models were reconstructed across five scales ranging from 40 × 40 × 40 to 120 × 120 × 120 voxels. To ensure statistical robustness and mitigate stochastic uncertainty, ten independent realizations were performed for each scale. Quantitative analysis reveals that while SNESIM maintains high accuracy in macroscopic parameters and second-order spatial statistics, it exhibits systematic deviations in microscopic topology and surface complexity. Specifically, as the scale expands, the coordination number decreases while intrinsic anisotropy is progressively lost, yet permeability does not drop proportionally. This paradox is attributed to structural homogenization driven by the loss of long-range directional correlations. These findings indicate that the algorithm tends toward structural homogenization during scale extrapolation, systematically weakening the directional transport properties of the original rock. This study provides a standardized benchmarking methodology that promotes the evolution from visual similarity toward functional equivalence, thereby enhancing the reliability of reservoir characterization and seepage prediction.