Single and multi-fractal dimension variation of tight sandstone by using centrifuge T2 spectral curve

Abstract

Pore-fracture structure distribution heterogeneity (PFSH) affects dynamic variation of porosity-permeability of tight sandstone reservoirs, then restricting gas production performance. A fractal model by low-field nuclear magnetic resonance technology (LF-NMR) has been used in the quantitative characterization of PFSH. Among some literature, PFSH was studied by using a saturated T₂ spectrum. However, there are few studies on fractal characteristics of T₂ spectral morphology in a centrifugal state and its influence on porosity-permeability parameters. In this paper, 30 tight sandstone samples were collected from Taiyuan Formation in Qinshui Basin. Then LF-NMR technology was used to analyze PFSH, and sample types were divided by using T₂ spectra difference under saturated and centrifugal conditions. Meanwhile, single (model 1 and 2) and multi-fractal model are adopted to calculate fractal parameters of saturated and centrifugal T₂ spectra, and then a difference in fractal parameters under different water conditions was compared. Correlation between different fractal parameters, pore structure and T_{2 cut-off} value are studied, and a mathematical prediction model for T_{2 cut-off} value by using fractal and pore structure parameters are established. The results are as follows. (1) All the samples are divided into four types A/B/C/D. For example, the type A sample is characterized by a single peak of T₂ spectrum and T₂ value is less than 10 ms, which indicates that this type belongs a smaller-pore developed. Type B sample is characterized by a single peak of T₂ spectrum and T₂ value is10–100 ms, which indicates that this type belongs to mesopore developed. (2) In saturated state (D_S), PFSH of type A sample by using model 1 and 2 is stronger than that of type B, followed by type C and D. Then the multifractal model shows that PFSH of type B sample is stronger than that of other sample types. Correlation between fractal dimension calculated by using single fractal and pore structure parameters is stronger than that of multifractal dimension. (3) T₂ spectrum in centrifugal state has fractal characteristics (D_i), and there are certain correlation D_i with D_s. Therefore, a mathematical prediction model for T_{2 cut-off} value by using fractal and pore structure parameters is established. © 2023 Society of Chemical Industry and John Wiley & Sons, Ltd.