Effect of Pore Structure Heterogeneity of Sandstone Reservoirs on Porosity–Permeability Variation by Using Single–Multi-Fractal Models

Abstract

Pore structure heterogeneity affects sandstone porosity and permeability and thus sandstone gas productivity. A total of 17 sandstone samples collected from the northwestern margin of the Junggar Basin in Xinjiang Province are investigated in this study. The pore-fracture system distribution of target sandstones is studied by high-pressure mercury injection tests. On this basis, single-and multi-fractal models are used to characterize pore structure heterogeneity, and the applicability of four models (Menger model, Sierpinski model, Thermodynamic model, multifractal model) to characterize pore and fracture distribution heterogeneity are discussed. Moreover, a correlation between fractal dimension, pore structure parameters, and variation coefficient of porosity−permeability is discussed based on overburden permeability test results. The results are as follows. (1) D S (fractal dimension of Sierpinski model) shows a significant correlation with pore volume percentage, so the Sierpinski model could better characterize fracture distribution heterogeneity quantitatively. Multifractal dimensions are consistent with those of Sierpinski and Thermodynamic models, which indicates that the single-and multiple-fractal models are consistent. (2) The porosity and permeability decrease as a power function with higher confining pressure. The porosity and permeability behavior changes at a critical conversion pressure value. For a confining pressure lower than this critical value, the porosity and permeability decrease largely. For confining pressures higher than this critical value, the porosity and permeability vary less. In contrast, permeability has a larger variation rate and is more obviously affected by confining pressure.(3) Pore compression space is affected by the permeability variation coefficient. Compressibility, porosity, and permeability variation coefficient have no relationship with pore structure parameters since compressibility is affected by pore structure, mineral composition, and other factors in sandstone samples.