Single- and Multifractal Dimension Variation of the Pore-Fracture System in Tight Sandstone by Using High-Pressure Mercury Intrusive Tests and Its Influence on Porosity–Permeability Variation

Micro-structures of the pore-fracture size distribution of target sandstone samples are studied through high-pressure mercury intrusion (HPMI) experiments, and the compressibility coefficient is quantitatively described by using overlying pressure porosity–permeability tests. Then, four single and multifractal models were used to quantitatively describe the fractal characteristics of mercury intrusion curves, and the relationship between different fractal models and pore structure parameters is analyzed. Furthermore, the applicability of fractal models in characterizing pore-fracture structures was explored. The results are as follows: (1) fractal model results show that fractal dimensions of type A by using Sierpinski (D S) and thermodynamics models (D M) are larger than those of type B, and fractal dimensions of type A by using Menger (D M) and multifractal models (D –10–D 10) are smaller than those of type B. (2) The Menger model is used to describe heterogeneity of smaller pore size distribution, which is proportional to volume percentage of pores with the diameter smaller than 100 nm; the thermodynamic model is used to describe heterogeneity of medium pore size distribution, which is proportional to the volume percentage of pores with a diameter of 100∼1000 nm; The Sierpinski model is used to describe heterogeneity of larger pore size distribution, which is proportional to volume percentage of pores with the diameter larger than 1000 nm; (3) permeability decreases in the form of power function with the increase of confining pressure, and the compressibility coefficient and permeability variation coefficient decrease with the increase of the compressibility coefficient. There is no significant correlation between the compressibility coefficient, permeability variation coefficient, and pore structure parameters.