New insights into pore fractal dimension from mercury injection capillary pressure in tight sandstone

Mercury injection capillary pressure (MICP) has been widely used for pore fractal dimension determination and thus leads to a variety of calculation models with different results. Here, taking the tight sandstone gas reservoir of Shaximiao Formation in Jinhua-Zhongtaishan area, central Sichuan Basin as the object, the theory, method and application of pore fractal dimension determination from MICP are explored. Based on Yu-Xia model and Washburn equation, rigorous analytical expressions on fractal dimension, capillary pressure and mercury saturation are deduced. After pre-processing including validation, consistency correction and shape-preserving interpolation, the fractal turning point is located with the local maximum of the front-back moving variance ratio of mercury saturation, and then the global, macropore and micropore fractal dimensions are determined respectively by nonlinear fitting. As suggested by the data processing results of the 39 MICP samples, there is no significant direct correlation between pore fractal dimensions and petrophysical properties represented by permeability. However, the combination of fractal model related parameters, especially global fractal dimension and entry pressure, can identify effectively reservoir quality ranks. Meanwhile, for gas layers with relatively high permeability, larger global fractal dimensions may imply roughly more favorable pore structure and better reservoir quality, while the total quality of the relatively low-permeability gas layers is poor and nearly independent of the fractal dimensions. The representative MICP-based pore fractal models, He-Hua and Shen-Li, are critically reviewed. The theoretical simplification and calculative approximate of these two models lead to some degree of error in pore fractal dimension determination, despite their slight correlation in the fitting results with those of the present model. This study may improve the understanding of the pore fractal dimension determined from MICP and provide reference for pore structure evaluation, reservoir quality classification and capillary pressure modeling.