Surface fractal analysis of pore structure of tight sandstones: Comparison of different models based on mercury intrusion porosimetry

Several fractal models have been widely used to evaluate the heterogeneity of tight sandstones based on mercury intrusion porosimetry (MIP). However, most of these models are pore fractal models rather than surface fractal models. Therefore, the suitability of existing surface fractal models for tight sandstones and the consistency of their results remain questionable. In the present work, a series of tight sandstones from the Upper Triassic Yanchang Formation, Ordos Basin, was studied. The relative pore surface heterogeneity degree was predicted using petrographic observations and petrophysical measurements. Three popular pore surface fractal models proposed by Neimark, Friesen and Mikula, and Zhang and Li were applied to calculate the surface fractal dimensions of these sandstones based on MIP data. The results of the fractal analyses from different models were not consistent. One or two regions could be identified by applying Neimark’s and Friesen and Mikula’s models. However, the results of the fractal analyses, obtained by using these two methods, were not consistent with the petrographic observations and petrophysical property measurements. In contrast, Zhang and Li’s model was applicable over the whole pore size range, and the results provided by their model were consistent with the petrographic observations and petrophysical property measurements: a negative correlation was observed between the fractal dimensions and porosity and permeability. Therefore, the fractal model proposed by Zhang and Li can be successfully used to characterize the pore surface roughness in this study.