Comparison of fractal dimensions from nitrogen adsorption data in shale via different models

The roughness of pore surfaces in shale reservoirs can affect the fluid flow, which makes it necessary to be characterized. Fractal dimension, a key component in fractal geometry, can be used to describe the surface irregularities. In this paper, we evaluated and compared the fractal dimensions of several shale samples with three major fractal models based on nitrogen adsorption isotherms. The results showed that Frenkel-Halsey-Hill (FHH), Neimark, and Wang-Li models all can be applied for fractal dimension characterization of shale samples. From theoretical thermodynamics, these three models should be considered identical based on the FHH equation. However, the experimental data obtained from these samples showed that the fractal dimensions that are derived from the Neimark model and Wang-Li model are the same while a discrepancy was observed with the results from the FHH model. The difference in the fractal dimensions in the experimental data among these three models was attributed to the micropore structures. It was found that as the micropore surface area or the micropore volume increases in the samples, the difference in the fractal dimensions would increase as well. If the number of micropores present in the samples is limited, all three models can become suitable for fractal dimension calculation in shale samples, otherwise, the Neimark or Wang-Li model is preferred.