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.

[1]  Yujie Yuan,et al.  Fractal analysis of the pore structure for clay bound water and potential gas storage in shales based on NMR and N2 gas adsorption , 2019, Journal of Petroleum Science and Engineering.

[2]  D. Avnir,et al.  Recommendations for the characterization of porous solids (Technical Report) , 1994 .

[3]  S. Blacher,et al.  Fractal Surface Analysis by Using Nitrogen Adsorption Data: The Case of the Capillary Condensation Regime , 1996 .

[4]  Zhiye Gao,et al.  A review of shale pore structure evolution characteristics with increasing thermal maturities , 2020, Advances in Geo-Energy Research.

[5]  Bo Liu,et al.  Mineralogy and element geochemistry of salinized lacustrine organic-rich shale in the Middle Permian Santanghu Basin: Implications for paleoenvironment, provenance, tectonic setting and shale oil potential , 2020 .

[6]  G. Beaucage.  Small-Angle Scattering from Polymeric Mass Fractals of Arbitrary Mass-Fractal Dimension , 1996 .

[7]  P. Pfeifer.  Fractals in Surface Science: Scattering and Thermodynamics of Adsorbed Films , 1988 .

[8]  M. Jaroniec.  Evaluation of the Fractal Dimension from a Single Adsorption Isotherm , 1995 .

[9]  Peter Pfeifer,et al.  Molecular fractal surfaces , 1984, Nature.

[10]  Baoquan Zhang,et al.  Determination of the Surface Fractal Dimension for Porous Media by Mercury Porosimetry , 1995 .

[11]  Shaofeng Li,et al.  Determination of the surface fractal dimension for porous media by capillary condensation , 1997 .

[12]  M. K. Wu.  The Roughness of Aerosol Particles: Surface Fractal Dimension Measured Using Nitrogen Adsorption , 1996 .

[13]  D. Avnir,et al.  Thermodynamics of gas adsorption on fractal surfaces of heterogeneous microporous solids , 1990 .

[14]  Peter Pfeifer,et al.  Fractal Analysis and Surface Roughness of Nonporous Carbon Fibers and Carbon Blacks , 1994 .

[15]  Yongbai Yin,et al.  Adsorption isotherm on fractally porous materials , 1991 .

[16]  Wu,et al.  Multilayer adsorption on a fractally rough surface. , 1989, Physical review letters.

[17]  T. Gentzis,et al.  Preliminary Investigation of the Effects of Thermal Maturity on Redox-Sensitive Trace Metal Concentration in the Bakken Source Rock, North Dakota, USA , 2020, ACS omega.

[18]  Ashutosh Kumar Singh,et al.  Fractal disposition, porosity characterization and relationships to thermal maturity for the Lower Permian Raniganj basin shales, India , 2018, Journal of Natural Gas Science and Engineering.

[19]  Peter Pfeifer,et al.  Fractal dimension as working tool for surface-roughness problems , 1984 .

[20]  Feng Yang,et al.  Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin, China , 2014 .

[21]  E. Barrett,et al.  (CONTRIBUTION FROM THE MULTIPLE FELLOWSHIP OF BAUGH AND SONS COMPANY, MELLOX INSTITUTE) The Determination of Pore Volume and Area Distributions in Porous Substances. I. Computations from Nitrogen Isotherms , 1951 .

[22]  Yujie Yuan,et al.  A comprehensive pore structure study of the Bakken Shale with SANS, N2 adsorption and mercury intrusion , 2019, Fuel.

[23]  S. Meng,et al.  Pore structure and its fractal dimensions of transitional shale: A cross-section from east margin of the Ordos Basin, China , 2019, Fuel.

[24]  Christopher R. Clarkson,et al.  Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion , 2013 .

[25]  Junhui Li,et al.  Stress sensitivity of tight reservoirs and its effect on oil saturation: A case study of Lower Cretaceous tight clastic reservoirs in the Hailar Basin, Northeast China , 2020 .

[26]  I. Gates,et al.  The effect of wall roughness on two-phase flow in a rough-walled Hele-Shaw cell , 2014, Journal of Petroleum Exploration and Production Technology.

[27]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[28]  D. H. Everett,et al.  INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY PHYSICAL CHEMISTRY DIVISION COMMISSION ON COLLOID AND SURFACE CHEMISTRY* Subcommittee on Characterization of Porous Solids RECOMMENDATIONS FOR THE CHARACTERIZATION OF POROUS SOLIDS , 2004 .

[29]  Q. Hu,et al.  Particle size effect on water vapor sorption measurement of organic shale: One example from Dongyuemiao Member of Lower Jurassic Ziliujing Formation in Jiannan Area of China , 2020, Advances in Geo-Energy Research.

[30]  R. Rezaee,et al.  Nanopore structures of isolated kerogen and bulk shale in Bakken Formation , 2018, Fuel.

[31]  A. Neimark.  A new approach to the determination of the surface fractal dimension of porous solids , 1992 .

[32]  Xipeng He,et al.  Organic nanopore structure and fractal characteristics of Wufeng and lower member of Longmaxi shales in southeastern Sichuan, China , 2019, Marine and Petroleum Geology.

[33]  Electrochemical determination of the fractal dimension of fractured surfaces , 1992 .

[34]  Mehdi Ostadhassan,et al.  Nanoscale pore structure characterization of the Bakken shale in the USA , 2017 .