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

Abstract

Comparison of the fractal dimensions from different fractal theories by using the same sample gas adsorption isotherm.

Techniques used to calculate shale fractal dimensions involve uncertainties and imprecisions that require more careful consideration

“…Many thanks to Kouqi Liu for clarifying aspects of the calculation methods used in (Liu et al, 2021) and Jianchao Cai and his associates (Tian et al, 2021) for providing some useful additional insights with respects of fractal dimensions and their analysis.…”

“…Two such techniques are those proposed by Neimark (1992) (NM method) and Wang and Li (1997) (WL method). These two alternative techniques have been evaluated in conjunction with the FHH technique for multiple samples of the Bakken Shale collected from across the Williston Basin (U.S.A.) and displaying a range of PSD (Liu et al, 2021). The results presented in that study highlighted differences between the fractal dimension values calculated by the NM, WL and FHH techniques, and that those differences are of greater magnitude in the shales with larger micro-pore areas and volumes.…”

“…Traditionally, fractal dimension has been considered to be independent of the magnitude of the pores and believed to respond only to the roughness of the pore surfaces (Mahamud and Novo, 2008;Sakhee-Pour and Li, 2016). However, correlations have been observed between fractal dimension and key physical properties of certain organic-rich shales (e.g., TOC, Tmax, micro-pore surface area and volume) (Hazra et al, 2018;Liu et al, 2021). These findings suggest that the 154 Wood, D. A.…”

“…The interpretation of gas-adsorption isotherms provides a means to estimate fractal dimension values (Sahouli et al, 1996). The techniques are now widely applied to petroleumrich shales (Clarkson et al, 2013;Yang et al, 2014;Wood and Hazra, 2017;Hazra et al, 2018;Liu et al, 2021;Tian et al, 2021), and the influence of a shale's thermal maturity on fractal dimension recognised (Hazra et al, 2018;Gao et al, 2020). Shale fractal dimension values published have been derived almost exclusively based on the interpretation of low-pressure gas adsorption isotherms exploiting the Frenkel-Halsey-Hill (FHH) model (Halsey, 1948;Hill, 1952;Greggs and Sing, 1982).…”

Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior

“…The authors now intend to apply this modeling approach to real adsorption phenomena such as those encountered in Love wave sensors [4], nitrogen adsorption [41] or oxygen adsorption [24].…”