Estimating Organic-Rich Shale Fractal Dimensions from Gas Adsorption Isotherms: Combining Different Methods Leads to More Reliable Values and Insight

Fabric and roughness of the pore-size distributions in organic-rich shales determine their fluid flow and storage capabilities. Accurate estimation of the pore-surface fractal dimension (D) provides valuable insight to these qualities in shales. Low-pressure gas adsorption isotherms are widely used for determining D, typically applying the Frenkel-Halsey-Hill (FHH) method. Other D estimation methods, proposed by Neimark (NM) and Wang and Li (WL), are theoretically consistent and mathematically related to the FHH model but yield distinctive D values for many shales. This study evaluates the mathematical relationships between the FHH, NM and WL fractal determination methods, and with the aid of twenty-six published adsorption isotherms from shales around the world, compares their similarities and differences. Uncertainties exist in establishing best-fit lines to curved data trends in the FHH and NM methods, and in fitting power curves to data trends in the NM and WL methods. The FHH and WL D values are found to be more consistent for whole isotherm and isotherm segment analysis than the NM D values, which are systematically higher. The reasons for this are explained in terms of their graphical relationships. This leads to a novel 10-step protocol for a more thorough determination of shale D values that incorporates all three methods and involves graphical analysis that clearly exposes the uncertainties associated with the values determined. Applying this protocol should derive reliable D values to compare with key shale properties such as surface area, surface volume, thermal maturity and organic richness in future research.