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.

富有机质页岩中孔径分布的结构和粗糙度决定了它们的流体流动和储存能力。对孔隙表面分形维数 ( D ) 的准确估计为页岩中的这些特性提供了宝贵的见解。低压气体吸附等温线广泛用于测定D，通常采用 Frenkel-Halsey-Hill (FHH) 方法。Neimark (NM) 和 Wang and Li (WL) 提出的其他D估计方法在理论上是一致的，并且在数学上与 FHH 模型相关，但产生了独特的D许多页岩的价值。本研究评估了 FHH、NM 和 WL 分形确定方法之间的数学关系，并借助世界各地 26 条已发表的页岩吸附等温线，比较了它们的异同。在 FHH 和 NM 方法中为弯曲数据趋势建立最佳拟合线以及在 NM 和 WL 方法中将功率曲线拟合到数据趋势中存在不确定性。的FHH和WL d值被发现是比NM整个等温线和吸附等温线段分析更一致的d值，它是系统地高。其原因将根据它们的图形关系进行解释。这导致了一种新颖的 10 步协议，用于更彻底地确定页岩D包含所有三种方法并涉及图形分析的值，该分析清楚地揭示了与所确定值相关的不确定性。应用该协议应推导出可靠的D值，以便与未来研究中的关键页岩属性（如表面积、地表体积、热成熟度和有机丰富度）进行比较。