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

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Abstract

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.

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Acknowledgements

Many thanks are due 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.

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Authors and Affiliations

  1. DWA Energy Limited, Lincoln, UK

    David A. Wood

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  1. David A. Wood
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Correspondence to David A. Wood.

Appendix: details of 26 published shale isotherms evaluated

Appendix: details of 26 published shale isotherms evaluated

The organic-rich shale adsorption isotherms evaluated with the fractal-dimension calculation methods have been compiled from published data from shale basins distributed around the world. These adsorption isotherms are displayed in Figs. 8, 9, 10 and 11. Details of the samples from which these isotherms are derived are listed below and available in the cited publications.

Figure 8
figure 8

Adsorption isotherms displayed for samples #1 to #7. N refers to the volume of adsorbate adsorbed by the sample

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Figure 9
figure 9

Adsorption isotherms displayed for samples #8 to #14. N refers to the volume of adsorbate adsorbed by the sample

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Figure 10
figure 10

Adsorption isotherms displayed for samples #15 to #21. N refers to the volume of adsorbate adsorbed by the sample

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Figure 11
figure 11

Adsorption isotherms displayed for samples #22 to #26. N refers to the volume of adsorbate adsorbed by the sample

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#1 Duvernay: shale (Canada) from Fig. 2a in Clarkson et al. (2013)

#2 Barnett: shale (USA) from Fig. 2a in Clarkson et al. (2013)

#3 Haynesville: shale (USA) from Fig. 2a in Clarkson et al. (2013)

#4 Woodford: shale (USA) from Fig. 2a in Clarkson et al. (2013)

#5 Eagle Ford: shale (USA) from Fig. 2a in Clarkson et al. (2013)

#6 Mont2 (Milk River): shale (Canada) from Fig. 2a in Clarkson et al. (2013)

#7 Muska1 (Horn River): shale (Canada) from Fig. 2a in Clarkson et al. (2013)

#8 Muska2 (Horn River): shale (Canada) from Fig. 2a in Clarkson et al. (2013)

#9 Marcellus 1: shale (USA) from Fig. 2a in Clarkson et al. (2013)

#10 Marcellus2: shale (USA) from Fig. 28d in Sinha (2017)

#11 Wolfcamp: shale (USA) (surface area 25 m2/g) from Fig. 28c in Sinha (2017)

#12 Bakken Immature: shale (USA) (surface area 16.44 m2/g) from Fig. 28a in Sinha (2017)

#13 Bakken1: sample #1 shale (USA) from Fig. 1 in Liu et al. (2021)

#14 Bakken 2: sample #16 (with low micropore volume) from Fig. 1 in Liu et al. (2021)

#15 Bakken 3: sample #18 (with high micropore volume) from Fig. 1 in Liu et al. (2021)

#16 Kimmeridge: from Fig. 1 (Kimmeridge Blackstone, UK) Zhao et al. (2017)

#17 Bowland (untreated): Upper Bowland Shale (UK) from Fig. 1 in Rigby et al. (2020)

#18 Bowland (treated): Thermally treated #17 samples from Fig. 1 in Rigby et al. (2020)

#19 Raniganj3: Sample CG1003 (Raniganj Basin, India) from Fig. 9 in Hazra et al. (2018)

#20 Raniganj13: Sample CG1013 (Raniganj Basin, India) from Fig. 10 in Hazra et al. (2018)

#21 Raniganj19: Sample CG1019 (Raniganj Basin, India) from Fig. 10 in Hazra et al. (2018)

#22 Longmaxi1: Sample W1-1 (Sichuan Basin, China) from Fig. 3a in Tian et al. (2021)

#23 Longmaxi5: Sample W1-5 (Sichuan Basin, China) from Fig. 3a in Tian et al. (2021)

#24 Fuling1: untreated sample from Fig. 12a Lu et al. (2020)

#25 Fuling2: sample treated with Argon at 4 MPa pressure from Fig. 12a Lu et al. (2020)

#26 Fuling3: sample treated with CO2 at 16 MPa pressure from Fig. 12d Lu et al. (2020)

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Wood, D.A. Estimating Organic-Rich Shale Fractal Dimensions from Gas Adsorption Isotherms: Combining Different Methods Leads to More Reliable Values and Insight. Nat Resour Res 30, 3551–3574 (2021). https://doi.org/10.1007/s11053-021-09909-2

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