Techniques used to calculate shale fractal dimensions involve uncertainties and imprecisions that require more careful consideration
Abstract view|1336|times PDF download|327|times Supplements download|84|times
Abstract
Surface roughness of shales has a key influence on the petroleum resources they are able to store and the fraction of them that can be recovered. The fractal dimension quantifies the degree of roughness and is influenced primarily by the pore surfaces within the shale that typically include micro-, meso-and macro-pores. Isotherms generated by gas adsorption experiments are the common data source used to derive estimates of fractal dimension. The Frenkel-Halsey-Hill fractal technique is the most widely applied fractal dimension estimation method. Other methods can derive fractal dimension from isotherm data but typically the values they generate are different from the Frenkel-Halsey-Hill derived fractal dimension values. Moreover, those differences can vary significantly depending on the type of shales involved. Those shales displaying more complex pore-scale distributions including extensive micro-porosity components tend to be associated with the greatest discrepancies. A comparison of three fractal dimension calculation methods applied to shales reveals aspects of their calculation and interpretation methods that explain the differences in the fractal dimension values they generate. This study identifies the uncertainties that should be taken into account when applying the methods and the appropriate curve fitting optimization configurations that should be evaluated. Taking these factors into account leads to more realistic selections of appropriate fractal dimension values from gas adsorption isotherms of organic-rich shales.
Cited as: Wood, D.A. Techniques used to calculate shale fractal dimensions involve uncertainties and imprecisions that require more careful consideration. Advances in Geo-Energy Research, 2021, 5(2): 153-165, doi: 10.46690/ager.2021.02.05
Keywords
References
Alturki, A. A., Maini, B. B., Gates, I. D. The effect of wall roughness on two-phase flow in a rough-walled Hele-Shaw cell. Journal of Petroleum Exploration and Production Technology, 2014, 4(4): 397-426.
Avnir, D., Farin, D., Pfeifer, P. Molecular fractal surfaces. Nature, 1984, 308: 261-263.
Avnir, D., Farin, D., Pfeifer, P. A discussion of some aspects of surface fractality and of its determination. New Journal of Chemistry, 1992, 16(4): 439-449.
Cai, J., Zhang, L., Wei, W. Modelling of Flow and Transport in Fractal Porous Media. Amsterdam, The Netherlands, Elsevier, 2020.
Frontline Solvers. Excel Solver–Optimization Methods, 2021.
Gao, Z., Fan, Y., Xuan, Q., et al. A review of shale pore structure evolution characteristics with increasing thermal maturities. Advances in Geo-Energy Research, 2020, 4(3): 247-259.
Gregg, S. J., Sing, K. S. W. Adsorption, Surface Area, and Porosity. 2nd ed. New York, USA, Academic Press, 1982.
Halsey, G. Physical adsorption on non-uniform surfaces. Journal Chemical Physics, 1948, 16(10): 931-937.
Hazra, B., Wood, D. A., Kumar, S., et al. Fractal disposition, porosity characterization and relationships to thermal maturity for the Lower Permian Raniganj basin shales, India. Journal of Natural Gas Science and Engineering, 2018, 59: 452-465.
Hill, T. L. Theory of physical adsorption. Advanced in Catalysis, 1952, 4: 211-258.
Jaroniec, M. Evaluation of the fractal dimension from a single adsorption isotherm. Langmuir, 1995, 11: 2316-2317.
Kiselev, A. V., Pavlova, L. F. Use of general equations of isotherms for the adsorption of benzene-n-hexane solutions on the adsorbents of various characters. Russian Chemical Bulletin, 1965, 14: 15-23.
Li, A., Ding, W., He, J., et al. Investigation of pore structure and fractal characteristics of organic-rich shale reservoir: A case study of Lower Cambrian Qiongzhusi formation in Malong block of eastern Yunnan Province, South China. Marine Petroleum Geology, 2016, 70: 46-57.
Liu, K., Ostadhassan, M., Jang, H. W., et al. Comparison of fractal dimensions from nitrogen adsorption data in shale via different models. Royal Society of Chemistry Advances, 2021, 11: 2298-2306.
Mahamud, M. M., Novo, M. F. The use of fractal analysis in the textural characterization of coals. Fuel, 2008, 87(2): 222-231.
Mandelbrot, B. B. Les objects fractals: Forme, hasard et dimension. Paris, France, Flammarion, 1975.
Neimark, A. New approach to the determination of the surface fractal dimension of porous solids. Physica A, 1992, 191(1-4): 258-262.
Pfeifer, P. Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. The Journal of Chemical Physics, 1983, 79: 3558.
Pfeifer, P. Fractal dimension as working tool for surface roughness problems. Applications of Surface Science, 1984, 18(1-2): 146-164.
Pfeifer, P., Cole, M. W. Fractals in surface science: Scattering and thermodynamics of adsorbed films II. New Journal of Chemistry, 1990, 14(3): 221-232.
Pfeifer, P., Wu, Y., Cole, M. W., et al. Multilayer adsorption on a fractally rough surface. Physical Review Letters, 1989, 62(17): 1997-2000.
Powles, J. G. On the validity of the Kelvin equation. Journal of Physics A: Mathematical and General, 1985, 18(9): 1551.
Sahouli, B., Blacher, S., Brouers, F. Fractal surface analysis by using nitrogen adsorption data: The case of the capillary condensation regime. Langmuir, 1996, 12(11): 2872-2874.
Sakhaee-Pour, A., Li, W. Fractal dimensions of shale. Journal of Natural Gas Science and Engineering, 2016, 30: 578-582.
Tian, Z., Wei, W., Zhou, S., et al. Experimental and fractal characterization of the microstructure of shales from Sichuan Basin, China. Energy & Fuels, 2021, 35 (5): 3899-3914.
Wang, F., Li, S. Determination of the surface fractal dimension for porous media by capillary condensation. Industrial & Engineering Chemistry Research, 1997, 36(5): 1598-1602.
Wood, D. A., Hazra, B. Characterization of organic-rich shales for petroleum exploration & exploitation: A review-Part 1: bulk properties, multi-scale geometry and gas adsorption. Journal of Earth Science, 2017, 28(5): 739-757.
Yang, F., Ning, Z., Liu, H. Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin, China. Fuel, 2014, 115: 378-384.
Yang, R., He, S., Yi, J., et al. Nano-scale pore structure and fractal dimension of organic-rich Wufeng-Longmaxi shale from Jiaoshiba area, Sichuan Basin: Investigations using FE-SEM, gas adsorption and helium pycnometry. Marine and Petroleum Geology, 2016, 70: 27-45.
Refbacks
- There are currently no refbacks.
Copyright (c) 2021 The Author(s)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.