Adsorption isotherms of fractal surfaces

Qi, Hao; Ma, Jian; Wong, Po‐zen

doi:10.1016/s0927-7757(02)00063-8

Cited by 140 publications

(104 citation statements)

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“…Among these, the FHH model is widely used and has been shown to be the most effective method for describing the irregular geometric and structural properties of shale [44][45][46]. Fractal dimension D can be calculated independently via the FHH equation combined with N2 adsorption isotherm data and the detailed process to derive fractal dimension D is discussed in Qi et al [47].…”

Section: Organic Geochemistrymentioning

confidence: 99%

Pore Structure and Fractal Characteristics of Niutitang Shale from China

Tang

Wang

et al. 2018

Minerals

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A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH) model. The relationships between total organic carbon (TOC) content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average), high thermal maturity (3.0% on average), low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA), pore volume (PV) and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.

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Section: Organic Geochemistrymentioning

confidence: 99%

Pore Structure and Fractal Characteristics of Niutitang Shale from China

Tang

Wang

et al. 2018

Minerals

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“…29,35,36 Among which, the FHH method has been widely and successfully used for calculating fractal dimension of porous materials using N 2 adsorption data, 18,28,37,38 which is also employed in this study. The FHH model can be expressed as follows:…”

Section: Fractal Dimension Theorymentioning

confidence: 99%

“…A = D − 3) can effectively perform the realistic fractal dimension. 18,29,38 Thus, in this study, the expression "A = D − 3" is adopted for the FHH model.…”

Section: Fractal Dimension Theorymentioning

confidence: 99%

Comparison of Pore Fractal Characteristics Between Marine and Continental Shales

Yao

Liu

et al. 2018

Fractals

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Fractal characterization offers a quantitative evaluation on the heterogeneity of pore structure which greatly affects gas adsorption and transportation in shales. To compare the fractal characteristics between marine and continental shales, nine samples from the Lower Silurian Longmaxi formation in the Sichuan basin and nine from the Middle Jurassic Dameigou formation in the Qaidam basin were collected. Reservoir properties and fractal dimensions were characterized for all the collected samples. In this study, fractal dimensions were originated ¶ Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. 1840016-1Fractals 2018.26. Downloaded from www.worldscientific.com by 13.66.222.141 on 06/19/19. Re-use and distribution is strictly not permitted, except for Open Access articles. J. Liu et al.from the Frenkel-Halsey-Hill (FHH) model with N 2 adsorption data. Compared to continental shale, marine shale has greater values of quartz content, porosity, specific surface area and total pore volume but lower level of clay minerals content, permeability, average pore diameter and methane adsorption capacity. The quartz in marine shale is mostly associated with biogenic origin, while that in continental shale is mainly due to terrigenous debris. The N 2 adsorption-desorption isotherms exhibit that marine shale has fewer inkbottle-shaped pores but more plate-like and slit-shaped pores than continental shale. Two fractal dimensions (D 1 and D 2 ) were obtained at P/P o of 0-0.5 and 0.5-1. The dimension D 2 is commonly greater than D 1 , suggesting that larger pores (diameter >∼ 4 nm) have more complex structures than small pores (diameter <∼ 4 nm). The fractal dimensions (both D 1 and D 2 ) positively correlate to clay minerals content, specific surface area and methane adsorption capacity, but have negative relationships with porosity, permeability and average pore diameter. The fractal dimensions increase proportionally with the increasing quartz content in marine shale but have no obvious correlation with that in continental shale. The dimension D 1 is correlative to the TOC content and permeability of marine shale at a similar degree with dimension D 2 , while the dimension D 1 is more sensitive to those of continental shale than dimension D 2 . Compared with dimension D 2 , for two shales, dimension D 1 is better associated with the content of clay minerals but has worse correlations with the specific surface area and average pore diameter.

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“…D s values that were obtained by fitting N 2 adsorption data for three shales to the FHH isotherm equation were lower (2.39, 2.24 and 2.20) than those obtained by smallangle neutron scattering (SANS; 2.83, 2.75 and 2.59) [66]. The differences were explained by showing that the theoretical adsorption isotherms that were obtained using a power-law distribution of uncoupled spherical pores exhibited the same general features as the experimental isotherms [66].…”

Section: Fractal Analysis Applied To Adsorption Datamentioning

confidence: 59%