Recent Advances on Fractal Modeling of Permeability for Fibrous Porous Media

Cai, Jianchao; Luo, Lingen; Ye, Ran; Zeng, Xiangfeng; Hu, Xiangyun

doi:10.1142/s0218348x1540006x

Cited by 114 publications

(38 citation statements)

References 70 publications

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“…Existing research found that fractal characteristics have a significant influence on gas adsorption/flow capacities, especially on the permeable pathways for methane transport during shale gas extraction, indicating that fractal properties probably influence the shale gas production and thus can be used as a parameter to evaluate the quality of a shale reservoir. [17][18][19] Therefore, improving the fractal characterization of pore structures in shale is of great importance for shale gas exploration and exploitation.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Comparison of Pore Fractal Characteristics Between Marine and Continental Shales

Yao

Liu

et al. 2018

Fractals

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“…The validity of the proposed model was verified by comparing the predictions to available numerical simulation results. Natural fractured rock masses are constituted by rock matrix and discontinuities (Cai et al 2014;Ma 2015), and the former one is a kind of porous media (Cai et al 2015;CuetoFelgueroso and Juanes 2016). A number of dual-porosity models have been established to quantify the permeability of porous media (Bibby 1981;Elsworth and Bai 1992;Vogel et al 2000;Li Y and Yu 2013).…”

Section: Permeability and Fracture-length Distributionmentioning

confidence: 99%

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

et al. 2016

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Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of twodimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracturelength distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.

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“…By introducing fractal theory, Cai et al (2010a) studied the SI law of single tortuous capillary. Furthermore, they developed this theory and made many applications in porous media based on fractal geometry (Cai et al, 2010b(Cai et al, , 2012(Cai et al, , 2014(Cai et al, , 2015. Sang (2012) studied the SI characteristics of a symmetric tree-like structure.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous imbibition in asymmetric branch-like throat structures in unconventional reservoirs

Shen

et al. 2017

Journal of Natural Gas Science and Engineering

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a b s t r a c tUnconventional reservoirs, especially shale plays, have abundant micro-nano pores. Large volume water was injected into the reservoir during hydraulic fracturing. Fracturing fluid can displace gas in pore spaces spontaneously, called spontaneous imbibition (SI), which has significant effects on the gas production after hydraulic fracturing. Throat structure in matrix is one of the key factors to influence SI process. In this work, at first, complex pore space is simplified as a spatial self-similar branch-like structure composed of several asymmetric sub-throats. Then, within asymmetric branch structure, the imbibition process is calculated by a newly established mathematical model, and the influence of both pore structure and fluid characteristics, including contract angle, viscosity, surface tension, are discussed. Finally, some lab experiments, especially SI tests, are included on shale and sandstone core plugs to verify our model. Results show that the coherence in wettability between the reservoir and the fracturing fluid is important to enhance the microscopic replacement effect. Pore size also has effect influence on imbibition curve. In addition, both in models and experiments, imbibition index n is useful to describe imbibition properties of rocks. In unconventional rock samples like shale, n is less than 0.4, while highpermeability sandstone, n approach to 0.5. These conclusions are useful to investigate the mechanism of spontaneous imbibition and microscopic displacement in unconventional reservoirs.

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Recent Advances on Fractal Modeling of Permeability for Fibrous Porous Media

Cited by 114 publications

References 70 publications

Comparison of Pore Fractal Characteristics Between Marine and Continental Shales

Comparison of Pore Fractal Characteristics Between Marine and Continental Shales

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

Spontaneous imbibition in asymmetric branch-like throat structures in unconventional reservoirs

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