Fractal permeability model for a complex tortuous fracture network

Xia, Binwei; Luo, Yafei; Hu, Huarui; Wu, Mingyang

doi:10.1063/5.0063354

Cited by 29 publications

(12 citation statements)

References 45 publications

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“…In the actual transport of gas molecules in microfractures, frictional resistance generated by gas molecules colliding with each other and between gas molecules and the wall is viscosity, that is, a physical measurement, and one of the factors affecting the percolation rate in shale’s microfractures . The mechanisms relating to viscosity generation in different flow regimes are different; consequently, flow rates differ, as shown in Figure .…”

Section: Apparent Shale Permeability Modelmentioning

confidence: 99%

“…The presence of a large number of fractures in shale gas, with its random distribution of fractures, results in a highly complex fracture network, which makes it difficult to describe its distribution pattern and has a significant impact on shale gas transport . Shale’s heterogeneity with, statistically, fractures that reflected the similarity between the fractal characteristics of its pore and fracture structure. , By considering the effects of fracture fall, including actual fracture curvature, and based on traditional cubic law, researchers have developed a complex, curved, discrete fracture permeability model . Shale being a typical dual-porosity structure, researchers have amalgamated gas flow, deformation, matrix-fracture interaction, and heat transference to develop a dual-porosity permeability model in order to investigate the interaction between the matrix-fracture microstructure and macroscopic behavior .…”

Section: Introductionmentioning

confidence: 99%

“…13,14 By considering the effects of fracture fall, including actual fracture curvature, and based on traditional cubic law, researchers have developed a complex, curved, discrete fracture permeability model. 12 Shale being a typical dual-porosity structure, researchers have amalgamated gas flow, deformation, matrix-fracture interaction, and heat transference to develop a dual-porosity permeability model in order to investigate the interaction between the matrix-fracture microstructure and macroscopic behavior. 15 However, none of the above studies considered the complex features of the fracture bifurcation structure, which over time has revealed that fractures in shale's low permeability reservoirs possess bifurcation characteristics similar to a tree network pattern.…”

Section: Introductionmentioning

confidence: 99%

“…With a detailed understanding of shale's gas transport mechanisms, it was found that gas flow was not merely controlled by a complex fracture network structure but was also associated with gas molecular properties. Gas viscosity is an important constituent when describing the flow characteristics of a gas 12 and is, moreover, a function of the Knudsen number, varying its effects with those of the Knudsen number. 33 Gas molecules in different flow regimes have different viscous velocities of gas flow, with no regular procedure to describe the viscosity of gases in the entire flow regime.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Study of Changes in Apparent Permeability in Shale’s Complex Microfracture Networks

Ding,

Li,

et al. 2023

Ind. Eng. Chem. Res.

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The microfracture structure in the reservoirs of shale has a strong influence on gas transport. To depict the transport characteristics of shale gas in widely developed microfractures, this paper has constructed a shale apparent permeability model based on fractal theory. Shale's microfracture structure was first identified as a bifurcation network, with the effects of effective stress and gas adsorption considered to obtain the dynamic fractal dimension definition equation. Effective viscosity was corrected by employing weighting factors relating to continuum flow viscosity and Knudsen diffusion viscosity. Finally, an apparent permeability model for shale was established by combining the three transport mechanisms of continuum flow, Knudsen's diffusion, and surface diffusion. The model was validated. The results showed that the viscosity flow rate of continuum flow and Knudsen diffusion increased under increasing pore pressure, revealing that the effect of a microfracture bifurcation network on shale's permeability was significant when shale gas was transported.

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Section: Apparent Shale Permeability Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Study of Changes in Apparent Permeability in Shale’s Complex Microfracture Networks

Ding,

Li,

et al. 2023

Ind. Eng. Chem. Res.

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“…The continuity equation of CBM flow in coal seams can be expressed by Darcy's law combined with mass conservation (Xia et al, 2021b;Ren et al, 2021):…”

Section: Fluid Governing Equations and Boundary Conditionsmentioning

confidence: 99%

Study on coalbed methane flow characteristics based on fractal bifurcation fracture network model

Jiang

Xia²,

Peng³

et al. 2023

Front. Earth Sci.

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The geometric structure and distribution of the fracture network significantly impact the coalbed methane flow characteristics. The indoor optical microscope test is utilized to analyze the distribution and structural characteristics of natural fractures in coal. The results indicate that the fracture network in coal consists primarily of irregular bifurcated fractures, but the influence of the bifurcation fracture network’s structural characteristics on permeability remains unclear. Therefore, the fracture network geometric structure characteristic parameters are considered in accordance with the fractal theory, and the analytical formula of the bifurcation fracture network permeability is established. Meanwhile, the bifurcation fracture network geometric model with varied structural parameters is reconstructed using the pixel probability decomposition algorithm. Finally, the influence of the key parameters of the reconstructed bifurcation fracture network on the coal seam permeability is analyzed through numerical simulation. The results indicate that the permeability of the bifurcated fracture network increases with the increase of fracture porosity φf, aperture ratio χ, and proportionality coefficient η, and decreases with the increase of tortuosity fractal dimension DT, bifurcation angle θ, fractal dimension Df, and bifurcation level n. Among them, fracture porosity and proportionality coefficient have the greatest influence on permeability, followed by tortuosity fractal dimension, aperture ratio.

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Influence of normal stress‐induced three‐dimensional rough fracture aperture heterogeneity on nonlinear seepage‐heat transfer coupling processes

Zhang,

Wang,

Han

et al. 2023

Num Anal Meth Geomechanics

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A clear understanding of the dependence of the heat transfer process on the flow field in three‐dimensional (3D) rough fractures is crucial for many underground projects. In this study, 3D rough rock fractures with heterogeneous apertures and mechanical effects are established. Navier‐Stokes flow and local heat balance theory are used to simulate the seepage‐heat transfer coupling process. Five normal stresses and five flow velocities are set to quantify the influence of aperture variability on the flow field and heat transfer behavior of the fractures. The results show that the change in fracture aperture caused by normal stress is the direct cause of the nonlinear distribution of the flow field and temperature fluctuation. A quantitative parameter of temperature fluctuation degree in the fracture is proposed, which decreases exponentially with increasing fracture aperture and increases with greater flow velocity. An empirical model is established to describe the relationship between the heat transfer coefficient and the ratio of hydraulic aperture to mechanical aperture. The correctness of the model is verified by published seepage‐heat transfer coupling test results. The model is extended to establish the relationship between the heat transfer coefficient and the volume fraction of eddy. It is confirmed that the heat transfer coefficient increases with the augmentation of nonlinear flow, and the reason why the results of evaluating the heat transfer coefficient by roughness alone in related experiments are inconsistent is revealed. The results enhance the understanding of convective heat transfer characteristics in 3D rough rock fractures.

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Fractal permeability model for a complex tortuous fracture network

Cited by 29 publications

References 45 publications

Study of Changes in Apparent Permeability in Shale’s Complex Microfracture Networks

Study of Changes in Apparent Permeability in Shale’s Complex Microfracture Networks

Study on coalbed methane flow characteristics based on fractal bifurcation fracture network model

Influence of normal stress‐induced three‐dimensional rough fracture aperture heterogeneity on nonlinear seepage‐heat transfer coupling processes

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