A fractal analytical model for Kozeny-Carman constant and permeability of roughened porous media composed of particles and converging-diverging capillaries

Xiao, Boqi; ZHU, HUAIZHI; Chen, Fengye; Long, Gongbo; Li, Yang

doi:10.1016/j.powtec.2023.118256

Cited by 91 publications

(11 citation statements)

References 53 publications

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“…Additionally, they may lack the ability to handle complex systems with nonlinear dynamics or large amounts of data, limiting their effectiveness in HEV powertrain applications. Analytical models rely on mathematical models to represent the underlying processes and relationships within a system [18,19]. These methods can be classified into three main categories: state estimation methods [20,21], parameter estimation methods [22,23], and equivalence space methods [24].…”

Section: Introductionmentioning

confidence: 99%

Process monitoring in hybrid electric vehicles based on dynamic nonlinear method

Wang,

Deprizon,

Kit

et al. 2024

J Appl Eng Science

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Highway third-level faults can significantly deteriorate the reliability and performance of hybrid electric vehicle (HEV) powertrains. This study presents a novel process monitoring method aimed at addressing this issue. We propose a multivariate statistical method based on dynamic nonlinear improvement, namely dynamic neural component analysis (DNCA). This method does not require the establishment of precise analytical models; instead, it only necessitates acquiring data from HEV powertrains. Through numerical simulation and real HEV experiments, we demonstrate the effectiveness of this approach in monitoring highway third-level faults. The testing outcomes demonstrate that DNCA outperforms traditional dynamic methods like dynamic principal component analysis (DPCA), conventional nonlinear methods such as kernel PCA (KPCA) and NCA, as well as traditional dynamic nonlinear methods like DKPCA.

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Section: Introductionmentioning

confidence: 99%

Process monitoring in hybrid electric vehicles based on dynamic nonlinear method

Wang,

Deprizon,

Kit

et al. 2024

J Appl Eng Science

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“…The first application of fractal geometry theory and methods to predict the permeability of porous media was the permeability model of fractured media proposed by Chang and Yortsos . Since then, many scholars have analyzed the pore structure of mudstones based on experiments such as liquid nitrogen adsorption experiments and nuclear magnetic resonance, calculated the permeability of mudstones using the Knudsen number ( Kn ) and the permeability equation, and analyzed the effects of fractal dimension and porosity of different diffusion zones on the permeability of mudstones. − There are also some scholars who introduced new parameters into the study of fractal percolation to derive new prediction models. − The most representative one is the study that introduced elasticity and other parameters into fractal seepage and established a nonlinear spherical seepage model for fractal composite reservoirs considering secondary pressure gradient, wellbore storage, surface coefficient, and effective radius under elastic external boundary conditions. The dimensionless bottomhole pressure in real space was obtained by variable substitution, similar construction method and numerical inversion, and characteristic curves were plotted to analyze the main parameters and the influence law of elasticity .…”

Section: Introductionmentioning

confidence: 99%

“…The dimensionless bottomhole pressure in real space was obtained by variable substitution, similar construction method and numerical inversion, and characteristic curves were plotted to analyze the main parameters and the influence law of elasticity . Some scholars have also used other methods to introduce fractal seepage theory to study the transport processes in the fractal of objects. − The most typical of them analyzed the crystalline column structure based on the fractal porous model and combined the result with the simulation of the percolation rate of the melt through the pore channels, revealing the influence of the pore structure, kinetics, sweating intensity separation and impurity migration in the crystallization and sweating intensity processes . In summary, most of the studies on fractal percolation introduced new parameters or methods into the original studies.…”

Section: Introductionmentioning

confidence: 99%

Full Pore Size Fractal Characteristics of Longmaxi Formation Shale in Luzhou–Changning Area and Its Influence on Seepage

Han,

Jiang,

Liang

et al. 2023

Energy Fuels

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The study of fractal percolation in shale pores is beneficial to the exploration and development of shale oil and gas, and the application of the fractal dimension to the characterization of percolation capacity can help to clarify the mechanism of gas percolation in shale. In this study, gas adsorption (CO 2 and N 2 ) and high-pressure mercury injection porosimetry (MICP) and gray correlation method are mainly used to investigate the shales of the Lower Silurian Longmaxi Formation in the Luzhou−Changning area in the southern Sichuan basin. In this study, we establish a new template to evaluate the degree of matching between the template and actual geological data considering the effects of shale fractal dimension, tortuosity, the Knudsen number (Kn), and porosity on permeability. The results reveal three observations. First, the deep organic shale pores of the Longmaxi Formation in the area have obvious multiscale fractal characteristics, and the fractal dimension (D) values reflect the complexity of shale pores at different scales. There are significant differences in the fractal dimensions among the three shale lithofacies types. Siliceous shale of D 1 with the highest micropore fractal dimension, D 2 with mesoporous, and D 3 with macroporous indicate more complex pore structures, which provide plenty of gas adsorption and enrichment spaces. These structures are conducive to gas accumulation. Second, there are complex correlations between the total organics content (TOC), the mineral composition, and the inhomogeneity parameters of shale. The TOC, siliceous mineral content, and inhomogeneity parameters of porosity, tortuosity, Kn, and D are positively correlated. The carbonate mineral content and clay mineral content are negatively correlated with the inhomogeneity parameters porosity, tortuosity, Kn, and D. Third and finally, based on correlation analysis, the three main parameters of D, porosity, and tortuosity were ultimately determined, and corresponding templates were established. It reflects that permeability, which is a parameter of seepage capacity, has a high correlation with fractal dimension, tortuosity, and porosity.

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“…Fractal theory has been widely used for the transportation of fluids in porous media. Xiao et al established the relationship between the K–C equation and the permeability of porous media based on fractal theory. , In addition, fractal theory has been applied to the capillary flow and diffusion of electrolytes in porous media. , Tree-like bifurcation networks were first applied to the study of blood transportation systems. Muray proposed the famous Murray’s law in the 1920s after continuous research and theoretical summarization .…”

Section: Introductionmentioning

confidence: 99%

“…Xiao et al established the relationship between the K–C equation and the permeability of porous media based on fractal theory. 6 , 7 In addition, fractal theory has been applied to the capillary flow and diffusion of electrolytes in porous media. 8 , 9 Tree-like bifurcation networks were first applied to the study of blood transportation systems.…”

Section: Introductionmentioning

confidence: 99%

New Model for Coal Gas Diffusion Based on the Fractal Tree-Like Bifurcation Network Structure

Han,

Liu,

Yang

et al. 2023

ACS Omega

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To investigate the nonstationary diffusion and transport law of gas in coal, an innovative fractal diffusion model based on fractal theory and a treelike bifurcation network under different diffusion modes were built. In addition, the quantitative relationships among the diffusion coefficient, temperature, pressure, and structural parameters were determined. The model considers the effect of pore tortuosity and connectivity on gas diffusion, which renders it more realistic than the previously presented single-pore diffusion models. Moreover, each parameter in the model has a definite physical meaning and does not contain any empirical constants. The applicability of the new model was verified by experimental data and other model. Subsequently, a sensitivity analysis of the gas diffusion coefficient was performed to study the effect of the microstructural parameters on gas diffusion. Finally, the dispersion degree of the diffusion coefficients at different temperatures and pressures was analyzed to determine the main influencing factors of gas diffusion at different diffusion stages in coal and study their evolution. The results show that the gas diffusion state is more sensitive to pressure variations. The diffusion behavior of gases in coal-based porous media is more influenced by the temperature and pressure at the beginning of the diffusion process.

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A fractal analytical model for Kozeny-Carman constant and permeability of roughened porous media composed of particles and converging-diverging capillaries

Cited by 91 publications

References 53 publications

Process monitoring in hybrid electric vehicles based on dynamic nonlinear method

Process monitoring in hybrid electric vehicles based on dynamic nonlinear method

Full Pore Size Fractal Characteristics of Longmaxi Formation Shale in Luzhou–Changning Area and Its Influence on Seepage

New Model for Coal Gas Diffusion Based on the Fractal Tree-Like Bifurcation Network Structure

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