A Novel Fractal Model for Gas Diffusion Coefficient in Dry Porous Media Embedded With a Damaged Tree-Like Branching Network

Xiao, Boqi; WANG, PEILONG; Wu, Jinsui; ZHU, HUAIZHI; LIU, MINGXING; LIU, YONGHUI; Long, Gongbo

doi:10.1142/s0218348x2250150x

Cited by 20 publications

(3 citation statements)

References 85 publications

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“…Figure A1a shows displacements and tractions on a pair of interface Elements Equations (A1) and (A2) correspond to Equations ( 4) and (23), respectively. The appendix only presents the essence of the local coordinate, the details of which can be found in Ref.…”

Section: Data Availability Statement: Not Applicablementioning

confidence: 99%

“…Recent decades saw an increasingly extensive interest in crack problems in multilayered elastic media due to their wide range of applications, including a stability analysis of construction for safety design [1][2][3][4][5], characterization of fractured porous media to optimize transport efficiency [6][7][8][9][10], and hydraulic-fracturing simulation for economic development of unconventional reservoirs [11][12][13][14][15], which has motivated the related works intensively in the latest decade [16][17][18][19][20]. The core component of hydraulic-fracturing simulation is well accepted to be the ability to model elastic response of a pressurized crack that intersects a number of layers, each of which is assumed to be homogeneous and isotropic individually [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

Lan,

Zhou,

et al. 2023

Mathematics

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Crack problems in multilayered elastic media have attracted extensive attention for years due to their wide applications in both a theoretical analysis and practical industry. The boundary element method (BEM) is widely chosen among various numerical methods to solve the crack problems. Compared to other numerical methods, such as the phase field method (PFM) or the finite element method (FEM), the BEM ensures satisfying accuracy, broad applicability, and satisfactory efficiency. Therefore, this paper reviews the state-of-the-art progress in a boundary-element analysis of the crack problems in multilayered elastic media by concentrating on implementations of the two branches of the BEM: the displacement discontinuity method (DDM) and the direct method (DM). The review shows limitation of the DDM in applicability at first and subsequently reveals the inapplicability of the conventional DM for the crack problems. After that, the review outlines a pre-treatment that makes the DM applicable for the crack problems and presents a DM-based method that solves the crack problems more efficiently than the conventional DM but still more slowly than the DDM. Then, the review highlights a method that combines the DDM and the DM so that it shares both the efficiency of the DDM and broad applicability of the DM after the pre-treatment, making it a promising candidate for an analysis of the crack problems. In addition, the paper presents numerical examples to demonstrate an even faster approximation with the combined method for a thin layer, which is one of the challenges for hydraulic-fracturing simulation. Finally, the review concludes with a comprehensive summary and an outlook for future study.

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Section: Data Availability Statement: Not Applicablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

Lan,

Zhou,

et al. 2023

Mathematics

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“…Xiao et al [24] proposed an effective thermal conductivity model with a micro-scale effect. Several investigators [25][26][27] have studied the effects of surface roughness on other aspects, such as gas diffusion in a tree-like branching network. Therefore, the influence of roughness should be considered in studies of the heat transport of a damaged tree-like branching network.…”

Section: Introductionmentioning

confidence: 99%

Thermal Conductivity Model of Porous Media Embedded with a Damaged Tree-like Branching Network Considering the Influence of Roughness

et al. 2022

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In the study of heat transfer in tree-like branching network, neither the heat convection caused by fluid flow in the tree-like branching network nor the asymmetric structure of the tree-like branching network can be ignored. In this work, we assume the porous media is embedded with a tree-like branching network that are characterized by damaged pipes. We investigated the effects of surface roughness on heat conduction and heat convection in the porous media embedded with the damaged tree-like branching network based on the fractal features of tree-like branching networks and the basic theory of thermodynamics. The proposed model for thermal conductivity can be expressed as a function of micro-structural parameters of the composite, such as the relative roughness, the ratio of thermal conductivity of the wall to that of the fluid in the micro-channel, the diameter ratio, the length ratio, the branching level, the number of damaged channels, the total number of branching levels, and the main tube porosity of the porous media. The effects of the micro-structural parameters of the model on its effective thermal conductivity have been analyzed in detail. It is believed that the joint expression of heat conduction and heat convection could enrich and develop the physical study of heat transport in porous media.

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A Fractal-Monte Carlo Approach to Simulate Kozeny–carman Constant of Roughened Fibrous Porous Media

Zhang¹,

Xiao²,

Long³

et al. 2023

Fractals

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The Kozeny–Carman (KC) equation is a well-known semi-empirical formula, which is used to calculate the permeability of porous media in the seepage field. The KC constant is an empirical constant in the KC equation. In this paper, based on the fractal theory, the Fractal-Monte Carlo technique is used to simulate the KC constant of the roughened fibrous porous media (RFPM) with micro-scale effects. There is no empirical constants in the proposed model, and each parameter has its physical meaning. The KC constant model of RFPM can be expressed as a function of structural parameters, including relative roughness ([Formula: see text], porosity ([Formula: see text], pore area fractal dimension ([Formula: see text], tortuosity fractal dimension ([Formula: see text], capillary diameter ([Formula: see text] and Knudsen number ([Formula: see text]. The result shows that the KC constant increases with increases in [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. On the contrary, with increases in [Formula: see text] and [Formula: see text], the KC constant decreases. In addition, the KC constant model constructed in the paper agrees well with the existing experimental data and the model. According to the proposed Fractal-Monte Carlo technique, it is possible to better clarify the transmission physical mechanism in RFPM with micro-scale effects.

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A Novel Fractal Model for Gas Diffusion Coefficient in Dry Porous Media Embedded With a Damaged Tree-Like Branching Network

Cited by 20 publications

References 85 publications

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

Thermal Conductivity Model of Porous Media Embedded with a Damaged Tree-like Branching Network Considering the Influence of Roughness

A Fractal-Monte Carlo Approach to Simulate Kozeny–carman Constant of Roughened Fibrous Porous Media

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