scholarly journals Application of fractal theory to predict the coal permeability of multi-scale pores and fractures

2021 ◽  
Vol 7 ◽  
pp. 10-18
Author(s):  
Zheng Zhao ◽  
Xiaoming Ni ◽  
Yunxing Cao ◽  
Yanxia Shi
Keyword(s):  
Fractal Theory ◽  
Coal Permeability ◽  
Multi Scale

scholarly journals Response of Floc Networks in Cemented Paste Backfill to a Pumping Agent

Metals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1906
Author(s):  
Jiaqi Zhu ◽  
Shunchuan Wu ◽  
Haiyong Cheng ◽  
Xiaojie Geng ◽  
Jin Liu
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Mineral Resources ◽  
Cemented Paste Backfill ◽  
Sem Image ◽  
Multi Scale ◽  
Paste Backfill ◽  
Engineering Significance ◽  
Deep Underground ◽  
Dominant Structure

Cemented paste backfill is critical for the development of green mines, the safe exploitation of mineral resources deep underground, and the efficient disposal of solid wastes produced by mining. In this paper, the mechanism underpinning how the pumping agent works was studied. The number, area, and fractal dimension of pores in the microstructure of fresh paste were quantitatively analyzed using scanning electron microscopy (SEM), image processing, and fractal theory, and the response of flocs was investigated. The results show that floc networks disintegrated and the liquid network became the dominant structure under the action of the pumping agent, which enhanced the lubrication and promotion of multi-scale particles. In addition, the force chains became fragile and scattered, diminishing the yield stress of the paste. The pores had a more homogenized dimension and the porosity was 15.52% higher. The increase in the fractal dimension of the pores indicated that there was a higher self-similarity, in terms of microstructure, with a strengthened liquid network. The migration of floc structures contributed to the enhancement of the fluidity and rheology of the paste. This study provides insights into the effects of floc and liquid networks on the performance of paste, and it is of engineering significance in terms of realizing safe and efficient CPB operations.

scholarly journals Mathematical Model for Effective Gas Diffusion Coefficient in Multi-scale Fractal Porous Media

2021 ◽  
Vol 248 ◽  
pp. 01026
Author(s):  
Du Zhehua
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Diffusion Coefficient ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Effective Diffusion ◽  
Gas Diffusion ◽  
Pore Connectivity ◽  
Multi Scale ◽  
Pore Area

Based on the capillary hypothesis and fractal theory, a mathematical model for calculating the effective gas diffusion coefficient in porous media is established. By using fractal geometry theory, pore area fractal dimension, tortuosity fractal dimension and pore connectivity are introduced to quantitatively characterize the real internal structure in the porous media. An effective gas diffusion coefficient model for the fractal porous media is derived, and the influence of multi-scale porous media microstructure parameters on the effective gas diffusion coefficient is discussed. The results show that effective gas diffusion coefficient approximates to linearly increase with the increase of porosity, the pore area fractal dimension and the effective gas diffusion coefficient is positive correlation, but the tortuosity fractal dimension is negatively related to it. In the case of different porosities, the gas effective diffusion coefficient varies with the change of the pore diameter ratio, the effective gas diffusion coefficient increases with the increase of pore connectivity.

Multi-scale numerical model for simulating concrete material based on fractal theory

2013 ◽  
Vol 26 (4) ◽  
pp. 344-352 ◽  
Author(s):  
Qiang Xu ◽  
Jianyun Chen ◽  
Jing Li ◽  
Mingming Wang
Keyword(s):  
Numerical Model ◽  
Fractal Theory ◽  
Concrete Material ◽  
Multi Scale

A FRACTAL PERMEABILITY MODEL FOR SHALE MATRIX WITH MULTI-SCALE POROUS STRUCTURE

Fractals ◽  
2016 ◽  
Vol 24 (01) ◽  
pp. 1650002 ◽  
Author(s):  
MAO SHENG ◽  
GENSHENG LI ◽  
SHOUCENG TIAN ◽  
ZHONGWEI HUANG ◽  
LIQIANG CHEN
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Shale Gas ◽  
Gas Permeability ◽  
Pore Space ◽  
Fractal Theory ◽  
Permeability Model ◽  
Multi Scale ◽  
Nanopore Structure

Nanopore structure and its multiscale feature significantly affect the shale-gas permeability. This paper employs fractal theory to build a shale-gas permeability model, particularly considering the effects of multiscale flow within a multiscale pore space. Contrary to previous studies which assume a bundle of capillary tubes with equal size, in this research, this model reflects various flow regimes that occur in multiscale pores and takes the measured pore-size distribution into account. The flow regime within different scales is individually determined by the Knudsen number. The gas permeability is an integral value of individual permeabilities contributed from pores of different scales. Through comparing the results of five shale samples, it is confirmed that the gas permeability varies with the pore-size distribution of the samples, even though their intrinsic permeabilities are the same. Due to consideration of multiscale flow, the change of gas permeability with pore pressure becomes more complex. Consequently, it is necessary to cover the effects of multiscale flow while determining shale-gas permeability.

Assessment of green roof incentive policies in European cities by a fractal analysis

2020 ◽  
Author(s):  
Pierre-Antoine Versini ◽  
Auguste Gires ◽  
Ioulia Tchiguirinskaia ◽  
Daniel Schertzer
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Ecosystem Services ◽  
Fractal Analysis ◽  
Fractal Theory ◽  
Green Roof ◽  
Green Roofs ◽  
Multi Scale ◽  
European Cities ◽  
Wide Range

<p>Green roofs represent a market of several tens millions of m<sup>2</sup> implemented every year in Europe. They appear to be particularly efficient to reduce the potential impact of new and existing urban developments by making the city “greener” and more resilient to climate change. Indeed, they provide several ecosystem services, particularly in stormwater management, urban heat island attenuation, and biodiversity conservation. For these reasons, municipalities are implementing specific policies to promote a large diffusion of green roofs on their territory. Nevertheless, to optimize their performances through urban scales, green roofs spatial distribution should be analysed.</p><p>In order to study the current green roof implementation and to assess the relevancy of the related policies, a multi-scale analysis based on fractal theory as been conducted. Such analysis, widely used in geophysics, is particularly suitable to characterize spatial fields exhibiting strong heterogeneity over wide range of scales. This fractal analysis was performed here to characterize the spatial distribution of green roofs in several European cities (London, Amsterdam, Geneva, Lyon, Paris, Berlin, Frankfort, Copenhagen, Oslo…). These cities have been chosen because: (i) GIS database containing the location and geometry of implemented green roofs is available, (ii) they have implemented various kind of green roofs policies.</p><p>The results show that every studied city depicts similar behaviour with the definition of three distinct scaling regimes. The second regime (between 16/32 and 512/1024 m) characterizes not only single roofs but their distribution in space which is what we are interested in. The fractal dimension charactering this regime is the most variable, ranging from 0.50 to 1.35 and illustrates some different degrees of progress in urban greening. It has to be noticed that the more ambitious incentive measures (where monetary subsidies are proposed) correspond to the cities characterized by the highest fractal dimension. Nevertheless, as these policies are relatively recent, they cannot completely explain the current green roof distribution (architectural history has also to be mentioned).</p><p>The obtained results demonstrate some significant inconsistencies between political ambition and their in situ realization. They illustrate the necessity to better take into account the spatial distribution of green roof implementations in order to optimize their performances. To provide ecosystem services at large scales, green roofs have to be widely and relevantly implemented. Fractal analysis can be seen as innovative multi-scale approach to adjust policies for this purpose.</p><p>This work has been made thanks to ANR EVNATURB project (https://hmco.enpc.fr/portfolio-archive/evnaturb/) and the Academic Chair “Hydrology for Resilient Cities”, a partnership between Ecole des Ponts ParisTech and the Veolia group.</p>

A multi-scale model of real contact area for linear guideway based on the fractal theory

2021 ◽  
pp. 095440622098336
Author(s):  
Xinxin Li ◽  
Zhimin Li ◽  
Sun Jin ◽  
Jichang Zhang
Keyword(s):  
Contact Area ◽  
Manufacturing Industry ◽  
Fractal Theory ◽  
Scale Model ◽  
Design Stage ◽  
Real Contact Area ◽  
The Real ◽  
Multi Scale ◽  
Real Contact ◽  
Proposed Model

High precision, efficiency and reliability are the unremitting pursuits of machinery manufacturing industry. As one of the pivotal function parts of high-end NC machine tool, precise linear guideway determines the machining precision and operation performance. Accurate evaluation and prediction of surface topography are the crucial effects on the matching performance of linear guideway. In this paper, the real contact area is regarded as a key parameter, a multi-scale method with the fractal theory is proposed. First, the contact area of a single asperity was obtained with Hertz contact theory. Afterwards, the contact area between rough surfaces was deduced by the fractal theory. Finally, using the proposed multi-scale contact mechanics model, the real contact area between rough plane and cylinder was obtained by integral solution. Compared with the former fractal model and GW model, the proposed model on the real contact area calculation of linear guideway is more accurate and comprehensive. The effect factors of load, fractal parameter and friction were discussed, the increasing rate of real contact area of smoother surface is greater as load increases. The proposed model may provide practical guidance for assembly accuracy and surface quality requirements at design stage.

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