The relationship between fractal properties of solid matrix and pore space in porous media

Dathe, Annette; Thullner, Martin

doi:10.1016/j.geoderma.2005.01.003

Cited by 103 publications

(59 citation statements)

References 32 publications

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“…Now, the fractal models of porous media are enjoying considerable popularity [1,9,18,3,5]. This is in part due to the relatively small number of parameters that can define a fractal porous of great complexity and rich structures.…”

Section: Introductionmentioning

confidence: 99%

“…This is in part due to the relatively small number of parameters that can define a fractal porous of great complexity and rich structures. Also, it is found experimentally and numerically that natural porous media are fractal objects in a certain range of length scales [1,11,3]. The fractal theory provides a new avenue for researchers to study the transport phenomena in porous media, and make it possible to reveal the phenomenon and rules of transport in porous media more in depth.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the effective thermal conductivity of fractal porous media

Huai

Wang

2007

Applied Thermal Engineering

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the effective thermal conductivity of fractal porous media

Huai

Wang

2007

Applied Thermal Engineering

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“…Fractal analysis is a useful tool to describe the natural structures with irregular component sizes and phase arrangements (Bartoli, et al 1991;Adler and Thovert 1993;Perfect and Kay 1995). Developments in fractal geometry help lead to better understanding of material properties and apparently chaotic processes in nature (Perrier, et al 1999;Perrier and Bird 2002;Lehmann, et al 2003;Dathe and Thullner 2005). In this study, the effect of soil particle sizes, distributions and solid thermal conductivity on the soil thermal conductivity were studied both experimentally and theoretically.…”

Section: Introductionmentioning

confidence: 98%

Fractal Approach to Calculate the Thermal Conductivity of Moist Soil

Cai¹,

Cui²,

Zheng³

et al. 2017

Proceedings of the IGSHPA Technical/Research Conference and Expo 2017

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The ground heat exchanger (GHE) is a key component in the design of a GSHP system and the effective thermal conductivity is one of the most important parameters that determine the heat transfer underground. In this paper, the effect of particle sizes and distributions on the sand thermal conductivity were studied both experimentally and analytically. Fractal method was considered for simulating the thermal conductivity of both dry and moist, unsaturated sand. Seven types of dry sand samples and six types of moist, unsaturated sand were selected in the experiments and results showed that both porosity, fractal dimension and particle size ratio affect the sand thermal conductivity. Based on the fractal theory, the fractal models were applied to predict the sand thermal conductivity under both dry and wet conditions. By comparing to the experimental findings, the proposed model was able to predict the variation on the sand thermal conductivity. However, the contact thermal resistance and water distribution pattern are two key impacts on the soil behaviors and need to be further studied.

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“…In particular, he observed that the multifractal spectrum of pore space is correlated with air permeability values measured from the corresponding core samples. Dathe and Thullner (2005) analyzed pore spaces in porous media using, respectively, monofractals and multifractal approaches where the authors tried to establish a relationship between fractal dimensions of pore spaces and solid phase. In this study, we use the multifractality concept on SEM images of carbonate rocks in order to achieve two main goals: the first is to evaluate pore spaces heterogeneities; the second is to assess the effect of magnification on multifractals descriptors and the estimated porosities.…”

Section: Introductionmentioning

confidence: 99%

Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates

Jouini¹,

Vega²,

Mokhtar³

2011

Nonlin. Processes Geophys.

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Abstract. Pore spaces heterogeneity in carbonates rocks has long been identified as an important factor impacting reservoir productivity. In this paper, we study the heterogeneity of carbonate rocks pore spaces based on the image analysis of scanning electron microscopy (SEM) data acquired at various magnifications. Sixty images of twelve carbonate samples from a reservoir in the Middle East were analyzed. First, pore spaces were extracted from SEM images using a segmentation technique based on watershed algorithm. Pores geometries revealed a multifractal behavior at various magnifications from 800x to 12 000x. In addition, the singularity spectrum provided quantitative values that describe the degree of heterogeneity in the carbonates samples. Moreover, for the majority of the analyzed samples, we found low variations (around 5 %) in the multifractal dimensions for magnifications between 1700x and 12 000x. Finally, these results demonstrate that multifractal analysis could be an appropriate tool for characterizing quantitatively the heterogeneity of carbonate pore spaces geometries. However, our findings show that magnification has an impact on multifractal dimensions, revealing the limit of applicability of multifractal descriptions for these natural structures.

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The relationship between fractal properties of solid matrix and pore space in porous media

Cited by 103 publications

References 32 publications

Analysis of the effective thermal conductivity of fractal porous media

Analysis of the effective thermal conductivity of fractal porous media

Fractal Approach to Calculate the Thermal Conductivity of Moist Soil

Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates

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