Special Issue "Applications of Fractal Geometry Theory in Porous Media"

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 January 2023 | Viewed by 1934

Special Issue Editor

Prof. Dr. Boming Yu
E-Mail Website
Guest Editor
School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
Interests: fractal geometry theory; transports in fractal media

Special Issue Information

Dear Colleagues,

Since B.B. Mandelbrot’s establishment of the Fractal Geometry Theory in nature in the 1980s, the theory has received steady worldwide attention and obtained great progress; nowadays, having been applied in many fields, such as mathematics, physics, material science and engineering, geophysics, oil/gas/water reservoir engineering, energy engineering, biomaterials, etc. It is well known that porous media widely exist in nature, laboratories and engineering, such as soils, oil/gas/water reservoirs, fibrous materials, concretes, ceramic materials, bio-materials, organic bodies, etc., whose microstructures exhibit the fractal characteristics. Many reports also show that the transport properties (such as thermal conductivities, permeabilities, gas diffusivities, electric conductivity, wave transport ability, etc.) are closely related to the microstructural parameters of porous media and, due to their complicated microstructures, it is still challenging to predict their transport properties. Fortunately, since the fractal geometry theory may be applied to porous media to characterize their microstructural parameters and properties, the area of the “Applications of Fractal Geometry Theory in Porous Media” has continuously been one of the most attractive research topics in the field of fractals and fractional orders.

This Special Issue focuses on the “Applications of Fractal Geometry Theory in Porous Media”. We invite you to submit comprehensive review articles and original research papers, this Special Issue covering, but not being limited to, the following topics:

  • Fractal geometry theory for porous media;
  • Applications of the fractal geometry theory in oil/gas/water reservoir engineering;
  • Applications of the fractal geometry theory in fibrous materials;
  • Applications of the fractal geometry theory in composites;
  • Applications of the fractal geometry theory in concretes;
  • Applications of the fractal geometry theory in soils;
  • Applications of the fractal geometry theory in geological structures;
  • Applications of the fractal geometry theory in ceramic and biomaterials;
  • Other fractal-based approaches and applications in porous media.

Prof. Dr. Boming Yu
Guest Editor

Manuscript Submission Information

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Published Papers (3 papers)

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Research

Article
Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric
Fractal Fract. 2022, 6(7), 353; https://doi.org/10.3390/fractalfract6070353 - 23 Jun 2022
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Abstract
Fractal characteristics and the fractal dimension are widely used in the description and characterization of rock fracture networks. They are important tools for coal mining, oil and gas transportation, and other engineering problems. However, due to the complexity of rock fracture networks and [...] Read more.
Fractal characteristics and the fractal dimension are widely used in the description and characterization of rock fracture networks. They are important tools for coal mining, oil and gas transportation, and other engineering problems. However, due to the complexity of rock fracture networks and the difficulty in directly applying the limit definition of the fractal dimension, the definition and application of the fractal dimension have become hot topics in related projects. In this paper, the traditional fractal calculation methods were reviewed. Using the traditional fractal theory and the head/tail breaks method, a new fractal dimension quantization model was established as a simple method of fractal calculation. This simple method of fractal calculation was used to calculate the fractal dimensions of three rock fracture networks. Through comparison with the box-counting dimension calculation results, it was verified that the model could calculate the fractal dimension of the fracture length of rock fracture networks, as well as quantify it accurately and effectively. In addition, we found a number of similarities between rock fracture networks and urban road traffic networks in GIS. The application of the space syntax metric to rock fracture networks prevents controversy with respect to the definition of the axis and it showed a good effect. Using the space syntax metric as a parameter can better reflect the space relationship of rock fractures than length. Through the calculation of the fractal dimension of the connection value and control value, it was found that the trend of the length fractal dimension was the same as that of the control value, whereas the fractal dimension of the connection value was the opposite. This further verifies the applicability of the space syntax metric in rock fracture networks. Full article
(This article belongs to the Special Issue Applications of Fractal Geometry Theory in Porous Media)
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Article
The Hausdorff Dimension and Capillary Imbibition
Fractal Fract. 2022, 6(6), 332; https://doi.org/10.3390/fractalfract6060332 - 16 Jun 2022
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Abstract
The time scaling exponent for the analytical expression of capillary rise tδ for several theoretical fractal curves is derived. It is established that the actual distance of fluid travel in self-avoiding fractals at the first stage of imbibition is in [...] Read more.
The time scaling exponent for the analytical expression of capillary rise tδ for several theoretical fractal curves is derived. It is established that the actual distance of fluid travel in self-avoiding fractals at the first stage of imbibition is in the Washburn regime, whereas at the second stage it is associated with the Hausdorff dimension dH. Mapping is converted from the Euclidean metric into the geodesic metric for linear fractals F governed by the geodesic dimension dg=dH/d, where d is the chemical dimension of F. The imbibition measured by the chemical distance g is introduced. Approximate spatiotemporal maps of capillary rise activity are obtained. The standard differential equations proposed for the von Koch fractals are solved. Illustrative examples to discuss some physical implications are presented. Full article
(This article belongs to the Special Issue Applications of Fractal Geometry Theory in Porous Media)
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Article
A Fractal Permeability Model of Tight Oil Reservoirs Considering the Effects of Multiple Factors
Fractal Fract. 2022, 6(3), 153; https://doi.org/10.3390/fractalfract6030153 - 11 Mar 2022
Cited by 1 | Viewed by 674
Abstract
The prediction of permeability and the evaluation of tight oil reservoirs are very important to extract tight oil resources. Tight oil reservoirs contain enormous micro/nanopores, in which the fluid flow exhibits micro/nanoscale flow and has a slip length. Furthermore, the porous size distribution [...] Read more.
The prediction of permeability and the evaluation of tight oil reservoirs are very important to extract tight oil resources. Tight oil reservoirs contain enormous micro/nanopores, in which the fluid flow exhibits micro/nanoscale flow and has a slip length. Furthermore, the porous size distribution (PSD), stress sensitivity, irreducible water, and pore wall effect must also be taken into consideration when conducting the prediction and evaluation of tight oil permeability. Currently, few studies on the permeability model of tight oil reservoirs have simultaneously taken the above factors into consideration, resulting in low reliability of the published models. To fill this gap, a fractal permeability model of tight oil reservoirs based on fractal geometry theory, the Hagen–Poiseuille equation (H–P equation), and Darcy’s formula is proposed. Many factors, including the slip length, PSD, stress sensitivity, irreducible water, and pore wall effect, were coupled into the proposed model, which was verified through comparison with published experiments and models, and a sensitivity analysis is presented. From the work, it can be concluded that a decrease in the porous fractal dimension indicates an increase in the number of small pores, thus decreasing the permeability. Similarly, a large tortuous fractal dimension represents a complex flow channel, which results in a decrease in permeability. A decrease in irreducible water or an increase in slip length results in an increase in flow space, which increases permeability. The permeability decreases with an increase in effective stress; moreover, when the mechanical properties of rock (elastic modulus and Poisson’s ratio) increase, the decreasing rate of permeability with effective stress is reduced. Full article
(This article belongs to the Special Issue Applications of Fractal Geometry Theory in Porous Media)
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