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Fractal Fract
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Applications of Fractal Geometry Theory in Porous Media
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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: closed (31 January 2023) | Viewed by 8732

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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (5 papers)

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Research

20 pages, 11409 KiB  
Article
Application of Multifractal Analysis Theory to Interpret T2 Cutoffs of NMR Logging Data: A Case Study of Coarse Clastic Rock Reservoirs in Southwestern Bozhong Sag, China
by Zefan Wang, Yanbin Yao, Ruying Ma, Xiaona Zhang and Guibin Zhang
Fractal Fract. 2023, 7(1), 57; https://doi.org/10.3390/fractalfract7010057 - 02 Jan 2023
Cited by 1 | Viewed by 1246
Abstract
The Paleocene Kongdian Formation coarse clastic rock reservoir in Bozhong Sag is rich in oil and gas resources and has huge exploration potential. However, the coarse clastic rock reservoir has the characteristics of a complex pore structure and strong heterogeneity, which restrict the [...] Read more.
The Paleocene Kongdian Formation coarse clastic rock reservoir in Bozhong Sag is rich in oil and gas resources and has huge exploration potential. However, the coarse clastic rock reservoir has the characteristics of a complex pore structure and strong heterogeneity, which restrict the accuracy of evaluating the reservoir’s physical properties, such as porosity and permeability, for field evaluation. Nuclear magnetic resonance (NMR) technology has become a popular methods for unconventional reservoir evaluation because it can obtain abundant reservoir physical property information and because of its ability to identify fluid characteristics information. The transverse relaxation time (T2) cutoff (T2C) value is an important input parameter in the application of NMR technology. The accuracy of the T2C value affects the accuracy of the reservoir evaluation. The standard method for determining the T2C value requires a series of complicated centrifugation experiments in addition to the NMR experiments, and its application scope is limited by obtaining enough core samples. In this study, 14 core samples from the coarse clastic rock reservoir in the southwestern Bozhong sag of the Bohai Bay Basin were selected, and NMR measurements were carried out under the conditions of fully saturated water and irreducible water to determine the T2C value. Based on the multifractal theory, the NMR T2 spectrum of the saturated sample was analyzed, and the results show that the NMR T2 distribution of the saturated sample has multifractal characteristics, and the multifractal parameter Dq and the singular intensity range Δα have a strong correlation with the T2C value. Thus, based on multiple regression analyses of the multifractal parameters with the experimental T2C value of 10 core samples, we propose a method to predict the T2C value. After applying this method to 4 samples that were not used in the modeling, we confirmed that this method can be used to predict the T2C value of core samples. Furthermore, we expanded this method to the field application of a production well in Bozhong sag by adding an empirical index in the model. The new model can be used to directly calculate the T2C value of NMR logging data, and it does not require any other extra data, such as those from core analysis. This method is applicable in fast reservoir evaluations by only using NMR logging data in the field. The research results improve the accuracy of field NMR logging reservoir evaluations. Full article
(This article belongs to the Special Issue Applications of Fractal Geometry Theory in Porous Media)
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19 pages, 4693 KiB  
Article
Numerical Investigation on Effective Elastic Modulus of Multifractal Porous Materials
by Yanan Xi, Lijie Wang, Yun Gao and Dong Lei
Fractal Fract. 2023, 7(1), 3; https://doi.org/10.3390/fractalfract7010003 - 20 Dec 2022
Cited by 1 | Viewed by 1003
Abstract
The design of a novel material necessitates a fundamental understanding of its structure–property relation. Inorganic porous materials (media) such as natural soil and rock, and artificial ceramic and cement, exhibit multifractal characteristics in view of their structural heterogeneity. This paper presents a numerical [...] Read more.
The design of a novel material necessitates a fundamental understanding of its structure–property relation. Inorganic porous materials (media) such as natural soil and rock, and artificial ceramic and cement, exhibit multifractal characteristics in view of their structural heterogeneity. This paper presents a numerical investigation of the effective elastic modulus of multifractal porous materials. Two types of deterministic and stochastic cascading algorithms are employed to synthesize the multifractal fields, and then a mathematical formula is proposed to perform the conversion from the intensity of a multifractal field to the local elastic modulus of a multifractal porous material. Furthermore, a finite element method is used to achieve the homogenization of the local elastic modulus. Special attention is paid to the dependence of the effective elastic modulus on the structural heterogeneity of multifractal porous materials. Full article
(This article belongs to the Special Issue Applications of Fractal Geometry Theory in Porous Media)
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14 pages, 3290 KiB  
Article
Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric
by Lili Sui, Heyuan Wang, Jinsui Wu, Jiwei Zhang, Jian Yu, Xinyu Ma and Qiji Sun
Fractal Fract. 2022, 6(7), 353; https://doi.org/10.3390/fractalfract6070353 - 23 Jun 2022
Cited by 7 | Viewed by 1651
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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12 pages, 569 KiB  
Article
The Hausdorff Dimension and Capillary Imbibition
by Didier Samayoa, Ernesto Pineda León, Lucero Damián Adame, Eduardo Reyes de Luna and Andriy Kryvko
Fractal Fract. 2022, 6(6), 332; https://doi.org/10.3390/fractalfract6060332 - 16 Jun 2022
Cited by 2 | Viewed by 1433
Abstract
The time scaling exponent for the analytical expression of capillary rise ℓ∼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 ℓ∼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/dℓ, where dℓ is the chemical dimension of F. The imbibition measured by the chemical distance ℓg 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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17 pages, 33572 KiB  
Article
A Fractal Permeability Model of Tight Oil Reservoirs Considering the Effects of Multiple Factors
by Zhongwei Wu, Chuanzhi Cui, Yong Yang, Chuanbao Zhang, Jian Wang and Xin Cai
Fractal Fract. 2022, 6(3), 153; https://doi.org/10.3390/fractalfract6030153 - 11 Mar 2022
Cited by 2 | Viewed by 1982
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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