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Fractal Fract
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Flow and Transport in Fractal Models of Rock Mechanics
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Flow and Transport in Fractal Models of Rock Mechanics

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

Deadline for manuscript submissions: 31 October 2025 | Viewed by 5293

Special Issue Editor

Dr. Kouqi Liu

E-Mail Website
Guest Editor
Institute of Energy, Peking University, Beijing 100871, China
Interests: fractal models; reservoir characterization; rock mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Flow and transport in fractal models have gained significant attention in the field of rock mechanics, particularly in the context of oil and gas production. Fractal models provide a powerful framework for understanding the complex behavior of fluid flow and transport in porous media with intricate geometries and heterogeneous structures. Fractal models can be applied in the study of flow and transport phenomena in oil and gas reservoirs. Additionally, fractal models, characterized by their self-similarity and non-integer dimensions, offer a versatile approach to capturing the multiscale nature of rock formations. These models consider the hierarchical arrangement of pores and fractures within the rock matrix, which can greatly influence fluid flow and transport properties. By incorporating fractal dimensions and scaling laws, researchers have been able to develop mathematical representations and computational simulations that accurately describe the behavior of fluids in such complex systems. In the oil and gas industry, understanding the flow and transport processes is crucial for optimizing production strategies, estimating reserves, and designing efficient recovery methods. Fractal models enable the analysis of key parameters such as permeability, porosity, and connectivity, which directly impact fluid flow behavior and can help predict production performance. Additionally, the use of fractal models allows for the investigation of transport phenomena, including dispersion, diffusion, and mixing, which are essential for assessing the efficiency of enhanced oil recovery techniques.

The focus of this Special Issue is to emphasize the significance of fractal models in providing valuable insights into the intricate flow and transport processes occurring in rock formations. Topics may include (but are not limited to):

  • Fractal-based characterization of reservoir heterogeneity;
  • Fractal modeling of fluid flow in unconventional reservoirs;
  • Fractal analysis of fracture networks in shale formations;
  • Transport phenomena in fractal porous media;
  • Fractal-based simulation methods for reservoir engineering;
  • Flow and transport in naturally fractured reservoirs using fractal models;
  • Fractal-based modeling of multiphase flow in porous media;
  • Fractal analysis of permeability in fractured reservoirs;
  • Fractal-based approaches for enhanced oil recovery in unconventional reservoirs;
  • New fractal model development;
  • Numerical simulation in fractal porous media.

Dr. Kouqi Liu
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.

Keywords

  • fractal models
  • rock mechanics
  • transport process
  • oil and gas industry
  • reservoir characterization
  • numerical solution

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Published Papers (4 papers)

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Research

21 pages, 18391 KiB  
Article
Multifractal Analysis of Geological Data Using a Moving Window Dynamical Approach
by Gil Silva, Fernando Pellon de Miranda, Mateus Michelon, Ana Ovídio, Felipe Venturelli, Letícia Moraes, João Ferreira, João Parêdes, Alexandre Cury and Flávio Barbosa
Fractal Fract. 2025, 9(5), 319; https://doi.org/10.3390/fractalfract9050319 - 16 May 2025
Viewed by 202
Abstract
Fractal dimension has proven to be a valuable tool in the analysis of geological data. For instance, it can be used for assessing the distribution and connectivity of fractures in rocks, which is important for evaluating hydrocarbon storage potential. However, while calculating a [...] Read more.
Fractal dimension has proven to be a valuable tool in the analysis of geological data. For instance, it can be used for assessing the distribution and connectivity of fractures in rocks, which is important for evaluating hydrocarbon storage potential. However, while calculating a single fractal dimension for an entire geological profile provides a general overview, it can obscure local variations. These localized fluctuations, if analyzed, can offer a more detailed and nuanced understanding of the profile’s characteristics. Hence, this study proposes a fractal characterization procedure using a new strategy based on moving windows applied to the analysis domain, enabling the evaluation of data multifractality through the Dynamical Approach Method. Validations for the proposed methodology were performed using controlled artificial data generated from Weierstrass–Mandelbrot functions. Then, the methodology was applied to real geological profile data measuring permeability and porosity in oil wells, revealing the fractal dimensions of these data along the depth of each analyzed case. The results demonstrate that the proposed methodology effectively captures a wide range of fractal dimensions, from high to low, in artificially generated data. Moreover, when applied to geological datasets, it successfully identifies regions exhibiting distinct fractal characteristics, which may contribute to a deeper understanding of reservoir properties and fluid flow dynamics. Full article
(This article belongs to the Special Issue Flow and Transport in Fractal Models of Rock Mechanics)
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20 pages, 11532 KiB  
Article
Experimental Study of Confining Pressure-Induced Fracture Network for Shale Gas Reservoir Under Triaxial Compression Conditions
by Jinxuan Han, Ming Gao, Yubo Wu, Ali Raza, Pei He, Jianhui Li, Yanjun Lu, Manping Yang and Hongjian Zhu
Fractal Fract. 2025, 9(5), 311; https://doi.org/10.3390/fractalfract9050311 - 13 May 2025
Viewed by 248
Abstract
The experimental study of shale fracture development is very important. As a channel of permeability, a fracture has a great influence on the development of shale gas. This study presents the results of a fracture evaluation in the Silurian Longmaxi Shale using the [...] Read more.
The experimental study of shale fracture development is very important. As a channel of permeability, a fracture has a great influence on the development of shale gas. This study presents the results of a fracture evaluation in the Silurian Longmaxi Shale using the laboratory triaxial compression experiments and CT reconstruction, considering both mechanical properties and fracture network multi-dimensional quantitative characterization. The results indicate that the plastic deformation stage of shale lasts longer under high confining pressure, whereas radial deformation is restricted. Confining pressure has a nice linear connection with both compressive strength and elastic modulus. The 2D fractal dimension of radial and vertical cracks is 1.09–1.28 when the confining pressure is between 5 and 25 MPa. The 3D fractal dimension of the fracture is 2.08–2.16. There is a linear negative correlation at high confining pressure (R2 > 0.80) and a weak linear association between the 3D fractal dimension of the fracture and confining pressure at low confining pressure. The fracture angle calculated by the volume weight of multiple main cracks has a linear relationship with the confining pressure (R2 > 0.89), and its value is 73.90°–52.76°. The fracture rupture rate and fracture complexity coefficient are linearly negatively correlated with confining pressure (R2 > 0.82). The Euler number can well characterize the connectivity of shale fractures, and the two show a strong linear positive correlation (R2 = 0.98). We suggest that the bedding plane gap compression, radial deformation limitation, and interlayer effect weakening are efficient mechanisms for the formation of shale fracture networks induced by confining pressure, and that confining pressure plays a significant role in limiting and weakening the development of shale fractures, based on the quantitative characterization results of fractures. Full article
(This article belongs to the Special Issue Flow and Transport in Fractal Models of Rock Mechanics)
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18 pages, 2500 KiB  
Article
Using Fractal Theory to Study the Influence of Movable Oil on the Pore Structure of Different Types of Shale: A Case Study of the Fengcheng Formation Shale in Well X of Mahu Sag, Junggar Basin, China
by Hong Zhang, Zhengchen Zhang, Zhenlin Wang, Yamin Wang, Rui Yang, Tao Zhu, Feifei Luo and Kouqi Liu
Fractal Fract. 2024, 8(4), 242; https://doi.org/10.3390/fractalfract8040242 - 20 Apr 2024
Cited by 6 | Viewed by 1729
Abstract
This study investigated the influence of movable oil on the pore structure of various shale types, analyzing 19 shale samples from Well X in the Mahu Sag of the Junggar Basin. Initially, X-ray diffraction (XRD) analysis classified the shale samples. Subsequently, the geochemical [...] Read more.
This study investigated the influence of movable oil on the pore structure of various shale types, analyzing 19 shale samples from Well X in the Mahu Sag of the Junggar Basin. Initially, X-ray diffraction (XRD) analysis classified the shale samples. Subsequently, the geochemical properties and pore structures of the samples, both pre and post oil Soxhlet extraction, were comparatively analyzed through Total Organic Carbon (TOC) content measurement, Rock-Eval pyrolysis, and nitrogen adsorption experiments. Additionally, fractal theory quantitatively described the impact of movable oil on the pore structure of different shale types. Results indicated higher movable oil content in siliceous shale compared to calcareous shale. Oil extraction led to a significant increase in specific surface area and pore volume in all samples, particularly in siliceous shale. Calcareous shale predominantly displays H2–H3 type hysteresis loops, indicating a uniform pore structure with ink-bottle-shaped pores. Conversely, siliceous shale exhibited diverse hysteresis loops, reflecting its complex pore structure. The fractal dimension in calcareous shale correlated primarily with pore structure, exhibiting no significant correlation with TOC content before or after oil extraction. Conversely, the fractal dimension changes in siliceous shale samples do not have a clear correlation with either TOC content or pore structure, suggesting variations may result from both TOC and pore structure. Full article
(This article belongs to the Special Issue Flow and Transport in Fractal Models of Rock Mechanics)
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13 pages, 12732 KiB  
Article
The Classification and Evaluation of an Interlayer Shale Oil Reservoir Based on the Fractal Characteristics of Pore Systems: A Case Study in the HSN Area, China
by Changsheng Lu, Xixin Wang, Shuwei Ma, Shaohua Li, Ting Xue and Qiangqiang Li
Fractal Fract. 2024, 8(3), 167; https://doi.org/10.3390/fractalfract8030167 - 14 Mar 2024
Cited by 3 | Viewed by 1761
Abstract
The evaluation of shale reservoir quality is of great significance for the exploration and development of shale oil. To more effectively study the distribution characteristics of shale reservoir quality, thin-section observation, scanning electron microscopy and pressure-controlled porosimetry were used to obtain the pore [...] Read more.
The evaluation of shale reservoir quality is of great significance for the exploration and development of shale oil. To more effectively study the distribution characteristics of shale reservoir quality, thin-section observation, scanning electron microscopy and pressure-controlled porosimetry were used to obtain the pore structure characteristics of shale in Chang 7, including pore types, pore size distribution, etc. In addition, the fractal dimensions of the shale samples were calculated based on pressure-controlled porosimetry data. The results show that residual interparticle pores, dissolution pores and clay-dominated pores were the main pore types. The overall pore size was mainly distributed between 3 nm and 50 μm. The pore system was divided into four types using fractal features, and the shale reservoir was divided into four types based on the proportion of different types of pore system. In different types of reservoirs, the production capacity of exploration wells varies significantly, as does the production capacity of horizontal wells. The classification of shale reservoirs using mercury intrusion fractal analysis proved to be suited for the efficient development of Chang 7 shale oil reservoirs. Full article
(This article belongs to the Special Issue Flow and Transport in Fractal Models of Rock Mechanics)
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