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Fractal Fract
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Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow...
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Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: 31 October 2026 | Viewed by 3579

Special Issue Editors

Prof. Dr. Meng Wang

E-Mail Website
Guest Editor
School of Resources and Geosciences, China University of Mining & Technology, Xuzhou 221116, China
Interests: fractal analysis; fractal characteristics; gas adsorption; CO2 sequestration; unconventional reservoirs
Dr. Weidong Xie

E-Mail Website
Guest Editor
School of Earth Sciences, Northeast Petroleum University, Daqing 163318, China
Interests: fractal analysis; fractal characteristics; gas adsorption; CO2 sequestration; unconventional reservoirs; pore structure

Special Issue Information

Dear Colleagues,

The field of Fractal Analysis for Gas Dynamics and Flow Modeling refers to the interdisciplinary of mathematical modeling and oil and gas reservoir geology, which serves the quantitative characterization and mathematical description of unconventional reservoir structures. These concepts focused on mathematical operations and precise evaluations of microscopic accumulation capacity, hydrocarbon-bearing ability, and mobility of coal, shale, and tight sandstone reservoirs. Focusing on the quantitative evaluation of reservoir classification and accurate prediction of hydrocarbon production. Additionally, the use of fractal analysis and modeling in unconventional reservoir structure and behavior provides theoretical reference for enhancing hydrocarbon recovery.

The focus of this Special Issue is to continue to advance research on topics relating to the theory, design, implementation, and application of fractal analysis and modeling in gas dynamics and flow modeling. Topics that are invited for submission include (but are not limited to):

  • Fractal theories for flow modeling;
  • Fractal descriptions of reservoir properties;
  • Fractal pore structure and topology analysis;
  • Fractal-based reservoir quality evaluation;
  • Fractal modeling of hydrocarbon transport in tight formations;
  • Fractal characterization of migration and accumulation processes;
  • Fractal modeling of hydrocarbon content and mobility evolution;
  • Fractals in fracture networks and dynamic permeability.

Prof. Dr. Meng Wang
Dr. Weidong Xie
Guest Editors

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 250 words) can be sent to the Editorial Office for assessment.

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 and fractional theory
  • fractal characteristics
  • gas dynamics
  • flow modeling
  • CO2 sequestration
  • pore structure
  • unconventional reservoirs
  • oil and gas migration

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

41 pages, 8076 KB  
Article
THMD Coupling Modelling and Crack Propagation Analysis of Coal Rock Under In Situ Liquid Nitrogen Fracturing
by Qiang Li, Yunbo Li, Dangyu Song, Rongqi Wang, Jienan Pan, Zhenzhi Wang and Chengtao Wang
Fractal Fract. 2026, 10(4), 274; https://doi.org/10.3390/fractalfract10040274 - 21 Apr 2026
Viewed by 388
Abstract
Liquid nitrogen (LN2) fracturing is a highly promising stimulation technology for unconventional reservoirs. Understanding its in situ fracture network formation mechanism is essential for engineering practice. This study investigates coal rock fracturing driven by the synergistic effect of thermal stress and [...] Read more.
Liquid nitrogen (LN2) fracturing is a highly promising stimulation technology for unconventional reservoirs. Understanding its in situ fracture network formation mechanism is essential for engineering practice. This study investigates coal rock fracturing driven by the synergistic effect of thermal stress and fluid pressure during LN2 injection. A coupled thermal–hydraulic–mechanical–damage (THMD) numerical model is developed, incorporating in situ stress conditions and LN2 phase change behavior. Through true triaxial LN2 fracturing simulations validated against physical experiments, the multi-field dynamic coupling behavior is systematically analyzed, revealing the synergistic mechanism of fracture propagation and permeability enhancement under cryogenic conditions. The results show the following: (1) The proposed model effectively reproduces the true triaxial LN2 fracturing process, with simulation results in good agreement with physical experiments. (2) LN2 fracturing exhibits distinct stage-wise characteristics: cryogenic temperatures induce thermal stress that triggers micro-crack initiation; the self-enhancing effects of damage and permeability significantly promote fracture propagation; fluid pressure then becomes the dominant driving force. (3) Coal rock damage follows a four-stage evolution—wellbore crack initiation, stable propagation, unstable propagation, and through-going failure—ultimately forming a complex spatial fracture network. (4) The horizontal stress ratio is a key factor controlling fracture morphology: a single dominant fracture forms under a high stress difference, whereas a multi-directional complex network develops under equal confining pressure. Fractal analysis reveals significant anisotropy and a non-monotonic stress response in the fracture complexity, reflecting structural evolution from multi-directional propagation to main channel connection. This study provides theoretical support for understanding LN2 fracturing mechanisms and optimizing field treatment parameters. Full article
(This article belongs to the Special Issue Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling)
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23 pages, 5404 KB  
Article
Predicting NMR T2 Cutoff in Deep Tight Sandstones via Multifractal Analysis of Fully Water-Saturated Spectra: A Non-Destructive Approach
by Tengyu Wang, Zhidong Bao, Zhongcheng Li, Haotian Han, Zongfeng Li, Lei Li and Shuyue Ban
Fractal Fract. 2026, 10(2), 129; https://doi.org/10.3390/fractalfract10020129 - 19 Feb 2026
Viewed by 569
Abstract
Accurately determining the T2 cutoff value is critical for evaluating fluid mobility in deep tight reservoirs, yet strong pore structure heterogeneity challenges traditional methods. This study proposes a non-destructive prediction method based on multifractal singularity spectrum analysis of nuclear magnetic resonance T [...] Read more.
Accurately determining the T2 cutoff value is critical for evaluating fluid mobility in deep tight reservoirs, yet strong pore structure heterogeneity challenges traditional methods. This study proposes a non-destructive prediction method based on multifractal singularity spectrum analysis of nuclear magnetic resonance T2 spectra. Using 10 tight sandstone cores from the Denglouku Formation (Songliao Basin), we quantify the intrinsic relationship between multifractal parameters and T2 cutoff values. Results indicate that the minimum generalized dimension (Dmin) and singularity spectrum width (Δα) are not merely mathematical fits but reveal the physical mechanisms controlling fluid binding in micro-throats. A multivariate regression model based on these parameters significantly outperforms traditional methods in accuracy (R2 > 0.85). This approach provides a robust, non-destructive tool for identifying reservoir ‘sweet spots’ without compromising core integrity. Full article
(This article belongs to the Special Issue Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling)
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17 pages, 5793 KB  
Article
Calculation Method of Bound Water Saturation in Unconventional Reservoirs Using Fractal Theory
by Zhengyuan Qin, Feng Yang, Zhiguo Li, Jinlong Jia, Fuqiang Shen, Stephen Grebby, Stuart Marsh and Wenlong Shen
Fractal Fract. 2026, 10(1), 13; https://doi.org/10.3390/fractalfract10010013 - 25 Dec 2025
Viewed by 1909
Abstract
The irreducible water saturation of reservoirs seriously restricts the efficient drainage of unconventional energy sources. NMR logging can be used to determine parameters such as total porosity, effective porosity, irreducible water saturation, and permeability, which play an important role in oil and gas [...] Read more.
The irreducible water saturation of reservoirs seriously restricts the efficient drainage of unconventional energy sources. NMR logging can be used to determine parameters such as total porosity, effective porosity, irreducible water saturation, and permeability, which play an important role in oil and gas identification. T2 cut off value identification using the NMR T2 spectrum is the key to clarifying the irreducible water saturation of unconventional reservoirs. In this paper, saturation and centrifugal T2 spectra of sandstone and coal samples are used to study and calculate the T2 cut off value, with methods including single fractal dimension, multi-fractal dimension, and spectrum morphological discrimination; in addition, the applicability of these three methods in characterizing T2 cut off is discussed. According to the morphological difference of the saturated T2 spectrum, relationships between morphological parameters and the T2 cut off of four types of sample are described. The parameters related to T2 cut off can be divided into two types: (1) the first type includes morphological parameters main peak position (TM) and smaller-pore volume percentage (SPVP); with an increase of T2 cut off, TM increases linearly and SPVP decreases exponentially, and the correlation between SPVP and T2 cut off is stronger than that of TM. (2) The other type includes fractal parameters D2 (fractal dimension of larger pore), D−10 – D10, and D−10/D10; with the increase of T2 cut off, single and multi-fractal dimensions all increase linearly, and the correlation between D2 and T2 cut off is stronger than that of the multi-fractal dimension. When calculating the T2 cut off of samples with macro-pores developed, spectrum morphological methods should be used preferentially, while the fractal dimension discrimination methods need be used for the T2 cut off of samples with developed micro-pores. Then, the T2 cut off value prediction and evaluation system are described. The overall results of this work can provide a theoretical basis for the inversion of bound water content in the original formation. Full article
(This article belongs to the Special Issue Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling)
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