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Fractal Analysis in Unconventional Reservoirs: Theory and Applications

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

Deadline for manuscript submissions: 31 May 2026 | Viewed by 4384

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Special Issue Editors

Dr. Dianshi Xiao

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Guest Editor

School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China
Interests: geological evaluation of unconventional reservoirs; experimental petrophysical characterization of complex reservoirs

Dr. Xixin Wang

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Guest Editor

School of Geosciences, Yangtze University, Wuhan 430100, China
Interests: reservoir characterization and modeling; AI-based geological interpretation

Dr. Nengwu Zhou

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Guest Editor

Sanya Offshore Oil & Gas Research Institute, Northeast Petroleum University, Sanya 572025, China
Interests: formation mechanism; characterization of unconventional reservoirs

Special Issue Information

Dear Colleagues,

The study of unconventional reservoirs has emerged as a critical frontier in energy exploration and development, driven by the unique challenges posed by their complex and heterogeneous pore structures. Fractal theory, with its ability to quantify irregular and self-similar patterns across multiple scales, has become an indispensable tool for characterizing the pore structure of unconventional reservoirs. By integrating fractal mathematics with advanced pore structure analysis techniques, researchers are gaining unprecedented insights into the connectivity, permeability, and fluid storage mechanisms of unconventional reservoirs—from shale and tight sandstones to coalbed methane formations. These advancements not only enhance our understanding of reservoir behavior but also play a pivotal role in evaluating reservoir quality, optimizing hydrocarbon recovery strategies, and reducing environmental risks associated with extraction processes.

The focus of this Special Issue is to showcase cutting-edge research that advances the theory, methodology, and application of fractal characterization and pore structure analysis in unconventional reservoirs. We aim to bring together interdisciplinary studies that bridge mathematics, geology, petroleum engineering, and material science, providing a comprehensive platform for exchanging innovative ideas and technical breakthroughs.

Dr. Dianshi Xiao
Dr. Xixin Wang
Dr. Nengwu Zhou
Guest Editors

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Keywords

fractal models for quantifying pore size distribution and surface roughness
multiscale pore structure analysis using fractal theory
fractal-based permeability and fluid flow simulation in low-permeability
correlation between fractal dimensions and reservoir properties (e.g., porosity, oiliness)
machine learning integrated with fractal analysis for reservoir classification and evaluation
fractal characterization of diagenetic processes and their impact on pore evolution
application of fractal theory in enhanced oil recovery (EOR) techniques for unconventional resources

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Published Papers (7 papers)

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Research

23 pages, 4334 KB

Open AccessArticle

Pore Structure and Fractal Characteristics of Low-Maturity Shales in the Upper-Fourth Shahejie Formation, Minfeng Sag

by Chijun Huang, Shaohua Li, Changsheng Lu, Zhihui Peng, Long Jiang, Yu Li and Siyu Yu

Fractal Fract. 2026, 10(4), 271; https://doi.org/10.3390/fractalfract10040271 - 21 Apr 2026

Viewed by 273

Abstract

An integrated analysis incorporating total organic carbon (TOC) content measurement, X-ray diffraction (XRD), scanning electron microscopy (SEM), and gas adsorption experiments was performed on core samples from Well FY1-4 of the upper-fourth Shahejie Formation (Es₄) in the Minfeng Sag. To address the lack of systematic research on the pore and fractal characteristics of organic-rich low-maturity shales in the Minfeng Sag (against the preponderance of studies on high-maturity shales), this study characterized the lithofacies, reservoir space and pore fractal features of the target low-maturity shale interval and clarified the sedimentary controls on lithofacies and key factors regulating pore fractal heterogeneity. The results reveal that the shale in the Es₄ of the study area exhibits low thermal maturity, with six distinct lithofacies identified. Organic-rich laminated calcareous shale lithofacies (RL-1) and organic-rich laminated calcareous/argillaceous mixed shale lithofacies (RL-2) represent the most favorable lithofacies, which are dominated by large mesopores and macropores. Their reservoir spaces were primarily composed of intergranular pores, intragranular pores, and organic pores, whereas the other lithofacies are dominated by small mesopores. The pore surface fractal dimension (D) was calculated using the Frenkel–Halsey–Hill (FHH) model based on low-temperature N₂ adsorption (LTNA) data. The meso-macropore system shows higher heterogeneity than the micropore system (D₂ > D₁). Both D₁ and D₂ exhibit a weak negative correlation with TOC and carbonate content and a positive correlation with clay content. In the initial depositional stage of the Es₄, the arid climate, weak terrigenous input, shallow lake depth, and high salinity resulted in the strongly reducing saline depositional environment with relatively low organic matter enrichment. As the climate became progressively humid in the middle and late stages, hydrodynamic conditions intensified, leading to a lithofacies transition from mixed shales to argillaceous calcareous shales. Increased TOC and carbonate contents reduce the pore fractal dimension of shale. Smaller fractal dimensions directly indicate a simple pore structure and regular pore surface in the shale oil reservoir of the Minfeng Sag, where reservoir space is dominated by large pores such as intercrystalline pores and dissolved pores. Such pore characteristics are more favorable for the enrichment of shale oil. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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15 pages, 2682 KB

Open AccessArticle

Pore Structure and Multifractal Characteristics of Tight Sandstone: A Case Study of the Jurassic Sangonghe Formation in Northern Turpan-Hami Basin, NW China

by Jiacheng Huang, Zongbao Liu, Bin Hao and Zhiwen Dong

Fractal Fract. 2026, 10(4), 259; https://doi.org/10.3390/fractalfract10040259 - 15 Apr 2026

Viewed by 272

Abstract

Pore structure and multifractal characteristics are two critical indicators for evaluating the heterogeneity of tight sandstone reservoirs. An integrated analysis comprising physical property tests, X-ray diffraction, casting thin sections, scanning electron microscopy, high-pressure mercury intrusion (HPMI), and constant-rate mercury intrusion (CRMI) is conducted on five samples from the Jurassic Sangonghe Formation in the northern Turpan-Hami Basin to investigate the full-scale pore size distribution (FPSD) and its multifractal characteristics. The results indicate that the pores in tight sandstone are mainly residual intergranular pores, dissolution pores, intercrystalline pores, and microfractures. The FPSD exhibits a bimodal or trimodal pattern, with dominant pore sizes ranging from 0.00516 μm to 1.15

μ m

. Two key multifractal parameters, the multifractal dimension range (

D_{m i n} - D_{m a x}

) and the relative dispersion (

R_{d}

), were utilized to effectively characterize pore structure heterogeneity and asymmetry. Higher

D_{m i n} - D_{m a x}

values correspond to stronger heterogeneity, whereas lower

R_{d}

values indicate a dominance of nanoscale pores. Furthermore,

D_{m i n} - D_{m a x}

and

R_{d}

exhibit negative correlations with permeability and clay mineral content, and positive correlations with feldspar content. This study demonstrates the utility of FPSD in characterizing pore structure and highlights the applicability of multifractal theory in assessing the heterogeneity of tight sandstone reservoirs. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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26 pages, 7013 KB

Open AccessArticle

Comparative Study on Pore Characteristics and Methane Adsorption Capacity of the Lower Silurian Longmaxi Shales with Different Lithofacies

by Xiaoming Zhang, Changcheng Han, Lanpu Chen, Jian Wang, Wanzhong Shi, Zhiguo Shu, Xiaomei Zhang, Hao Chen, Lin Meng and Yuzuo Liu

Fractal Fract. 2026, 10(3), 154; https://doi.org/10.3390/fractalfract10030154 - 27 Feb 2026

Viewed by 338

Abstract

In this study, shale samples with diverse lithofacies from the Lower Silurian Longmaxi Formation in the Fuling Field were investigated to evaluate the variations in pore characteristics and methane adsorption capacity (MAC) of different shale lithofacies. A set of experiments were performed, such as total organic carbon (TOC) content, X-ray diffraction (XRD), field emission–scanning electron microscopy (FE-SEM), low-pressure gas (CO₂/N₂) adsorption, and high-pressure methane adsorption. Combined with TOC content and mineral composition, three types of shale lithofacies were identified, including organic-rich (OR) argillaceous-rich siliceous (S-3) shale lithofacies, organic-moderate (OM) argillaceous/siliceous mixed (M-2) shale lithofacies, and organic-lean (OL) siliceous-rich argillaceous (CM-1) shale lithofacies. Through detailed comparative analyses, we found that OR S-3 shales possess the maximum TOC content, the most developed heterogeneous organic micro-mesopores, the largest pore volume (PV), and the highest pore surface area (PSA); consequently, they display the strongest MAC. Conversely, OL CM-1 shales have the lowest TOC content and the highest clay content, and thus the smallest PSA and the poorest methane adsorption performance. In conclusion, considering the excellent gas storage potential, sustained shale gas production, and brittle response to hydraulic fracturing, OR S-3 shales are superior to shale gas exploration and exploitation compared with OM M-2 and OL CM-1 shales. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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24 pages, 6929 KB

Open AccessArticle

Multifractal Characteristics of Tight Sandstone Pore Structure Based on Nuclear Magnetic Resonance in Benxi Formation, Ordos Basin, China

by Peipei Liu, Yuming Liu, Jiagen Hou, Lei Bao and Qi Chen

Fractal Fract. 2026, 10(3), 153; https://doi.org/10.3390/fractalfract10030153 - 27 Feb 2026

Viewed by 287

Abstract

Quantifying the heterogeneity of pore-throat structure and evaluating reservoir quality are of great significance in the exploration and development of tight sandstone oil and gas reservoirs. This study focused on 10 samples of tight sandstone from the Benxi Formation in the Ordos Basin of China. Based on nuclear magnetic resonance (NMR) and combined with the theory of multifractal analysis to calculate multifractal parameters, the pore structure and fractal characteristics of tight sandstone reservoirs were characterized. The results showed that the dominant minerals are quartz, clay minerals, rock fragments and calcite, while feldspar content is relatively minor. The NMR T₂ spectra all exhibited bimodal characteristics. The pore size distribution of the reservoir has multifractal characteristics. The multifractal parameters D_min-D_max range from 2.02 to 2.88, D_min/D_max ranges from 3.69 to 5.11, and △α ranges from 2.441 to 3.316. Different mineral components had different effects on the fractal characteristics. The increase in quartz content retained more primary intergranular pores, affecting the fractal dimension of large pores, and weakening the heterogeneity of the pores. The increase in calcite and clay minerals corresponded to the enhancement of micropores and mesopores, increasing the heterogeneity of the pore structure. Based on the reservoir classification using multifractal parameters, the evolution of pore heterogeneity in tight sandstone rocks can be quantified, thereby effectively evaluating reservoir quality. Overall, reservoirs with larger D_min-D_max and D_min/D_max values, smaller △α, weaker porosity heterogeneity, and better connectivity are favorable areas for hydrocarbon exploration and development. The comprehensive fractal characterization of tight sandstone reservoirs demonstrates the applicability of multifractal dimensions in characterizing the heterogeneity of pore structures in tight sandstones, and is a key factor in improving the exploration effectiveness and development benefits of tight sandstone oil and gas reservoirs. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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30 pages, 8888 KB

Open AccessArticle

Influence of Key Parameters on the Fractal Dimension and Impact on Gas-Bearing Capacity: A Case Study from the Lower Shihezi Formation, Ordos Basin

by Lei Bao, Yuming Liu, Qi Chen, Zhanyang Zhang and Jiagen Hou

Fractal Fract. 2025, 9(12), 799; https://doi.org/10.3390/fractalfract9120799 - 5 Dec 2025

Cited by 1 | Viewed by 678

Abstract

Pore–throat structure and gas distribution are critical factors in evaluating the quality of tight sandstone reservoirs and hydrocarbon resource potential. Twelve tight sandstone samples from the Lower Permian Shihezi Formation in Hangjin Banner, Ordos Basin, were selected for CTS, X-ray diffraction, HPMI, and gas displacement NMR analyses. By converting the T₂ spectra into pore–throat distributions and applying fractal methods, we quantitatively analyzed the influences of multiple factors on gas distribution characteristics across different pore–throat sizes. The main results are as follows: All samples exhibit a three-stage pore–throat distribution, defining mesopores, micropores, and nanopores; quartz content mainly influences the fractal dimension of mesopores by enhancing structural stability and gas storage capacity, whereas clay minerals control the fractal characteristics of nanopores by increasing pore–throat complexity. An increase in clay mineral content increases the fractal dimension, indicating stronger reservoir heterogeneity and consequently poorer gas-bearing capacity. Larger pore–throat parameters (R_m, S_k, and S_max) correspond to lower fractal dimensions, indicating better connectivity and greater gas storage capacity. Among these factors, pore–throat parameters exert the most significant influence on the fractal dimensions of mesopores and micropores, jointly determining the overall connectivity and the upper limit of the reservoir’s gas-bearing capacity. The results demonstrate that larger pore–throat parameters and higher quartz content help reduce the fractal dimension and enhance the gas-bearing capacity of tight reservoirs. This research enhances understanding of pore–throat structures and gas-bearing capacity in low-permeability reservoirs and provides a theoretical basis for exploration, development, and enhanced recovery in the study area. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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22 pages, 8911 KB

Open AccessArticle

Heterogeneity and Cause Analysis of Organic Pore in Upper Permian Shale from Western Hubei, South China

by Yang Liu, Yuying Zhang, Zhiliang He, Shuangfang Lu, Rui Yang and Yifei Li

Fractal Fract. 2025, 9(11), 731; https://doi.org/10.3390/fractalfract9110731 - 12 Nov 2025

Cited by 1 | Viewed by 767

Abstract

Organic pores serve as crucial storage spaces for shale gas, whose morphology and structure vary significantly among different types of organic matter, directly influencing the storage and seepage capacity of shale gas. The Upper Permian shale in the Western Hubei Trough formed in diverse sedimentary facies and has undergone multiple geological activities, resulting in strong heterogeneity of organic pores across different strata and regions. To figure out the heterogeneous characteristics of organic pores and the forming reason, the occurrence state of organic matter, pore morphology, and structural parameters (pore size, specific surface area, pore volume, and fractal dimension) of the Upper Permian shale in Western Hubei, have been discussed in detail, based on the data of field emission scanning electron microscopy and low-temperature nitrogen adsorption experiments conducted on the extracted organic matter. On this basis, fractal dimension theory was applied to discuss the heterogeneity of organic pores in different layers, and the reason for heterogeneity has been analyzed in detail. The results indicate that the occurrence mode of organic matter in different layers presents various characteristics: in the Gufeng Formation, the organic matters distribute primarily dispersed in flocculent state; at the bottom of Wujiaping Formation, they occur as isolated individuals, while the organic matters turn into discontinuous laminated distribution in the middle and upper Wujiaping Formation; in the Dalong Formation, the organic matters show continuous parallel banded distribution. Moreover, the morphology and structural parameters of organic pores exhibit obvious changes from the Gufeng Formation to the Dalong Formation: (a) the pore morphology shows the changed trend as extremely complex-simple-complex; (b) the specific surface area and pore volume follow the trend as large-small-large; (c) the pore size distribution displays in the pattern of bimodal-unimodal-bimodal; (d) the data of fractal dimension show the variation of high–low–high. Overall, the various sedimentary environments during the Upper Permian shale depositional period determined the differences in organic sources, which dominated the heterogeneity of organic pores in shale. These data clarify the development and variation characteristics of organic matter pores under different depositional environments, providing a theoretical basis for shale gas exploration and development during the transition from marine to marine–continental facies. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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26 pages, 7763 KB

Open AccessArticle

Reservoir Characteristics and Influencing Factors of Different Lithofacies of WF-LMX Formation Shale in Zigong Area, Sichuan Basin

by Changchang Wang, Qinghai Xu, Litao Xu, Fancheng Zeng, Huan Li, Zhicheng Huang, Jiayi Li, Kun Wang and Mengyuan Li

Fractal Fract. 2025, 9(11), 706; https://doi.org/10.3390/fractalfract9110706 - 31 Oct 2025

Cited by 2 | Viewed by 925

Abstract

An integrated analysis including total organic carbon (TOC), X-ray diffraction (XRD), scanning electron microscopy (SEM), and gas adsorption experiments was conducted on core samples from the deep Wufeng–Longmaxi (WF-LMX) Formation in the Zigong area to characterize its lithofacies and reservoir characteristics and their influencing factors. The results suggest that eight distinct lithofacies are distinguished and argillaceous/calcareous mixed siliceous shale lithofacies (S-1) is the most optimal lithofacies. The pore surface fractal dimension (D) was derived by applying the Frenkel–Halsey–Hil (FHH) model to low-temperature N₂ adsorption (LTNA) data. The meso-macropore regime shows higher heterogeneity than the micropore regime (since D₂ > D₁). Both D₁ and D₂ show a significant positive relation with TOC and carbonate content, a slight negative correlation with quartz content, and no clear link with clay content. In the initial depositional stage of the LMX Formation, a low-energy, stagnant, and strongly reducing environment facilitated the accumulation of siliceous biogenic sediments, leading to the formation of siliceous shale characterized by high paleoproductivity. In the middle to late stages of LMX Formation deposition, increased input of terrigenous clastic material, shallower water depths, and the gradual disruption of the anoxic conditions resulted in diminished paleoproductivity, causing a transition from siliceous shale to a mixed shale lithofacies. Increased TOC and carbonate content enhance pore heterogeneity, with TOC predominantly influencing micropores and carbonates controlling macropores. In contrast, higher quartz content inhibits pore development. Full article

(This article belongs to the Special Issue Fractal Analysis in Unconventional Reservoirs: Theory and Applications)

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