Fractal-Based Modeling and Quantitative Analysis of Hydraulic Fracture Complexity in Digital Cores

Hydraulic fracturing in shale reservoirs is affected by microscale structural and material heterogeneity. However, studies on fracture responses to the injection rate across different microstructural types remain limited. To examine the coupled effects of microstructure and flow rate on fracture propagation and mineral damage, high-fidelity digital rock models were constructed from SEM images of shale cores, representing quartz grains and ostracod laminae. Coupled hydro-mechanical damage simulations were conducted under varying injection rates. Fracture evolution and complexity were evaluated using three quantitative parameters: stimulated reservoir area, fracture ratio, and fractal dimension. The results show that fracture morphology and mineral failure are strongly dependent on both the structure and injection rate. All three parameters increase with the flow rate, with the ostracod model showing abrupt complexity jumps at higher rates. In quartz-dominated models, fractures tend to deflect and bypass weak cement, forming branches. In ostracod-lamina models, higher injection rates promote direct penetration and multi-point propagation, resulting in a radial–branched–nested fracture structure. Mineral analysis shows that quartz exhibits brittle failure under high stress, while organic matter fails more readily in tension. These findings provide mechanistic insights into the coupled influence of microstructure and flow rate on hydraulic fracture complexity, with implications for optimizing hydraulic fracturing strategies in heterogeneous shale formations.

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Publication Details

Journal
Mathematics
Published
2025-08-22
DOI
https://doi.org/10.3390/math13172700
Primary Topic
Hydraulic Fracturing and Reservoir Analysis
Type
article
Field-Weighted Citation Impact
0.00

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article

Fractal-Based Modeling and Quantitative Analysis of Hydraulic Fracture Complexity in Digital Cores

Zhengzhao Liang, Licai Zheng, Xin Liu, Siwei Meng et al.
Mathematics
Hydraulic Fracturing and Reservoir Analysis
article

Fractal-Based Modeling and Quantitative Analysis of Hydraulic Fracture Complexity in Digital Cores

Zhengzhao Liang, Licai Zheng, Xin Liu, Siwei Meng, Yue-Peng Wang, Tianjiao Li, Na Wu
article en

Abstract

Hydraulic fracturing in shale reservoirs is affected by microscale structural and material heterogeneity. However, studies on fracture responses to the injection rate across different microstructural types remain limited. To examine the coupled effects of microstructure and flow rate on fracture propagation and mineral damage, high-fidelity digital rock models were constructed from SEM images of shale cores, representing quartz grains and ostracod laminae. Coupled hydro-mechanical damage simulations were conducted under varying injection rates. Fracture evolution and complexity were evaluated using three quantitative parameters: stimulated reservoir area, fracture ratio, and fractal dimension. The results show that fracture morphology and mineral failure are strongly dependent on both the structure and injection rate. All three parameters increase with the flow rate, with the ostracod model showing abrupt complexity jumps at higher rates. In quartz-dominated models, fractures tend to deflect and bypass weak cement, forming branches. In ostracod-lamina models, higher injection rates promote direct penetration and multi-point propagation, resulting in a radial–branched–nested fracture structure. Mineral analysis shows that quartz exhibits brittle failure under high stress, while organic matter fails more readily in tension. These findings provide mechanistic insights into the coupled influence of microstructure and flow rate on hydraulic fracture complexity, with implications for optimizing hydraulic fracturing strategies in heterogeneous shale formations.

MathematicsVol. 13(17)
Tianjin University (CN), Dalian University of Technology (CN), Dalian University (CN), Research Institute of Petroleum Exploration and Development (CN)
National Natural Science Foundation of China, China Postdoctoral Science Foundation, Fundamental Research Funds for the Central Universities
Openalex Percentile: Top 78%
Hydraulic Fracturing and Reservoir Analysis
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