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

Xin Liu, Yuepeng Wang, Tianjiao Li (), Zhengzhao Liang, Siwei Meng, Licai Zheng and Na Wu
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Xin Liu: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Yuepeng Wang: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Tianjiao Li: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Zhengzhao Liang: State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Siwei Meng: PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China
Licai Zheng: Sanying Precision Instruments Co., Ltd., Tianjin 300399, China
Na Wu: College of Civil Engineering and Architecture, Dalian University, Dalian 116622, China

Mathematics, 2025, vol. 13, issue 17, 1-22

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.

Keywords: hydraulic fracturing; microstructure heterogeneity; quartz grains; ostracod laminae; coupled hydro-mechanical damage simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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