Key Takeaways & Executive Findings
- •• A new propagation criterion for hydraulic fractures is derived from the micro-cracking mechanism at the mineral particle scale, integrating pore pressure gradients and macroscopic boundary stresses. • The disturbed skeleton stress induced by gradient pore water pressure is equal to the pore water pressure difference, and the mechanical shape factor a/b is around 1 but greater than 0.5. • Micro-cracks initiate among mineral particles, connect to form micro-hydraulic fracture surfaces, and open to form macro-hydraulic fractures, with initiation occurring at the micro-cracking initiation pressure (MCIP). • The theoretical MCIP values calculated by the proposed criterion closely match experimental measurements, validating the model.
Abstract
Hydraulic fracture (HF) formed in rock significantly helps with the development of geo-energy and geo-resources. The HF formation condition was challenging to understand, with obscure rock micro-cracking mechanisms being a key factor. The rock micro-cracking mechanism under gradient pore water pressure was analyzed on the scale of mineral particles and it was combined with macroscopic boundary conditions of rock hydraulic fracturing, obtaining the propagation criterion of HF in rock based on the rock micro-cracking mechanism which was verified by experiment. The results show that the disturbed skeleton stress induced by the disturbance of gradient pore water pressure in rock equals the pore water pressure difference. The overall range of the defined mechanical shape factor a/b is around 1, but greater than 0.5. Under the combined influence of pore water pressure differences and macroscopic boundary stresses on the rock micro-cracking, micro-cracks form among rock mineral particles, micro-cracks connect to form micro-hydraulic fracture surfaces, and micro-hydraulic fracture surfaces open to form macro-hydraulic fractures. HF begins to form at the micro-cracking initiation pressure (MCIP), which was tested by keeping the HF tip near the initiation point. The theoretical value of MCIP calculated by the proposed propagation criterion is close to MCIP tested.
1. Introduction
The HFs formed in rock could create the channel for fluid transportation, improve the reservoir permeability, and reconstruct the rock structure, which is crucial in the development of geo-energy and geo-resources such as coal, oil, and gas etc. [1–3]. The initiation and propagation conditions of the HFs are one of the foundations for the theory revealing the propagation laws of HF and the important parameters in the scheme design of hydraulic fracturing engineering, which carry important research implications.
The initiation and propagation conditions of the HFs are theoretically delineated by the hydraulic fracture propagation criteria. The existing ones were given from various approaches, including stress (including the stress intensity factors), strain, deformation, and damage energy dissipation/ dissipating rate [4]. Among them, the hydraulic fracture propagation criteria on stress criterion have analytical solutions in mathematical form, whose parameters could be determined by conventional mechanical tests, and were widely used in practice. This kind of hydraulic fracture propagation criteria discussed two cases of initiation and propagation. (1) For the case of initiation, the most famous one may be the H-W formula proposed by Hubbert M.K. and Willis D.G. in 1957. The H-W formula was proposed based on the tensile stress criterion using the analytical solutions of the surrounding rock stress field around a circular hole [5]. The H-W formula may not take into account the effect of pore water pressure on the rock cracking deeply [6], and subsequent improved studies [6–8] consider it by adopting an indirect analogy method that compares pore pressure to thermal stress, which may not directly reveal the influencing mechanism of pore water pressure on the HF formation. (2) For the case of propagation, traditionally using the linear elastic fracture mechanics to explain the HF propagating would encounter obstacles in addressing the stress singularity issue since the fracture length significantly exceeds the fracture width in terms of the physical shape of the extended HF [4]. To address this, the stress intensity factors were introduced in the hydraulic fracture propagation criteria under the assumption of rock as a continuous medium. For example, the well-known Khristianovich-Geertsma-de Klerk (KGD) model [9] and the Perkins-Kern-Nordgren (PKN) model [10] both have the core idea of comparing the stress intensity factor (K) caused by principal stresses, fluid pressure within the HF, and pore pressure, with the fracture toughness (KⅠC) of the rock material to
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CAI Qingwang, HUANG Bingxiang, ZHAO Xinglong, XING Yuekun (2025). Propagation criterion of hydraulic fracture in rock based on the rock micro-cracking mechanism. SinoTechIntel Verified Research. https://doi.org/10.1016/j.ijmst.2025.01.006
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a new propagation criterion for hydraulic fractures based on the micro-cracking mechanism at the mineral particle scale, which integrates pore pressure gradients and macroscopic boundary stresses. The criterion is validated experimentally and provides a more direct understanding of pore pressure effects on fracture formation.
How does the proposed criterion differ from existing ones?
Existing criteria often rely on linear elastic fracture mechanics and treat rock as a continuous medium, leading to stress singularity issues. This new criterion analyzes micro-cracking at the mineral particle scale, directly incorporating pore pressure differences and avoiding the singularity problem.
What is the micro-cracking initiation pressure (MCIP)?
MCIP is the pressure at which hydraulic fractures begin to form, corresponding to the initiation of micro-cracks among rock mineral particles. The theoretical MCIP calculated by the proposed criterion closely matches experimental values.
What is the significance of the mechanical shape factor a/b?
The mechanical shape factor a/b is defined in the model and its overall range is around 1 but greater than 0.5. It influences the stress distribution and the propagation criterion, and its value is determined from the micro-cracking mechanism.
How was the proposed criterion verified?
The criterion was verified by experiments where the hydraulic fracture tip was kept near the initiation point, and the measured MCIP was compared with the theoretical value calculated from the criterion, showing close agreement.
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