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Simulating Hydraulic Fracture Re-orientation in Heterogeneous Rocks with an Improved Discrete Element Method

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Abstract

Understanding the hydraulic fracture (HF) re-orientation mechanism from artificial weaknesses is critical to screen-out prevention in the petroleum industry and caveability management in the mining industry. An improved discrete element method is proposed and incorporated in the Universal Distinct Element Code (UDEC) to simulate hydraulic fracturing in heterogeneous rocks, and its reliability is validated against previous laboratory experiments. The effects of rock heterogeneity and rock strength on HF re-orientation are unveiled to fill the research gaps in the existing knowledge. The results show that the proposed UDEC T-W (Trigon-Weibull distribution) model can well simulate HF propagation in rock samples of different homogeneity degrees and yields more realistic simulation results compared with the classic extended finite element method (XFEM). The HF re-orientation process depends on the combined effect of all the influencing factors. HFs tend to be directed by perforations if hydraulic fracturing is performed in relatively heterogeneous rocks, while the differential stress is more likely to dictate the HF propagation paths if rocks become relatively homogeneous. We also find that higher rock strength weakens the impact of the differential stress and favours the control of perforations over HF propagation. Finally, recommendations are provided for effective utilization of hydraulic fracturing at the mine site.

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Abbreviations

BEM:

Boundary element method

DDM:

Displacement discontinuity method

DEM:

Discrete element method

FEM:

Finite element method

HF:

Hydraulic fracture

NF:

Natural fracture

PFC:

Particle Flow Code

RFPA:

Realistic failure process analysis

UDEC:

Universal Distinct Element Code

XFEM:

Extended finite element method

A :

Joint aperture, m

a max :

The maximum allowable joint hydraulic aperture, m

a res :

Minimum allowable joint hydraulic aperture, m

a zero :

The joint hydraulic aperture at zero normal stress, m

c :

Cohesion, MPa

k s :

Shear stiffness, GPa·m

k n :

Normal stiffness, GPa·m

l :

Joint length, m

m :

The homogeneity index in the Weibull distribution

P(u):

The probability density function for a given u value in the Weibull distribution

Q :

The flow rate, m3/s

μ :

Fluid dynamic viscosity, Pa·s

u 0 :

The mean value of a given material property

Δp :

The pressure difference between two adjacent domains, MPa

σ v :

The vertical in-situ stress, MPa

σ hmax :

The maximum horizontal in-situ stress, MPa

σ hmin :

The minimum horizontal in-situ stress, MPa

σ d :

The differential stress, MPa

σ 1 :

The maximum principal stress, MPa

σ 3 :

The minimum principal stress, MPa

σ T cont :

Contact tensile strength, MPa

c cont :

Contact cohesion, MPa

ϕ cont :

The contact friction angle, °

ϕ :

The internal friction angle, °

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Acknowledgements

The work of this paper is financially supported by National Natural Science Foundation of China (Grant No. 51974293), the Jiangsu Province Science Foundation for Youths (Grant No. BK20180658), State Key Laboratory of Coal Resources and Safe Mining (Grant No. SKLCRSM18X009) and China Postdoctoral Science Foundation (Grant No. 2018M632422). The first author of this paper would like to thank his deceased grandmother, Chongfen Ran, for the love and care received from childhood. Constructive comments and suggestions from Professor Panos Papanastasiou and the anonymous reviewers are genuinely appreciated.

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Authors and Affiliations

  1. State Key Laboratory of Coal Resources and Safe Mining, School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

    Qingyuan He & Lei Zhu

  2. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Yingchun Li

  3. WA School of Mines: Minerals, Energy and Chemical Engineering, Curtin University, Kalgoorlie, WA, 6430, Australia

    Danqi Li

  4. School of Civil Engineering, Henan Polytechnic University, Jiaozuo, 454000, China

    Boyang Zhang

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  1. Qingyuan He
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He, Q., Zhu, L., Li, Y. et al. Simulating Hydraulic Fracture Re-orientation in Heterogeneous Rocks with an Improved Discrete Element Method. Rock Mech Rock Eng 54, 2859–2879 (2021). https://doi.org/10.1007/s00603-021-02422-1

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