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Phase-Field Modelling of Interactions Between Hydraulic Fractures and Natural Fractures

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Abstract

Hydraulic fracturing is a widely used technique applied in unconventional reservoirs to generate large fracture networks. Interactions between hydraulic fracture (HF) and natural fracture (NF) can impact the fracture topology and thus the subsequent productivity. Despite a large number of studies on HF–NF interactions, the HF propagation path is normally judged based on ad-hoc criteria to decide whether crossing or deflection occurs and the mechanism behind has not yet reached a unified understanding. Here, we use a phase-field model (PFM), which is based on a unified fracture propagation criterion, to investigate the influence of in-situ stress, fracturing operational parameters and NF orientation and strength. We analyze the mechanism behind different propagation patterns resulting from different kinds of NFs—non-cemented and cemented ones under different conditions. In particular, we compare the total energies between the symmetric propagation and asymmetric propagation to verify the minimum energy propagation path. Our results indicate that a higher stress anisotropy more likely leads to HF–NF crossing and a less fracture complexity. Injection rate influences propagation speed and fracture complexity. Within a certain range (30°, 45°, 60° in this study), the larger the approaching angle is, the more complex the fractures become. With the increasing strength contrast between NF and rock matrix, the material heterogeneity increases, encouraging HF to form complex fractures. Opening more strongly cemented NFs, which act as a barrier for propagation, consumes more energy than HF propagation outside the interface. Lower stress anisotropy and higher injection rate lead to higher initiation pressure, requiring more energy for propagation.

Highlights

  • A phase field model based on a unified fracture propagation criterion is used to study the interactions between hydraulic fractures and natural fractures.

  • The mechanism behind different propagation patterns resulting from non-cemented and cemented natural fractures under different conditions is analyzed.

  • A parameter denoted as complexity degree is used to describe fracturing effect through the sensitive analyses.

  • The total energies between the symmetric propagation and asymmetric propagation are compared to verify the minimum energy propagation path.

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Notes

  1. Duarte and his colleagues overcame most of difficulties (Gupta et al. 2015; Sanchez-Rivadeneira and Duarte 2020).

Abbreviations

\(\Psi\) :

Total energy

\(\psi_{\varepsilon }\) :

Strain energy density

\(\overrightarrow {u}\) :

Displacement

\(\overrightarrow {\varepsilon }\) :

Linear strain

\(G_{c}\) :

Critical energy release rate

\(\overrightarrow {b}\) :

Body force

\(\overrightarrow {{f_{t} }}\) :

Traction force

λ, μ :

Lamé constants

E :

Elastic modulus

υ :

Poisson’s ratio

\(\overrightarrow {{\sigma_{0} }}\) :

Initial stress field

\(\alpha\) :

Biot’s coefficient

p :

Fluid pressure

v :

Phase-field variable

l s :

Regularisation length parameter

k :

Numerical stability parameter

H :

History reference field

\(\sigma^{por}\) :

Cauchy stress tensor

c 1, c 2 :

Two thresholds of the domain

S :

Storage coefficient

\(\overrightarrow {{v_{D} }}\) :

Darcy velocity

ρ :

Flow density

q m :

Source term

\(\varepsilon_{v}\) :

Volumetric strain

n :

Porosity

c :

Fluid compressibility

K vr :

Bulk modulus

K :

Effective fluid permeability

μ :

Effective fluid viscosity

L f :

Fracture length

h :

Effective element size

\(\delta\) :

Complexity degree

\(N_{frac}\) :

Element number with the phase-field value υ greater than 0.95

\(N_{total}\) :

Element number in the whole domain

\(G_{c}^{{\text{int}}}\) :

Energy release rate at the interface

\(G_{c}^{{e - {\text{int}} }}\) :

Effective interface energy release rate over a certain length m

\(G_{c}^{bulk}\) :

The other subdomain excluding the diffused interface with a length of m

\(\alpha_{1}\), \(\alpha_{2}\) :

Coefficients of the phase-field profile

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Acknowledgements

The research was supported by the National Natural Science Foundation of China (Nos. 51904041 and 52174166), the China Scholarships Council program (202006050136) and the DAAD Research Grants—Short-Term Grants, 2021 (57552337), and was conducted at Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences during a one year visit of the first author. HH is grateful for the support from the Helmholtz Association’s Initiative and Networking Fund (contract number VH–NG-1516). KY acknowledges the support of the Deutsche Forschungsgemeinshaft (projector number YO 312/1-1) and by the Japan Oil, Gas and Metals National Corporation (JOGMEC).

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Authors and Affiliations

  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Xiaoxuan Li, Yongjiang Luo & Yunpei Liang

  2. School of Resources and Safety Engineering, Chongqing University, Chongqing, 400044, China

    Xiaoxuan Li, Yongjiang Luo & Yunpei Liang

  3. Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, Telegrafenberg, 14473, Potsdam, Germany

    Xiaoxuan Li & Hannes Hofmann

  4. Department of Environmental Informatics, Helmholtz Centre for Environmental Research‐UFZ, Leipzig, Germany

    Keita Yoshioka

  5. Department of Civil Engineering, University of Manitoba, Winnipeg, Canada

    Keita Yoshioka

Authors
  1. Xiaoxuan Li
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  2. Hannes Hofmann
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  3. Keita Yoshioka
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  4. Yongjiang Luo
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  5. Yunpei Liang
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Corresponding authors

Correspondence to Yongjiang Luo or Yunpei Liang.

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Li, X., Hofmann, H., Yoshioka, K. et al. Phase-Field Modelling of Interactions Between Hydraulic Fractures and Natural Fractures. Rock Mech Rock Eng 55, 6227–6247 (2022). https://doi.org/10.1007/s00603-022-02970-0

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  • DOI: https://doi.org/10.1007/s00603-022-02970-0

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