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A New Three-Dimensional Numerical Model Based on the Equivalent Continuum Method to Simulate Hydraulic Fracture Propagation in an Underground Coal Mine

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Abstract

Hydraulic fracturing has been proven to be the most efficient way to improve the permeability of coal seams. In this work, the hydraulic fracture propagation in an underground coal mine was numerically investigated. A new numerical approach was developed based on the equivalent continuum methodology to model the hydro-mechanical behavior of multiple fractures in three dimensions. It was solved using a hybrid combination of the embedded element method (EEM) and the finite volume method (FVM) using an iterative coupling schema. The FVM was employed to calculate the pressure field, while the EEM was used to track the displacement discontinuity caused by fractures. A fracture constitutive model was implemented to describe the aperture variation, shear slippage, and shear dilation for both contact and open fractures, as well as for contact and open criteria. To verify the developed model, two benchmark examples were presented. Then, the developed model was used to numerically investigate hydraulic fracture propagation in Datong underground coal mine in Songzao in Chongqing. According to the numerical study, it was found that (1) a fracture network created by a hydraulic fracturing operation in a coal mine is more complex than the ideal cross-cutting-shape, H-shape, T-shape, and Z-shape patterns; (2) the orientation of the minimum principal stress controlled the main propagation direction; (3) the complexity of the fracture pattern is controlled by the geological structure, the in situ stress and the injection rate.

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Abbreviations

A :

Connection area of the two neighbor elements

b :

Fracture width

B :

Volumetric force vector

C :

Cohesion

D :

Hook tensor expressed in matrix form

E :

Young’s modulus

f :

Failure function

F :

Force vector

G :

Shear modulus

k f :

Fracture permeability

k ij,f :

Permeability tensor

k n :

Normal stiffness

k s :

Shear stiffness

L :

Fracture length

m :

Nodal mass

P :

Fluid pressure

q :

Flow rate

Q s :

Source term

S :

Fracture spacing

t n, t s, t t :

Normal and the tangential traction

t n0, t s0, t t0 :

Cohesive strengths

T :

Internal force vector calculated using the integral of stresses over element volume

u :

Displacement vector

v :

Velocity vector

V :

Volume

w :

Fracture aperture

α :

Damping coefficient

γ:

Correction factor resulting from fracture roughness

δ ij :

Kronecker tensor

µ :

Fluid dynamic viscosity

ρ m :

Rock density

σ :

Cauchy stress tensor

υ :

Poisson ratio

φ :

Dilation angle

ϕ :

Frictional angle

Δε :

Strain increment tensor

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Acknowledgements

The work presented in this paper is funded by the National Natural Science Foundation of China (no. 51774056), the National Science Fund for Distinguished Young Scholars of China (no. 51625401), the Chongqing Research Program of Basic Research and Frontier Technology (no. cstc2017jcyjB0252), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT_17R112). Dr. Zhou is the principle developer of the 3D numerical model. Mr. Su worked the multiple fracture constitutive model into the new numerical model. Prof. Lu gave informative discussion in the numerical application. Dr. Ge carried out the numerical application. Dr. Zhang gave the idea to use EEM to describe the mechanical behavior of multiple fractures. Mr. Shen conducted part of the implementation work. We would like to thank LetPub (http://www.letpub.com) for providing linguistic assistance during the preparation of this manuscript.

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

    Lei Zhou, Xiaopeng Su, Yiyu Lu, Zhaolong Ge, Zhenyu Zhang & Zhonghui Shen

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  1. Lei Zhou
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  2. Xiaopeng Su
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  3. Yiyu Lu
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  4. Zhaolong Ge
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  6. Zhonghui Shen
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Correspondence to Zhaolong Ge.

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Zhou, L., Su, X., Lu, Y. et al. A New Three-Dimensional Numerical Model Based on the Equivalent Continuum Method to Simulate Hydraulic Fracture Propagation in an Underground Coal Mine. Rock Mech Rock Eng 52, 2871–2887 (2019). https://doi.org/10.1007/s00603-018-1684-x

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