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Numerical investigation of the hydromechanical response of a natural fracture during fluid injection using an efficient sequential coupling model

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Abstract

Hydraulic fracturing is a complicated hydromechanical coupled process, especially in shale gas and deep geothermal reservoirs, in which natural fractures exist. Due to the geological complexity caused by invisibility, and the challenge and high cost in field investigations, numerical modeling becomes an alternative. In this paper, an integrated numerical model is developed to investigate the hydromechanical behavior of a natural fracture during the fluid injection. In the developed model, the mechanical behavior of the fracture including fracture opening, closure, shear dilation, and shear failure is described by proposed constitutive equations; meanwhile, the hydraulic process is simplified as the fluid flows through two parallel planes. The coupled mechanical and hydraulic equations are sequentially formulated in an implicit schema by combining the finite different method and the finite volume method. The advantage of this numerical schema is that the two coupled processes are solved separately and only one sub-iteration is needed. Thus, the solution is efficient and stable than that formulated in a monolithic coupling. Besides, the implicit formulation of the flow equation makes it possible to set a relative large time step. The developed model is verified through three numerical examples. Then, it is used to investigate the hydromechanical behavior of a natural fracture during the fluid injection with a fictive reservoir. Sensitivity studies with variations in the stress state, the fluid injection rate, the fluid viscosity, and the injection form are conducted. The simulation results show that the mechanism in the far field is mainly dominated by shear dilation in contact condition, whereas the mechanism near the injection could be mixed shear–tension in either the contact or the separation conditions. With the increase in the shear stress and the injection length, decrease in the injection rate and the fluid viscosity, the fracture state near the injection will change from separation to contact, the injection pressure will decline below the primary normal stress, and the dominated mechanism is shear dilation. The findings in this study give a better understanding of the mechanical mechanism and the pressure response of a natural fracture during the fluid injection.

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Abbreviations

b i :

Gravity acceleration (m/s2)

c :

Cohesion (Pa)

D :

Physical matrix

f :

External force (N)

e 1 :

Elastic parameter (Pa)

e 2 :

Elastic parameter (Pa)

F :

Total force acting on a grid point (N)

G :

Shear modulus (Pa)

h :

Hydrostatic height (m)

K :

Bulk modulus (Pa)

k n :

Normal stiffness (Pa/m)

k s :

Shear stiffness (Pa/m)

l c :

Characteristic length of the rock mach element (m)

Qs:

Source term (1/s)

t :

Time (s)

v fi :

Fluid velocity in the i-direction (m/s)

v i :

Velocity (m/s)

w :

Fracture aperture (m)

ε :

Strain (-)

u :

Displacement (m)

ρ f :

Fluid density (kg/m3)

ρ m :

Rock density (kg/m3)

σ n,eff = σ n + αP f :

Effective normal stress (Pa)

α :

Effective stress coefficient (−)

σ s :

Shear stress (Pa)

σ n :

Normal stress (Pa)

τ max :

Shear strength (Pa)

ϕ :

Frictional angle (°)

μ :

Viscosity (Pa s)

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Acknowledgments

The work presented in this paper was funded by National Natural Science Foundation of China (No. 51504043) and National Basic Research Program of China (No. 2014CB239206).

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Authors and Affiliations

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

    Lei Zhou, Xiaopeng Su, Yiyu Lu & Yang Gou

  2. Energy Research Center of Lower Saxony, Goslar, Germany

    Zhengmeng Hou & Yang Gou

Authors
  1. Lei Zhou
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  2. Xiaopeng Su
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  3. Zhengmeng Hou
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  4. Yiyu Lu
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  5. Yang Gou
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Correspondence to Yang Gou.

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Zhou, L., Su, X., Hou, Z. et al. Numerical investigation of the hydromechanical response of a natural fracture during fluid injection using an efficient sequential coupling model. Environ Earth Sci 75, 1263 (2016). https://doi.org/10.1007/s12665-016-6078-3

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  • DOI: https://doi.org/10.1007/s12665-016-6078-3

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