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An Analytical Model for Assessing Stability of Pre-Existing Faults in Caprock Caused by Fluid Injection and Extraction in a Reservoir

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Abstract

Induced seismicity and fault reactivation associated with fluid injection and depletion were reported in hydrocarbon, geothermal, and waste fluid injection fields worldwide. Here, we establish an analytical model to assess fault reactivation surrounding a reservoir during fluid injection and extraction that considers the stress concentrations at the fault tips and the effects of fault length. In this model, induced stress analysis in a full-space under the plane strain condition is implemented based on Eshelby’s theory of inclusions in terms of a homogeneous, isotropic, and poroelastic medium. The stress intensity factor concept in linear elastic fracture mechanics is adopted as an instability criterion for pre-existing faults in surrounding rocks. To characterize the fault reactivation caused by fluid injection and extraction, we define a new index, the “fault reactivation factor” η, which can be interpreted as an index of fault stability in response to fluid pressure changes per unit within a reservoir resulting from injection or extraction. The critical fluid pressure change within a reservoir is also determined by the superposition principle using the in situ stress surrounding a fault. Our parameter sensitivity analyses show that the fault reactivation tendency is strongly sensitive to fault location, fault length, fault dip angle, and Poisson’s ratio of the surrounding rock. Our case study demonstrates that the proposed model focuses on the mechanical behavior of the whole fault, unlike the conventional methodologies. The proposed method can be applied to engineering cases related to injection and depletion within a reservoir owing to its efficient computational codes implementation.

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Abbreviations

D :

A homogeneous, isotropic infinite elastic medium

Ω:

A reservoir domain in D

D – Ω:

The surrounding rock (i.e., the caprock)

\( \varepsilon_{ij}^{*} \) :

An eigenstrain within the reservoir Ω

\( \delta_{ij} \) :

The Kronecker delta

α :

The Biot–Willis coefficient

∆T :

Temperature change

∆P :

Pore pressure change

ψ :

Coefficient of linear thermal expansion for the solid

µ :

Shear modulus for the solid

v :

Poisson’s ratio for the solid

λ :

Lame constant for the solid

C ijkl :

Elastic stiffness tensor for the solid

\( \Delta u_{i} ({\mathbf{x}}) \) :

Displacement field caused by the eigenstrain \( \varepsilon_{ij}^{*} \)

\( \Delta \varepsilon_{ij} ({\mathbf{x}}) \) :

Strain tensor caused by the eigenstrain \( \varepsilon_{ij}^{*} \)

\( \Delta \sigma_{ij} ({\mathbf{x}}) \) :

Stress tensor caused by the eigenstrain \( \varepsilon_{ij}^{*} \)

\( G_{ij} ({\mathbf{x}},{\mathbf{x}}^{{\prime }} ) \) :

The Green’s function

\( G_{ij,k} \) :

First derivation of the Green’s function

\( G_{ij,kp} \) :

Second derivative of the Green’s functions

γ ij :

Normalized stress arching ratios

x 10, x 20 :

Coordinates of the center of a fault

2l :

Length of the fault

θ :

Fault dip angle

x 1(t), x 2(t):

Coordinate of each point on fault surfaces

σ 11 :

In-situ horizontal principle stress

σ 22 :

In-situ vertical principle stress

σ p :

Compressive stress on the fault surfaces under in situ stress

τ p :

Absolute value of the shear stress on the fault surfaces under in situ stress

Δσ p :

Perturbed compressive stress on the fault surfaces

Δτ p :

Perturbed shear stress on the fault surfaces

f :

Friction coefficient

φ :

Reservoir tilt angle

K 0 :

Mode-II SIF under uniformly distributed in situ tectonic stress

ΔK up, ΔK down :

Disturbed mode-II SIFs for the upper and lower tips of a fault, respectively

ΔK :

Representative disturbed mode-II SIF for a fault [ΔK = max (ΔK up, ΔK down)]

η :

Fault reactivation factor

K c :

In-situ rock mode-II fracture toughness

PSC:

Pore pressure/stress coupling

SIF:

Stress intensity factor

LEFM:

Linear elastic fracture mechanics

∆CFS :

The Coulomb failure stress change

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Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 11102218, and 41172285). Additionally, we would like to thank the reviewers for providing insightful comments and suggestions to the manuscript.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Lei Wang, Bing Bai, Xiaochun Li, Mingze Liu, Haiqing Wu & Shaobin Hu

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  1. Lei Wang
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  3. Xiaochun Li
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Correspondence to Lei Wang, Bing Bai or Xiaochun Li.

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Wang, L., Bai, B., Li, X. et al. An Analytical Model for Assessing Stability of Pre-Existing Faults in Caprock Caused by Fluid Injection and Extraction in a Reservoir. Rock Mech Rock Eng 49, 2845–2863 (2016). https://doi.org/10.1007/s00603-016-0933-0

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