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Experimental Observations of Gas-sorption-Induced Strain Gradients and their Implications on Permeability Evolution of Shale

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Abstract

Gas adsorption/desorption can result in swelling/shrinking of the matrix in fractured shale. The significant contrast in permeability between fractures and matrix results in an extended duration for the equilibration of the gas injection or depletion-created pressure difference. This spatially non-uniform pressure dissipation induces non-uniform deformations inside the matrix. We follow this response with carefully constrained laboratory measurements integrated with numerical modelling to explore the relation between the strain gradients that develop in the matrix adjacent to fractures and the evolution of permeability each under conditions of constant confining pressure. The microstructures of the sample were characterized by X-ray computed tomography, field-emission scanning electron microscopy and mercury injection capillary pressure porosimetry. A distributed array of strain gauges was attached to the matrix to directly measure the evolving strain. Then a 3D multiphysics numerical model was built to model the evolution of strain gradients from initial to ultimate equilibrium. The influence of these strain gradients on the evolution of fracture permeability is evaluated by a non-uniform strain-based permeability model. The results indicate that the swelling of the matrix near fractures can also compress the matrix away from the fracture under constant confining pressure conditions. Under the influence of the matrix–fracture interaction, a transient and complex distribution of strain gradients develops within the matrix.

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Abbreviations

b 0 :

Initial fracture aperture (m)

Δb :

Fracture aperture change (m)

f i :

The component of body force in the i –direction (N)

E :

Young's modulus (MPa)

G :

Shear modulus (MPa)

K :

Bulk modulus (MPa)

k m :

The permeability of matrix system (m2)

k m0 :

The initial permeability of matrix system (m2)

k f :

The permeability of fracture system (m2)

k f0 :

The initial permeability of fracture system (m2)

M:

The molecular mass of gas (kg/mol)

p m :

The gas pressure in the matrix systems (MPa)

p f :

The gas pressure in the fracture systems (MPa)

p L :

Langmuir pressure (MPa)

p :

Pore pressure (MPa)

R :

The universal gas constant (J/(mol K))

T :

The absolute gas temperature (K)

u i :

The component of displacement in the i-direction (m)

V L :

Langmuir volume constant (m3/kg)

Φ m :

The porosity of matrix system

Φ f :

The porosity of fracture system

\(\bar{\sigma}\) :

Mean compressive stress (MPa)

\(\varepsilon_e\) :

Total effective volumetric strain

\(\varepsilon_m\) :

Volumetric strain in the shale matrix

\(\varepsilon_{mp}\) :

Effective-stress-induced volumetric strain

\(\varepsilon_{ms}\) :

Sorption-induced volumetric strain

\(\varepsilon_{f}\) :

Fracture strain

\(\varepsilon_{f}^{t}\) :

Uniform strain component

\(\varepsilon\prime_{f}\) :

Non-uniform strain component

\(\varepsilon_{L}\) :

Langmuir volumetric strain constant

ν :

Poisson ratio

α :

Biot coefficient

ρ s :

Shale density (kg/m3)

ρ a :

Gas density at atmospheric pressure (kg/m3)

ρ g :

Gas density (kg/m3)

μ :

Dynamic viscosity of the gas (mPa s)

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Acknowledgements

This work was funded by the Natural Science Foundation of China (41972184), the Fund of Outstanding Talents in Discipline of China University of Geosciences (Wuhan) (102-162301192664), the Natural Science Foundation of Hebei Province (E2020209074), and the Fundamental Research Funds for National Universities, China University of Geosciences (Wuhan). These supports are gratefully acknowledged.

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Authors and Affiliations

  1. School of Resources and Geosciences, China University of Mining and Technology, Xuzhou, 221116, China

    Rui Shi & Mingyao Wei

  2. Key Laboratory of Tectonics and Petroleum Resources, Ministry of Education, China University of Geosciences, Wuhan, 430074, China

    Rui Shi, Xiaoming Wang & Zhizhuang Wang

  3. Department of Chemical Engineering, School of Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia

    Jishan Liu

  4. Department of Energy and Mineral Engineering, G3 Centre and Energy Institute, The Pennsylvania State University, University Park, PA, 16802, USA

    Rui Shi & Derek Elsworth

  5. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110004, China

    Guanglei Cui

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  1. Rui Shi
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Correspondence to Xiaoming Wang.

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Research Highlights

A dense array of strain gauges is used to constrain the complex evolution of strain in shales containing a fracture. Complex transient and non-uniform strains develop as a result of even uniform confining stress. These strain gradients suggest a heterogeneous evolution of fracture permeability that can be rationalized from the mechanics of deformation.

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Shi, R., Liu, J., Wang, X. et al. Experimental Observations of Gas-sorption-Induced Strain Gradients and their Implications on Permeability Evolution of Shale. Rock Mech Rock Eng 54, 3927–3943 (2021). https://doi.org/10.1007/s00603-021-02473-4

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