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The Effective Stress Coefficient of Coal: A Theoretical and Experimental Investigation

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Abstract

The effective stress coefficient (ESC) is a key parameter in the linear poroelastic effective stress formulation. In fluid-bearing porous media, the effective stress is the difference between total stress and a fraction of the pore fluid pressure controlled by the ESC. The ESC is either measured in the laboratory or estimated by empirical models using field data. Among different techniques, sonic velocity measurements are widely used to estimate the ESC. The structure of coal, however, has some inherent differences to other porous rocks which in turn affect its hydromechanical behavior. For instance, there is no clear definition of grains and matrix in coal making it unclear whether coal, even when saturated by a non-sorbing gas, follows the same principles of sonic-based estimation of the ESC applicable to other rocks. In this study, we develop a model based on the percolation theory and ultrasonic measurements of coal samples saturated with non-sorbing gases to obtain the ESC. To assess the assumptions used in the development of this model, we measured the ESC of different coal samples through two independent, extensive sets of hydromechanical experiments: static and dynamic (ultrasonic). We then compared the results of these experiments with each other and with some of the existing models and evaluated the performance of the percolation-based model in depth.

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Availability of data and materials

Obtained data that support the findings of this study are available from the corresponding author on request.

Abbreviations

\(\sigma\) :

Total stress

\(\sigma^{\prime}\) :

Effective stress

p :

Pore pressure

\(P_{{\text{d}}}\) :

The differential pressure between the confinement and pore pressure

\(\gamma\) :

Effective stress coefficient (ESC) from the static (hydromechanical) experiment

\(\gamma^{{{\text{dyn}}}}\) :

Effective stress coefficient (ESC) from the dynamic (ultrasonic) experiment

K :

Bulk modulus from the static (hydromechanical) experiment

\(K^{{{\text{dyn}}}}\) :

Bulk modulus from the dynamic (ultrasonic) experiment

K s :

Solid bulk modulus from the static (hydromechanical) experiment

\(K_{{\text{s}}}^{{{\text{dyn}}}}\) :

Solid bulk modulus from the dynamic (ultrasonic) experiment

G :

Shear modulus from the static (hydromechanical) experiment

\(G^{{{\text{dyn}}}}\) :

Shear modulus from the dynamic (ultrasonic) experiment

G s :

Shear modulus of solid from the static (hydromechanical) experiment

\(G_{{\text{s}}}^{{{\text{dyn}}}}\) :

Shear modulus of solid from the dynamic (ultrasonic) experiment

\(\rho_{{\text{b}}}\) :

Bulk density

\(\rho_{{\text{s}}}\) :

Solid density

E :

Young’s modulus

\(\phi\) :

Porosity

\(\phi_{{\text{N}}}\) :

Critical porosity

V p :

Compressional (P) wave velocity

\(V_{{\text{p}}}^{{\text{s}}}\) :

Compressional (P) wave velocity of the solid phase

V s :

Shear (S) wave velocity

\(V_{{\text{s}}}^{{\text{s}}}\) :

Shear (S) wave velocity of the solid phase

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Acknowledgements

This work was supported by the Australian Coal Association Research Program (ACARP), project number C27027. Adelina Lv acknowledges the Australian Government Research Training Program for the PhD scholarship.

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Australian Coal Association Research Program (ACARP), project number C27027.

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Authors and Affiliations

  1. School of Minerals and Energy Resources Engineering, UNSW Australia, Sydney, NSW, 2052, Australia

    Adelina Lv, Mohammad Ali Aghighi & Hamid Roshan

  2. Department of Civil Engineering, Monash University, Melbourne, VIC, 3800, Australia

    Hossein Masoumi

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  1. Adelina Lv
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  2. Mohammad Ali Aghighi
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  3. Hossein Masoumi
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  4. Hamid Roshan
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Lv, A., Aghighi, M.A., Masoumi, H. et al. The Effective Stress Coefficient of Coal: A Theoretical and Experimental Investigation. Rock Mech Rock Eng 54, 3891–3907 (2021). https://doi.org/10.1007/s00603-021-02476-1

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