Viscoelastic Behavior of Rocks Saturated with Sorptive Gases: A Heuristic Internal Variables Approach
Publication: International Journal of Geomechanics
Volume 23, Issue 10
Abstract
Recent thermodynamics-based constitutive modeling has enabled robust formulations for complex coupled mechanical, hydraulic, thermal, and chemical interactions. Despite such advances, the constitutive modeling of fractured sorptive media with complex mechanical behavior has attracted less attention. We present a new sorptive poroviscoelastic model for fractured rocks that specifically integrates the rate-dependent viscous flow into the coupled fracture fluid flow and matrix gas desorption processes using the two-potential framework, mixture theory, and continuum mechanics. The proposed dissipative viscoelastic strain rate evolution law is governed by the applied stress variable and the amount of gas adsorbed in the matrix pores. The model is exemplified through the simulation of gas production from a sorptive shale formation. The numerical results show that poroviscoelasticity becomes dominant at late production times when the pore-pressure and desorption fronts have progressed significantly. It is revealed that time-dependent stress accumulation can reach high magnitudes which can cause fracture closure that risks impedance to further gas production. Neglecting viscoelastic multiphysics effects in the modeling of fractured sorptive rocks can reduce the accuracy of the predicted production data. In addition, the contribution of desorption-induced viscoelasticity to bulk rock deformation may be substantial in shales and other highly adsorbing rocks and may also be the key to explaining some of the complexities encountered during drilling or hydraulic fracturing operations.
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Data Availability Statement
All data that support the findings of this study are available from the corresponding authors upon reasonable request.
Acknowledgments
The authors acknowledge the support of the Australian Research Council (ARC) through Discovery Project Grant No. DP200102517.
References
Abousleiman, Y., A. H.-D. Cheng, C. Jiang, and J.-C. Roegiers. 1993. “A micromechanically consistent poroviscoelasticity theory for rock mechanics applications.” Int. J. Rock Mech. Min. Sci. 30: 1177–1180. https://doi.org/10.1016/0148-9062(93)90090-Z.
Aghighi, M. A., A. Lv, and H. Roshan. 2021. “Non-equilibrium thermodynamics approach to mass transport in sorptive dual continuum porous media: A theoretical foundation and numerical simulation.” J. Nat. Gas Sci. Eng. 87: 103757. https://doi.org/10.1016/j.jngse.2020.103757.
Ahmad, M., A. Hussain, R. Koo, H. Nguyen’s, and M. Haghighi. 2012. “Evaluation of free porosity in shale gas reservoirs (Roseneath and Murteree Formations case study).” APPEA J. 52: 603. https://doi.org/10.1071/aj11049.
Ahsanizadeh, S., and L. P. Li. 2015. “Visco-hyperelastic constitutive modeling of soft tissues based on short and long-term internal variables.” Biomed. Eng. Online 4–29. https://doi.org/10.1186/s12938-015-0023-7.
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© 2023 American Society of Civil Engineers.
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Received: Sep 2, 2022
Accepted: Apr 18, 2023
Published online: Aug 3, 2023
Published in print: Oct 1, 2023
Discussion open until: Jan 3, 2024
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