Abstract
Several regions of the world have abundant oil shale resources, but accessing this energy supply poses a number of challenges. One particular difficulty is the thermomechanical behavior of the material. When heated to sufficient temperatures, thermal conversion of kerogen to oil, gas, and other products takes place. This alteration of microstructure leads to a complex geomechanical response. In this work, we develop a thermoplasticity model for oil shale. The model is based on critical state plasticity, a framework often used for modeling clays and soft rocks. The model described here allows for both hardening due to mechanical deformation and softening due to thermal processes. In particular, the preconsolidation pressure—defining the onset of plastic volumetric compaction—is controlled by a state variable representing the kerogen content of the material. As kerogen is converted to other phases, the material weakens and plastic compaction begins. We calibrate and compare the proposed model to a suite of high-temperature uniaxial and triaxial experiments on core samples from a pilot in situ processing operation in the Green River Formation. We also describe avenues for future work to improve understanding and prediction of the geomechanical behavior of oil shale operations.
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Abbreviations
- A :
-
Frequency factor (1/s)
- \({\mathbb{C}}^e\) :
-
Elastic stiffness tensor (Pa)
- \(E_{\text {a}}\) :
-
Primary activation energy (kcal/mol)
- E :
-
Young’s modulus (Pa)
- e :
-
Deviatoric strain (–)
- f :
-
Yield function
- g :
-
Plastic potential
- G :
-
Shear modulus (Pa)
- \(H_{\text {v}},H_{\text {t}},H_{\text {k}}\) :
-
Hardening law coefficients (Pa, Pa/\(^\circ \)C, Pa)
- k :
-
Kerogen content (%)
- K :
-
Bulk modulus (Pa)
- M :
-
Slope of the critical state line (–)
- \({\mathbb{P}}\) :
-
Anisotropic projection tensor (–)
- \(R_{\text {o}}\) :
-
Vitrinite reflectance (%)
- u :
-
Displacement (m)
- \(p_{\text {c}}\) :
-
Preconsolidation pressure (Pa)
- \(p'\) :
-
Mean effective stress invariant (Pa)
- q :
-
von Mises stress invariant (Pa)
- \(q_{\text {A}}\) :
-
Anisotropic von Mises stress invariant (Pa)
- s :
-
Deviatoric stress (Pa)
- T :
-
Temperature (\(^\circ \)C)
- \(\alpha \) :
-
Thermal expansion coefficient (1/\(^\circ \)C)
- \(\beta _{\text {s}},\beta _{\text {c}}\) :
-
Non-associativity multipliers
- \({\boldsymbol{\epsilon}} \) :
-
Strain (–)
- \(\epsilon _{\text {v}}\) :
-
Volumetric strain invariant (–)
- \(\epsilon _{\text {s}}\) :
-
Deviatoric strain invariant (–)
- \(\gamma \) :
-
Elastic softening coefficient (1/\(^\circ \)C)
- \(\dot{\lambda }\) :
-
Plastic multiplier
- \(\nu \) :
-
Poisson’s ratio (–)
- \({\boldsymbol{\sigma '}} \) :
-
Effective stress (Pa)
- 1 :
-
Second-order unit tensor
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Acknowledgments
This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Funding was provided by American Shale Oil, LLC, which is a joint venture of Genie Energy and Total S.A. Data were procured from New England Research (White River Junction, VT) and MetaRock Laboratories (Houston, TX).
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Submitted to the GeoProc 2015 Special Issue of Rock Mechanics and Rock Engineering.
Alan K. Burnham formerly affiliated at American Shale Oil, Rifle, CO, USA.
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White, J.A., Burnham, A.K. & Camp, D.W. A Thermoplasticity Model for Oil Shale. Rock Mech Rock Eng 50, 677–688 (2017). https://doi.org/10.1007/s00603-016-0947-7
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DOI: https://doi.org/10.1007/s00603-016-0947-7