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Assessment of a Hybrid Continuous/Discontinuous Galerkin Finite Element Code for Geothermal Reservoir Simulations

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Abstract

FALCON (Fracturing And Liquid CONvection) is a hybrid continuous/discontinuous Galerkin finite element geothermal reservoir simulation code based on the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework being developed and used for multiphysics applications. In the present work, a suite of verification and validation (V&V) test problems for FALCON was defined to meet the design requirements, and solved to the interests of enhanced geothermal system modeling and simulation. The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of FALCON solution methods. The test problems vary in complexity from a single mechanical or thermal process, to coupled thermo-hydro-mechanical processes in geological porous medium. Numerical results obtained by FALCON agreed well with either the available analytical solutions or experimental data, indicating the verified and validated implementation of these capabilities in FALCON. Whenever possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the FALCON code.

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Abbreviations

c w :

Specific heat capacity of fluid (J kg −1 K−1)

c r :

Specific heat capacity of rock (J kg −1 K−1)

g :

Magnitude of gravitational force (m s−2)

K m :

Average thermal conductivity of the porous medium (W m−1 K−1)

k :

Reservoir intrinsic permeability (m2)

Pe h :

Element Peclet number

p :

Fluid pressure (Pa)

\( \acute{Q} \) :

Thermal energy source/sink (J s−1)

q :

Flux (Darcy velocity) vector (m s −1)

\( \acute{q} \) :

Specific mass source/sink (or injection/production rate) (kg m−3 s−1)

T :

Fluid temperature (K)

t :

Time (s)

u :

Displacement vector (with three components) (m)

α :

Biot effective stress coefficient

β :

Thermal expansion coefficient

μ :

Fluid viscosity (Pa s)

ρ :

Fluid density (kg m−3)

ρ r :

Rock density (kg m−3)

\( \sigma \) :

Second-rank stress tensor (with six unknown components) (Pa)

ϕ :

Reservoir porosity

∇:

Vector differential operator (m−1)

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Acknowledgments

The work described in this paper was supported by the U.S. Department of Energy, under DOE Idaho Operations Office Contract. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. This information was prepared as an account of work associated by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

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Authors and Affiliations

  1. Department of Energy Resource Recovery and Sustainability, Idaho National Laboratory, 1955 N Fremont Ave, Idaho Falls, ID, 83415, USA

    Yidong Xia, Robert Podgorney & Hai Huang

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  1. Yidong Xia
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  2. Robert Podgorney
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  3. Hai Huang
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Correspondence to Yidong Xia.

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Xia, Y., Podgorney, R. & Huang, H. Assessment of a Hybrid Continuous/Discontinuous Galerkin Finite Element Code for Geothermal Reservoir Simulations. Rock Mech Rock Eng 50, 719–732 (2017). https://doi.org/10.1007/s00603-016-0951-y

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