Skip to main content
Erschienen in: Rock Mechanics and Rock Engineering 3/2017

17.03.2016 | Original Paper

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

verfasst von: Yidong Xia, Robert Podgorney, Hai Huang

Erschienen in: Rock Mechanics and Rock Engineering | Ausgabe 3/2017

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Avdonin NA (1964) Some formulas for calculating the temperature field of a stratum subject to thermal injection. Neft’i Gaz 3:37–41 Avdonin NA (1964) Some formulas for calculating the temperature field of a stratum subject to thermal injection. Neft’i Gaz 3:37–41
Zurück zum Zitat Bahrami D, Danko G, Fu P, Guo B, Podgorney R, White M, Xia Y (2015). Poroelastic and Self-Propped Single Fracture THM Models for EGS Studies. In: proceedings of the 40th Stanford Geothermal Workshop, Stanford, California, USA Bahrami D, Danko G, Fu P, Guo B, Podgorney R, White M, Xia Y (2015). Poroelastic and Self-Propped Single Fracture THM Models for EGS Studies. In: proceedings of the 40th Stanford Geothermal Workshop, Stanford, California, USA
Zurück zum Zitat Balay S, Abhyankar S, Adams M, Brown J, Brune P, Buschelman K et al. (2014). PETSc Users Manual Revision 3.5 (No. ANL-95/11 Rev. 3.5), Argonne National Laboratory Balay S, Abhyankar S, Adams M, Brown J, Brune P, Buschelman K et al. (2014). PETSc Users Manual Revision 3.5 (No. ANL-95/11 Rev. 3.5), Argonne National Laboratory
Zurück zum Zitat Brooks AN, Hughes TJ (1982) Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-stokes equations. Comput Methods Appl Mech Eng 32(1):199–259CrossRef Brooks AN, Hughes TJ (1982) Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-stokes equations. Comput Methods Appl Mech Eng 32(1):199–259CrossRef
Zurück zum Zitat Brownell DH, Garg SK, Pritchett JW (1977) Governing equations for geothermal reservoirs. Water Resour Res 13(6):929–934CrossRef Brownell DH, Garg SK, Pritchett JW (1977) Governing equations for geothermal reservoirs. Water Resour Res 13(6):929–934CrossRef
Zurück zum Zitat Cockburn B, Karniadakis GE, Shu CW (2000) The development of discontinuous Galerkin methods. Springer, Berlin Heidelberg, pp 3–50 Cockburn B, Karniadakis GE, Shu CW (2000) The development of discontinuous Galerkin methods. Springer, Berlin Heidelberg, pp 3–50
Zurück zum Zitat Cooper JR, Dooley RB (2008). Release of the IAPWS formulation 2008 for the viscosity of ordinary water substance Cooper JR, Dooley RB (2008). Release of the IAPWS formulation 2008 for the viscosity of ordinary water substance
Zurück zum Zitat Elder JW (1967) Transient convection in a porous medium. J Fluid Mech 27(03):609–623CrossRef Elder JW (1967) Transient convection in a porous medium. J Fluid Mech 27(03):609–623CrossRef
Zurück zum Zitat Faust CR, Mercer JW (1979a) Geothermal reservoir simulation: 1. Mathematical models for liquid- and vapor-dominated hydrothermal systems. Water Resour Res 15(1):23–30CrossRef Faust CR, Mercer JW (1979a) Geothermal reservoir simulation: 1. Mathematical models for liquid- and vapor-dominated hydrothermal systems. Water Resour Res 15(1):23–30CrossRef
Zurück zum Zitat Faust CR, Mercer JW (1979b) Geothermal reservoir simulation: 2. Numerical solution techniques for liquid- and vapor-dominated hydrothermal systems. Water Resour Res 15(1):31–46CrossRef Faust CR, Mercer JW (1979b) Geothermal reservoir simulation: 2. Numerical solution techniques for liquid- and vapor-dominated hydrothermal systems. Water Resour Res 15(1):31–46CrossRef
Zurück zum Zitat Gaston D, Newman C, Hansen G, Lebrun-Grandie D (2009) MOOSE: a parallel computational framework for coupled systems of nonlinear equations. Nucl Eng Des 239(10):1768–1778CrossRef Gaston D, Newman C, Hansen G, Lebrun-Grandie D (2009) MOOSE: a parallel computational framework for coupled systems of nonlinear equations. Nucl Eng Des 239(10):1768–1778CrossRef
Zurück zum Zitat Graf T (2009). Simulation of geothermal flow in deep sedimentary basins in Alberta. Alberta Energy Resources Conservation Board Graf T (2009). Simulation of geothermal flow in deep sedimentary basins in Alberta. Alberta Energy Resources Conservation Board
Zurück zum Zitat Hascoet L, Pascual V (2013) The Tapenade Automatic Differentiation tool: principles, model, and specification. ACM Trans Math Softw (TOMS) 39(3):20CrossRef Hascoet L, Pascual V (2013) The Tapenade Automatic Differentiation tool: principles, model, and specification. ACM Trans Math Softw (TOMS) 39(3):20CrossRef
Zurück zum Zitat Heroux MA, Bartlett RA, Howle VE, Hoekstra RJ, Hu JJ, Kolda TG et al (2005) An overview of the Trilinos project. ACM Trans Math Softw (TOMS) 31(3):397–423CrossRef Heroux MA, Bartlett RA, Howle VE, Hoekstra RJ, Hu JJ, Kolda TG et al (2005) An overview of the Trilinos project. ACM Trans Math Softw (TOMS) 31(3):397–423CrossRef
Zurück zum Zitat Hughes TJ, Mallet M, Akira M (1986) A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput Methods Appl Mech Eng 54(3):341–355CrossRef Hughes TJ, Mallet M, Akira M (1986) A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput Methods Appl Mech Eng 54(3):341–355CrossRef
Zurück zum Zitat ITASCA Consulting Group (1997). FALC 3D, Fast Lagrangian Analysis of Continua in 3 Dimensions, Version 2.0 ITASCA Consulting Group (1997). FALC 3D, Fast Lagrangian Analysis of Continua in 3 Dimensions, Version 2.0
Zurück zum Zitat Jaeger JC, Cook NG, Zimmerman R (2009). Fundamentals of Rock Mechanics. Wiley Jaeger JC, Cook NG, Zimmerman R (2009). Fundamentals of Rock Mechanics. Wiley
Zurück zum Zitat Knoll DA, Keyes DE (2004) Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J Comput Phys 193(2):357–397CrossRef Knoll DA, Keyes DE (2004) Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J Comput Phys 193(2):357–397CrossRef
Zurück zum Zitat Luo H, Xia Y, Li S, Nourgaliev R, Cai C (2012) A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids. J Comput Phys 231(16):5489–5503CrossRef Luo H, Xia Y, Li S, Nourgaliev R, Cai C (2012) A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids. J Comput Phys 231(16):5489–5503CrossRef
Zurück zum Zitat Luo H, Xia Y, Spiegel S, Nourgaliev R, Jiang Z (2013) A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids. J Comput Phys 236:477–492CrossRef Luo H, Xia Y, Spiegel S, Nourgaliev R, Jiang Z (2013) A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids. J Comput Phys 236:477–492CrossRef
Zurück zum Zitat Oldenburg CM, Pruess K (1995) Dispersive transport dynamics in a strongly coupled groundwater-brine flow system. Water Resour Res 31(2):289–302CrossRef Oldenburg CM, Pruess K (1995) Dispersive transport dynamics in a strongly coupled groundwater-brine flow system. Water Resour Res 31(2):289–302CrossRef
Zurück zum Zitat Podgorney R, Huang H, Gaston D (2010) A fully coupled, implicit, finite element model for simultaneously solving multiphase fluid flow, heat transport, and rock de-formation. Geotherm Resour Counc Trans 34:427–432 Podgorney R, Huang H, Gaston D (2010) A fully coupled, implicit, finite element model for simultaneously solving multiphase fluid flow, heat transport, and rock de-formation. Geotherm Resour Counc Trans 34:427–432
Zurück zum Zitat Podgorney RK, Huang H, Lu C, Gaston D, Permann C, Guo L, Andrs D (2011) FALCON: a physics-based, massively parallel, fully-coupled, finite element model for simultaneously solving multiphase fluid flow, heat transport, and rock deformation for geothermal reservoir simulation, Idaho National Laboratory Report. Idaho National Laboratory Report INL/EXT-11-23351 Podgorney RK, Huang H, Lu C, Gaston D, Permann C, Guo L, Andrs D (2011) FALCON: a physics-based, massively parallel, fully-coupled, finite element model for simultaneously solving multiphase fluid flow, heat transport, and rock deformation for geothermal reservoir simulation, Idaho National Laboratory Report. Idaho National Laboratory Report INL/EXT-11-23351
Zurück zum Zitat Pollard DD, Holzhausen G (1979) On the mechanical interaction between a fluid- filled fracture and the earth’s surface. Tectonophysics 53(1):27–57CrossRef Pollard DD, Holzhausen G (1979) On the mechanical interaction between a fluid- filled fracture and the earth’s surface. Tectonophysics 53(1):27–57CrossRef
Zurück zum Zitat Pruess K, Oldenburg CM, Moridis GJ (1999) TOUGH2 User’s Guide Version 2. Lawrence Berkeley National Laboratory Pruess K, Oldenburg CM, Moridis GJ (1999) TOUGH2 User’s Guide Version 2. Lawrence Berkeley National Laboratory
Zurück zum Zitat Reed WH, Hill TR (1973) Triangular Mesh Methods for the Neutron Transport Equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory Reed WH, Hill TR (1973) Triangular Mesh Methods for the Neutron Transport Equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory
Zurück zum Zitat Rutqvist J, Wu YS, Tsang CF, Bodvarsson G (2002) A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. Int J Rock Mech Min Sci 39(4):429–442CrossRef Rutqvist J, Wu YS, Tsang CF, Bodvarsson G (2002) A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. Int J Rock Mech Min Sci 39(4):429–442CrossRef
Zurück zum Zitat Trangenstein JA (2009) Numerical solution of hyperbolic partial differential equations. Cambridge University Trangenstein JA (2009) Numerical solution of hyperbolic partial differential equations. Cambridge University
Zurück zum Zitat Wagner W, Cooper JR, Dittmann A, Kijima J, Kretzschmar HJ, Kruse A, Willkommen T (2000) The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. J Eng Gas Turbines Power 122(1):150–184CrossRef Wagner W, Cooper JR, Dittmann A, Kijima J, Kretzschmar HJ, Kruse A, Willkommen T (2000) The IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. J Eng Gas Turbines Power 122(1):150–184CrossRef
Zurück zum Zitat Xia Y, Liu X, Luo H (2014a) A Finite Volume Method Based on WENO Reconstruction for Compressible Flows on Hybrid Grids. In: proceedings of the 52nd AIAA Aerospace Sciences Meeting, AIAA Paper No. 2014-0939, National Harbor, Maryland, USA Xia Y, Liu X, Luo H (2014a) A Finite Volume Method Based on WENO Reconstruction for Compressible Flows on Hybrid Grids. In: proceedings of the 52nd AIAA Aerospace Sciences Meeting, AIAA Paper No. 2014-0939, National Harbor, Maryland, USA
Zurück zum Zitat Xia Y, Luo H, Frisbey M, Nourgaliev R (2014b) A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. Comput Fluids 98:134–151CrossRef Xia Y, Luo H, Frisbey M, Nourgaliev R (2014b) A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. Comput Fluids 98:134–151CrossRef
Metadaten
Titel
Assessment of a Hybrid Continuous/Discontinuous Galerkin Finite Element Code for Geothermal Reservoir Simulations
verfasst von
Yidong Xia
Robert Podgorney
Hai Huang
Publikationsdatum
17.03.2016
Verlag
Springer Vienna
Erschienen in
Rock Mechanics and Rock Engineering / Ausgabe 3/2017
Print ISSN: 0723-2632
Elektronische ISSN: 1434-453X
DOI
https://doi.org/10.1007/s00603-016-0951-y

Weitere Artikel der Ausgabe 3/2017

Rock Mechanics and Rock Engineering 3/2017 Zur Ausgabe