Skip to main content
Erschienen in: Rock Mechanics and Rock Engineering 6/2014

01.11.2014 | Original Paper

Simulation of the Steady-State Flow in Discrete Fracture Networks with Non-Conforming Meshes and Extended Finite Elements

verfasst von: S. Berrone, C. Fidelibus, S. Pieraccini, S. Scialò

Erschienen in: Rock Mechanics and Rock Engineering | Ausgabe 6/2014

Einloggen

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

search-config
loading …

Abstract

In this paper a numerical method for the simulation of the steady-state fluid flow in discrete fracture networks is described. It is based on the use of non-conforming meshes, enrichment functions and an optimization procedure. The meshing process is performed on each fracture independently of the other fractures, i.e. without geometrical conformity at the intersections (traces). The slope discontinuities due to the flux exchange at the traces are then captured with the enrichment functions of the extended finite elements, and finally a functional is minimized by resorting to an optimization procedure. The method can be easily implemented for parallel computers being based on many small independent problems. In order to show the effectiveness of the method and the quality of the results, simulations of fluid flow in simple networks are illustrated.

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 Baghbanan A, Jing LR (2007) Hydraulic properties of fractured rock masses with correlated fracture length and aperture. Int J Roch Mech Min 44(5):704–719CrossRef Baghbanan A, Jing LR (2007) Hydraulic properties of fractured rock masses with correlated fracture length and aperture. Int J Roch Mech Min 44(5):704–719CrossRef
Zurück zum Zitat Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Internat. J. Numer. Methods Eng 45:601–620CrossRef Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Internat. J. Numer. Methods Eng 45:601–620CrossRef
Zurück zum Zitat Belytschko T, Möes N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements, Int J Numer Methods Eng 50:993-1013CrossRef Belytschko T, Möes N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements, Int J Numer Methods Eng 50:993-1013CrossRef
Zurück zum Zitat Berrone S (2006) Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients. Modélisation Mathématique et Analyse Numérique 40(6):991–1021 Berrone S (2006) Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients. Modélisation Mathématique et Analyse Numérique 40(6):991–1021
Zurück zum Zitat Berrone S (2009) A local-in-space-timestep approach to a finite element discretization of the heat equation with a posteriori estimates. SIAM J Numer Anal 47(4):3109–3138CrossRef Berrone S (2009) A local-in-space-timestep approach to a finite element discretization of the heat equation with a posteriori estimates. SIAM J Numer Anal 47(4):3109–3138CrossRef
Zurück zum Zitat Berrone S (2010) Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations. Modélisation Mathématique et Analyse Numérique 44(3):455–484 Berrone S (2010) Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations. Modélisation Mathématique et Analyse Numérique 44(3):455–484
Zurück zum Zitat Berrone S, Pieraccini S, Scialò S (2013) A PDE-constrained optimization formulation for discrete fracture network flows. SIAM J Sci Comput 35(2):B487–B510CrossRef Berrone S, Pieraccini S, Scialò S (2013) A PDE-constrained optimization formulation for discrete fracture network flows. SIAM J Sci Comput 35(2):B487–B510CrossRef
Zurück zum Zitat Berrone S, Pieraccini S, Scialò S (2013) On simulations of discrete fracture network flows with an optimization-based extended finite element method. SIAM J Sci Comput 35(2):A908–A935CrossRef Berrone S, Pieraccini S, Scialò S (2013) On simulations of discrete fracture network flows with an optimization-based extended finite element method. SIAM J Sci Comput 35(2):A908–A935CrossRef
Zurück zum Zitat Berrone S, Pieraccini S, Scialò S (2014) An optimization approach for large scale simulations of discrete fracture network flows. J Comput Phys 256:838–853CrossRef Berrone S, Pieraccini S, Scialò S (2014) An optimization approach for large scale simulations of discrete fracture network flows. J Comput Phys 256:838–853CrossRef
Zurück zum Zitat Bogdanov II, Mourzenko VV, Thovert JF, Adler PM (2003) Effective permeability of fractured porous media in steady state flow. Water Resour Res 39(1):1023–1038 Bogdanov II, Mourzenko VV, Thovert JF, Adler PM (2003) Effective permeability of fractured porous media in steady state flow. Water Resour Res 39(1):1023–1038
Zurück zum Zitat Bour O, Davy P, Darcel C, Odling N (2002) A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway). J Geophys Res 107(B6):ETG 4-1–ETG 4-12 Bour O, Davy P, Darcel C, Odling N (2002) A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway). J Geophys Res 107(B6):ETG 4-1–ETG 4-12
Zurück zum Zitat Cravero M, Fidelibus C (1999) A code for scaled flow simulations on generated fracture networks. Comput Geosci 25(2):191–195CrossRef Cravero M, Fidelibus C (1999) A code for scaled flow simulations on generated fracture networks. Comput Geosci 25(2):191–195CrossRef
Zurück zum Zitat Cvetkovic V, Painter S, Outters N, Selroos JO (2004) Stochastic simulation of radionuclide migration in discretely fractured rock near the Aspo Hard Rock Laboratory. Water Resour Res. doi:10.1029/2003WR002655 Cvetkovic V, Painter S, Outters N, Selroos JO (2004) Stochastic simulation of radionuclide migration in discretely fractured rock near the Aspo Hard Rock Laboratory. Water Resour Res. doi:10.​1029/​2003WR002655
Zurück zum Zitat Daux C, Möes N, Dolbow J, Sukumar N, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Methods Eng 48:1741–1760CrossRef Daux C, Möes N, Dolbow J, Sukumar N, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Methods Eng 48:1741–1760CrossRef
Zurück zum Zitat De Dreuzy JR, Davy P, Bour O (2001) Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2, permeability of networks based on log-normal distribution of apertures. Water Resour Res 37(8):2079–2095CrossRef De Dreuzy JR, Davy P, Bour O (2001) Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2, permeability of networks based on log-normal distribution of apertures. Water Resour Res 37(8):2079–2095CrossRef
Zurück zum Zitat Dershowitz WS (1984) Rock joints systems, PhD thesis, Massachussets Institute of Technology, Cambridge Dershowitz WS (1984) Rock joints systems, PhD thesis, Massachussets Institute of Technology, Cambridge
Zurück zum Zitat Dershowitz WS, Einstein HH (1988) Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21(1):21–51CrossRef Dershowitz WS, Einstein HH (1988) Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21(1):21–51CrossRef
Zurück zum Zitat Dershowitz WS, Miller I (1995) Dual porosity fracture flow and transport. Geophys Res Lett 22(11):1441–1444CrossRef Dershowitz WS, Miller I (1995) Dual porosity fracture flow and transport. Geophys Res Lett 22(11):1441–1444CrossRef
Zurück zum Zitat Dershowitz WS, Lee G, Geier J, Foxford T, LaPointe P, Thomas A (1998) FracMan interactive discrete feature data analysis, geometric modeling, and exploration simulation, user documentation, v2.6, Golder Associates Inc., Redmond, Washington Dershowitz WS, Lee G, Geier J, Foxford T, LaPointe P, Thomas A (1998) FracMan interactive discrete feature data analysis, geometric modeling, and exploration simulation, user documentation, v2.6, Golder Associates Inc., Redmond, Washington
Zurück zum Zitat Doe T, Osnes J (1985) Interpretation of fracture geometry from well tests, paper presented at the International Symposium on Rock Joints, Björkliden, Sweden Doe T, Osnes J (1985) Interpretation of fracture geometry from well tests, paper presented at the International Symposium on Rock Joints, Björkliden, Sweden
Zurück zum Zitat Erhel J, De Dreuzy J, Poirriez B (2009) Simulation in three-dimensional discrete fracture networks. SIAM J Sci Comput 31(4):2688–2705CrossRef Erhel J, De Dreuzy J, Poirriez B (2009) Simulation in three-dimensional discrete fracture networks. SIAM J Sci Comput 31(4):2688–2705CrossRef
Zurück zum Zitat Fidelibus C (2007) The 2D hydro-mechanically coupled response of a rock mass with fractures via a mixed BEM–FEM technique. Int J Numer Anal Met 31(11):1329–1348CrossRef Fidelibus C (2007) The 2D hydro-mechanically coupled response of a rock mass with fractures via a mixed BEM–FEM technique. Int J Numer Anal Met 31(11):1329–1348CrossRef
Zurück zum Zitat Fidelibus C, Barla G, Cravero M (1997) A mixed solution for two-dimensional unsteady flow in fractured porous media. Int J Numer Anal Met 21(9):619–633CrossRef Fidelibus C, Barla G, Cravero M (1997) A mixed solution for two-dimensional unsteady flow in fractured porous media. Int J Numer Anal Met 21(9):619–633CrossRef
Zurück zum Zitat Fidelibus C, Cammarata G, Cravero M (2009) Hydraulic characterization of fractured rocks. In: Abbie M, Bedford JS (eds) Rock mechanics: new research. Nova Science Publishers Inc., New York, pp 233–262 Fidelibus C, Cammarata G, Cravero M (2009) Hydraulic characterization of fractured rocks. In: Abbie M, Bedford JS (eds) Rock mechanics: new research. Nova Science Publishers Inc., New York, pp 233–262
Zurück zum Zitat Fries T-P (2008) A corrected xfem approximation without problems in blending elements, Int J Numer Methods Eng 75:503–532CrossRef Fries T-P (2008) A corrected xfem approximation without problems in blending elements, Int J Numer Methods Eng 75:503–532CrossRef
Zurück zum Zitat Fries T-P, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84:253–304 Fries T-P, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84:253–304
Zurück zum Zitat Kaiser R, Kolditz O, Rother T (1999) Modelling of flow in fractured aquifers using automatic grid adaptation, paper presented at 28th IAHR conference on hydraulic engineering for sustainable water resources management, Int Assoc Hydraul Res Graz, Austria. Kaiser R, Kolditz O, Rother T (1999) Modelling of flow in fractured aquifers using automatic grid adaptation, paper presented at 28th IAHR conference on hydraulic engineering for sustainable water resources management, Int Assoc Hydraul Res Graz, Austria.
Zurück zum Zitat Long JCS, Remer JS, Wilson CR, Witherspoon PA (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 23(3):645–658CrossRef Long JCS, Remer JS, Wilson CR, Witherspoon PA (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 23(3):645–658CrossRef
Zurück zum Zitat Long JCS, Billaux D (1987) From field data to fracture network modeling: an example incorporating spatial structure. Water Resour Res 23(7):1201–1216CrossRef Long JCS, Billaux D (1987) From field data to fracture network modeling: an example incorporating spatial structure. Water Resour Res 23(7):1201–1216CrossRef
Zurück zum Zitat Martinez-Landa L, Carrera J (2006) A methodology to interpret cross-hole tests in a granite block. J Hydrol 325(1–4):222–240CrossRef Martinez-Landa L, Carrera J (2006) A methodology to interpret cross-hole tests in a granite block. J Hydrol 325(1–4):222–240CrossRef
Zurück zum Zitat Maryška J, Severýn O, Vorhalík M (2004) Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model. Comput Geosci 8:217–234CrossRef Maryška J, Severýn O, Vorhalík M (2004) Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model. Comput Geosci 8:217–234CrossRef
Zurück zum Zitat Miller I, Lee G, Dershowitz WS, Sharp G (1994) MAFIC, matrix/fracture interaction code with solute transport, user documentation, version 1.5, Report 9231089, Golder Associates Inc., Redmond Miller I, Lee G, Dershowitz WS, Sharp G (1994) MAFIC, matrix/fracture interaction code with solute transport, user documentation, version 1.5, Report 9231089, Golder Associates Inc., Redmond
Zurück zum Zitat Möes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150CrossRef Möes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150CrossRef
Zurück zum Zitat Mustapha H, Mustapha K (2007) A new approach to simulating flow in discrete fracture network with an optimized mesh. SIAM J Sci Comput 29(4):1439–1459CrossRef Mustapha H, Mustapha K (2007) A new approach to simulating flow in discrete fracture network with an optimized mesh. SIAM J Sci Comput 29(4):1439–1459CrossRef
Zurück zum Zitat Neuman SP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13(1):124–147CrossRef Neuman SP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13(1):124–147CrossRef
Zurück zum Zitat Nordqvist AW, Tsang YW, Tsang C-F, Dverstorp B, Andersson J (1996) Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks. J Contam Hydrol 22(1–2):39–66CrossRef Nordqvist AW, Tsang YW, Tsang C-F, Dverstorp B, Andersson J (1996) Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks. J Contam Hydrol 22(1–2):39–66CrossRef
Zurück zum Zitat Peratta A, Popov V (2006) A new scheme for numerical modelling of flow and transport processes in 3D fractured porous media. Adv Water Resour 29(1):42–61CrossRef Peratta A, Popov V (2006) A new scheme for numerical modelling of flow and transport processes in 3D fractured porous media. Adv Water Resour 29(1):42–61CrossRef
Zurück zum Zitat Pichot G, Erhel J, De Dreuzy J (2012) A generalized mixed hybrid mortar method for solving flow in stochastic discrete fracture networks. SIAM J Sci Comput 34(1):B86–B105CrossRef Pichot G, Erhel J, De Dreuzy J (2012) A generalized mixed hybrid mortar method for solving flow in stochastic discrete fracture networks. SIAM J Sci Comput 34(1):B86–B105CrossRef
Zurück zum Zitat Pouya A, Courtois A (2002) Definition of the permeability of fractured rock masses by homogenisation methods. C R Geosci 334(13):975–979CrossRef Pouya A, Courtois A (2002) Definition of the permeability of fractured rock masses by homogenisation methods. C R Geosci 334(13):975–979CrossRef
Zurück zum Zitat Sarda S, Jeannin L, Basquet R, Bourbiaux BJ (2002) Hydraulic characterization of fractured reservoirs: simulation on discrete fracture models. SPE Res Eval Eng 5(2):154–162 Sarda S, Jeannin L, Basquet R, Bourbiaux BJ (2002) Hydraulic characterization of fractured reservoirs: simulation on discrete fracture models. SPE Res Eval Eng 5(2):154–162
Zurück zum Zitat Sukumar N, Chopp DL, Moës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190:6183–6200CrossRef Sukumar N, Chopp DL, Moës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190:6183–6200CrossRef
Zurück zum Zitat Vorhalík M, Maryška J, Severýn O (2007) Mixed and nonconforming finite element methods on a system of polygons. Appl Numer Math 57(2):176–193CrossRef Vorhalík M, Maryška J, Severýn O (2007) Mixed and nonconforming finite element methods on a system of polygons. Appl Numer Math 57(2):176–193CrossRef
Metadaten
Titel
Simulation of the Steady-State Flow in Discrete Fracture Networks with Non-Conforming Meshes and Extended Finite Elements
verfasst von
S. Berrone
C. Fidelibus
S. Pieraccini
S. Scialò
Publikationsdatum
01.11.2014
Verlag
Springer Vienna
Erschienen in
Rock Mechanics and Rock Engineering / Ausgabe 6/2014
Print ISSN: 0723-2632
Elektronische ISSN: 1434-453X
DOI
https://doi.org/10.1007/s00603-013-0513-5

Weitere Artikel der Ausgabe 6/2014

Rock Mechanics and Rock Engineering 6/2014 Zur Ausgabe