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Modeling Deep Geothermal Reservoirs: Recent Advances and Future Perspectives

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Abstract

Modeling geothermal reservoirs is a key issue of a successful geothermal energy development. After over 40 years of study, many models have been proposed and applied to hundreds of sites worldwide. Nevertheless, with increasing computational capabilities, new efficient methods become available. The aim of this paper is to present recent progress on potential methods and seismic (post-)processing, as well as fluid and thermal flow simulations for porous and fractured subsurface systems. Commonly used procedures in industrial energy exploration and production such as forward modeling, seismic migration, and inversion methods together with continuum and discrete flow models for reservoir monitoring and management are explained, and some numerical examples are presented. The paper ends with the description of future fields of studies and points out opportunities, perspectives, and challenges.

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References

  • Addis MA (1997) The stress-depletion response of reservoirs. In: SPE annual technical conference and exhibition, San Antonio, 5–8 Oct 1997

    Google Scholar 

  • Adler PM, Thovert JF (1999) Theory and applications in porous media. Fractures and fracture networks, vol 15. Kluwer Academic, Dordrecht

    Google Scholar 

  • Aitken M (2010) Why we still don’t understand the social aspects of wind power: a critique of key assumptions with the literature. Energy Policy 38:1834–1841

    Article  Google Scholar 

  • Altmann J, Dorner A, Schoenball M, Müller BIR, Müller T (2008) Modellierung von porendruckinduzierten Änderungen des Spannungsfeldes in Reservoiren. In: Kongressband, Geothermiekongress 2008, Karlsruhe

    Google Scholar 

  • Arbogast T (1989) Analysis of the simulation of single phase flow through a naturally fractured reservoir. SIAM J Numer Anal 26:12–29

    Article  MathSciNet  MATH  Google Scholar 

  • Arbogast T, Douglas J, Hornung U (1990) Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J Math Anal 21:823–836

    Article  MathSciNet  MATH  Google Scholar 

  • Assteerawatt A (2008) Flow and transport modelling of fractured aquifers based on a geostatistical approach. PhD thesis, Institute of Hydraulic Engineering, University of Stuttgart

    Google Scholar 

  • Augustin M (2012) On the role of poroelasticity for modeling of stress fields in geothermal reservoirs. Int J Geomath 3:67–93

    Article  MathSciNet  MATH  Google Scholar 

  • Augustin M (2014) A method of fundamental solutions in poroelasticity to model the stress field in geothermal reservoirs. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Augustin M, Freeden W, Gerhards C, Möhringer S, Ostermann I (2012) Mathematische Methoden in der Geothermie. Math Semesterber 59:1–28

    Article  MathSciNet  MATH  Google Scholar 

  • Auradou H (2009) Influence of wall roughness on the geometrical, mechanical and transport properties of single fractures. J Phys D Appl Phys 42:214015

    Article  Google Scholar 

  • Auriault J-L (1973) Contribution à l’étude de la consolidation des sols. PhD thesis, L’Université scientifique et médicale de Grenoble

    Google Scholar 

  • Axelsson G, Gunnlaugsson E (2000) Long-term monitoring of high- and low-enthalpy fields under exploitation. In: World geothermal congress 2000, pre-congress course, Kokonoe

    Google Scholar 

  • Baisch S, Carbon D, Dannwolf U, Delacou B, Delvaux M, Dunand F, Jung R, Koller M, Martin C, Sartori M, Secanell R, Vorös R (2009) Deep heat mining Basel – seismic risk analysis. SERIANEX. Technical report, study prepared for the Departement für Wirtschaft, Soziales und Umwelt des Kantons Basel-Stadt, Amt für Umwelt und Energie

    Google Scholar 

  • Barenblatt GI, Zheltov IP, Kochina IN (1960) Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. PMM Sov Appl Math Mech 24:852–864

    MATH  Google Scholar 

  • Barnett AH, Betcke T (2008) Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains. J Comput Phys 227:7003–7026

    Article  MathSciNet  MATH  Google Scholar 

  • Bauer M, Freeden W, Jacobi H, Neu T (2014a) Energiewirtschaft 2014. Springer Spektrum, Wiesbaden

    Book  Google Scholar 

  • Bauer M, Freeden W, Jacobi H, Neu T (2014b) Handbuch Tiefe Geothermie. Springer Spektrum, Berlin/Heidelberg

    Book  Google Scholar 

  • Baysal E, Kosloff DD, Sherwood JWC (1983) Reverse time migration. Geophysics 48: 1514–1524

    Article  Google Scholar 

  • Baysal E, Kosloff DD, Sherwood JWC (1984) A two-way nonreflecting wave equation. Geophysics 49:132–141

    Article  Google Scholar 

  • Bear J (1972) Dynamics of fluids in porous media. Elsevier, New York

    MATH  Google Scholar 

  • Bear J, Tsang CF, de Marsily G (1993) Flow and contaminant transport in fractured rock. Academic, San Diego

    Google Scholar 

  • Berkowitz B (1995) Analysis of fracture network connectivity using percolation theory. Math Geol 27:467–483

    Article  Google Scholar 

  • Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25:852–864

    Article  Google Scholar 

  • Billette F, Brandsberg-Dahl S (2005) The 2004 BP velocity benchmark. In: 67th annual international meeting EAGE, Madrid. Expanded abstracts. EAGE

    Google Scholar 

  • Biondi BL (2006) Three-dimensional seismic imaging. Society of Exploration Geophysicists, Tulsa

    Google Scholar 

  • Biot MA (1935) Le problème de la consolidation des matières argileuses sous une charge. Ann Soc Sci Brux B55:110–113

    Google Scholar 

  • Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:151–164

    MATH  Google Scholar 

  • Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185

    Article  MathSciNet  MATH  Google Scholar 

  • Blakely RJ (1996) Potential theory in gravity & magnetic application. Cambridge University Press, Cambridge

    Google Scholar 

  • Blank L (1996) Numerical treatment of differential equations of fractional order. Technical report, numercial analysis report, University of Manchester

    Google Scholar 

  • Bleistein N (1987) On the imaging of reflectors in the Earth. Geophysics 49:931–942

    Article  Google Scholar 

  • Bleistein N, Cohen JK, Stockwell JW (2000) Mathematics of multidimensional seismic imaging, migration, and inversion. Springer, New York

    MATH  Google Scholar 

  • Bödvarsson G (1964) Physical characteristics of natural heat sources in Iceland. In: Proceedings of the United Nations conference on new sources of energy, vol 2. United Nations

    Google Scholar 

  • Bollhöfer M, Grote MJ, Schenk O (2008) Algebraic multilevel preconditioner for the Helmholtz equation in heterogeneous media. SIAM J Sci Comput 31:3781–3805

    Article  MathSciNet  MATH  Google Scholar 

  • Bonomi E, Pieroni E (1998) Energy-tuned absorbing boundary conditions. In: 4th SIAM international conference on mathematical and numerical aspects of wave propagation, Colorado School of Mines

    Google Scholar 

  • Bording RP, Liner CL (1994) Theory of 2.5-D reverse time migration. In: Proceedings, 64th annual international meeting: society of exploration geophysicists, Los Angeles

    Google Scholar 

  • Brouwer GK, Lokhorst A, Orlic B (2005) Geothermal heat and abandoned gas reservoirs in the Netherlands. In: Proceedings world geothermal congress 2005, Antalya

    Google Scholar 

  • Browder FE (1962) Approximation by solutions of partial differential equations. Am J Math 84:134–160

    Article  MathSciNet  MATH  Google Scholar 

  • Brown SR (1987) Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 92:1337–1347

    Article  Google Scholar 

  • Buhmann MD (2003) Radial basis functions: theory and implementations. Cambridge monographs on applied and computational mathematics, vol 12. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Buske S (1994) Kirchhoff-Migration von Einzelschußdaten. Master thesis, Institut für Meteorologie und Geophysik der Johann Wolfgang Goethe Universität Frankfurt am Main

    Google Scholar 

  • Chen M, Bai M, Roegiers JC (1999) Permeability tensors of anisotropic fracture networks. Math Geol 31:355–373

    Article  Google Scholar 

  • Chen Z, Huan G, Ma Y (2006) Computational methods for multiphase flows in porous media. Computational science & engineering, vol 2. SIAM, Philadelphia

    Google Scholar 

  • Cheng H-P, Yeh G-T (1998) Development and demonstrative application of a 3-D numerical model of subsurface flow, heat transfer, and reactive chemical transport: 3DHYDROGEOCHEM. J Contam Hydrol 34:47–83

    Article  Google Scholar 

  • Claerbout J (2009) Basic Earth imaging. Stanford University, Stanford

    Google Scholar 

  • Darcy HPG (1856) Les Fontaines Publiques de la Ville de Dijon. Victor Dalmont, Paris

    Google Scholar 

  • de Boer R (2000) Theory of porous media – highlights in historical development and current state. Springer, Berlin

    Book  MATH  Google Scholar 

  • Deng F, McMechan GA (2007) 3-D true amplitude prestack depth migration. In: Proceedings, SEG annual meeting, San Antonio

    Book  Google Scholar 

  • Dershowitz WS, La Pointe PR, Doe TW (2004) Advances in discrete fracture network modeling. In: Proceedings, US EPA/NGWA fractured rock conference, Portland, pp 882–894

    Google Scholar 

  • Diersch H-J (1985) Modellierung und numerische Simulation geohydrodynamischer Transportprozesse. PhD thesis, Akademie der Wissenschaften der DDR

    Google Scholar 

  • Diersch H-J (2000) Numerische Modellierung ober- und unterirdischer Strömungs- und Transportprozesse. In: Martin H, Pohl M (eds) Technische Hydromechanik 4 – Hydraulische und numerische Modelle. Verlag Bauwesen, Berlin

    Google Scholar 

  • Dietrich P, Helmig R, Sauter M, Hötzl H, Köngeter J, Teutsch G (2005) Flow and transport in fractured porous media. Springer, Berlin

    Book  Google Scholar 

  • Du X, Bancroft JC (2004) 2-D wave equation modeling and migration by a new finite difference scheme based on the Galerkin method. Technical report, CREWES

    Book  Google Scholar 

  • Durst P, Vuataz FD (2000) Fluid-rock interactions in hot dry rock reservoirs: a review of the HDR sites and detailed investigations of the Soultz-sous-Forets system. In: Proceedings of the world geothermal congess 2000, Kyushu-Tohoku

    Google Scholar 

  • Eberle S (2014) Forest fire determination: theory and numerical aspects. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Eberle S, Freeden W, Matthes U (2015) Forest fire spreading. In Freeden W, Nashed B, Sonar T (Eds) Handbook of Geomathematics, 2nd Edn. Springer

    Google Scholar 

  • Eker E, Akin S (2006) Lattice Boltzmann simulation of fluid flow in synthetic fractures. Transp Porous Media 65:363–384

    Article  Google Scholar 

  • Ene HI, Poliševski D (1987) Thermal flow in porous media. D. Reidel, Dordrecht

    Book  MATH  Google Scholar 

  • Engelder T, Fischer MP (1994) Influence of poroelastic behaviour on the magnitude of minimum horizontal stress, S h , in overpressured parts of sedimentary basins. Geology 22:949–952

    Article  Google Scholar 

  • Engl W, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer Academic, Dordrecht

    Book  MATH  Google Scholar 

  • Ernstson K, Alt W (2013) Gravity and geomagnetic methods in geothermal exploration: understanding and misunderstanding. World Min 65:115–122

    Google Scholar 

  • Evans KF, Cornet FH, Hashida T, Hayashi K, Ito T, Matsuki K, Wallroth T (1999) Stress and rock mechanics issues of relevance to HDR/HWR engineered geothermal systems: review of developments during the past 15 years. Geothermics 28:455–474

    Article  Google Scholar 

  • Expertengruppe “Seismisches Risiko bei hydrothermaler Geothermie” (2010) Das seismische Ereignis bei Landau vom 15. August 2009, Abschlussbericht. Technical report, on behalf of the Ministerium für Umwelt, Landwirtschaft, Ernährung, Weinbau und Forsten des Landes Rheinland-Pfalz

    Google Scholar 

  • Fehlinger T (2009) Multiscale formulations for the disturbing potential and the deflections of the vertical in locally reflected physical geodesy. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Fisher N, Lewis T, Embleton B (1993) Statistical analysis of spherical data. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Fomin S, Hashida T, Shimizu A, Matsuki K, Sakaguchi K (2003) Fractal concept in numerical simulation of hydraulic fracturing of the hot dry rock geothermal reservoir. Hydrol Process 17:2975–2989

    Article  Google Scholar 

  • Ford NJ, Simpson A (2001) The numerical solution of fractional differential equations: speed versus accuracy. Numer Algorithms 26:333–346

    Article  MathSciNet  MATH  Google Scholar 

  • Foulger G, Natland J, Presnall D, Anderson D (2005) Plates, plumes, and paradigms. Geological Society of America, Boulder

    Google Scholar 

  • Freeden C (2013) The role and the potential of communication by analysing the social acceptance of the German deep geothermal energy market. Master thesis, University of Plymouth

    Google Scholar 

  • Freeden W (1980) On the approximation of external gravitational potential with closed systems of (trial) functions. Bull Geod 54:1–20

    Article  MathSciNet  Google Scholar 

  • Freeden W (1981) On approximation by harmonic splines. Manuscr Geod 6:193–244

    MATH  Google Scholar 

  • Freeden W (1983) Least squares approximation by linear combination of (multi-)poles. Report 344, Departement of Geodetic Science and Surveying, The Ohio State University, Columbus

    Google Scholar 

  • Freeden W (1999) Multiscale modelling of spaceborne geodata. Teubner, Stuttgart

    MATH  Google Scholar 

  • Freeden W (2011) Metaharmonic lattice point theory. CRC/Taylor & Francis, Boca Raton

    MATH  Google Scholar 

  • Freeden W (2015) Geomathematics: Its Role, Its Aim, and Its Potential. In: Freeden W, Nashed Z, Sonar T (Eds) Handbook of Geomathematics, 2nd Edn. Springer

    Chapter  Google Scholar 

  • Freeden W, Blick C (2013) Signal decorrelation by means of multiscale methods. World Min 65:304–317

    Google Scholar 

  • Freeden W, Gerhards C (2010) Poloidal and toroidal field modeling in terms of locally supported vector wavelets. Math Geosci 42:817–838

    Article  MathSciNet  MATH  Google Scholar 

  • Freeden W, Gerhards C (2013) Geomathematically oriented potential theory. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  • Freeden W, Gutting M (2013) Special functions of mathematical (geo-)physics. Birkhäuser, Basel

    Book  MATH  Google Scholar 

  • Freeden W, Kersten H (1981) A constructive approximation theorem for the oblique derivative problem in potential theory. Math Methods Appl Sci 3:104–114

    Article  MathSciNet  MATH  Google Scholar 

  • Freeden W, Mayer C (2003) Wavelets generated by layer potentials. Appl Comput Harm Anal 14:195–237

    Article  MathSciNet  MATH  Google Scholar 

  • Freeden W, Michel V (2004) Multiscale potential theory with applications to geoscience. Birkhäuser, Boston

    Book  MATH  Google Scholar 

  • Freeden W, Nutz H (2011) Satellite gravity gradiometry as tensorial inverse problem. Int J Geomath 2:123–146

    Article  MathSciNet  MATH  Google Scholar 

  • Freeden W, Nutz H (2014) Mathematische Methoden. In: Bauer M, Freeden W, Jacobi H, Neu T (eds) Handbuch Tiefe Geothermie. Springer, Heidelberg, pp 125–222

    Google Scholar 

  • Freeden W, Reuter R (1990) A constructive method for solving the displacement boundary-value problem of elastostatics by use of global basis systems. Math Methods Appl Sci 12:105–128

    Article  MathSciNet  MATH  Google Scholar 

  • Freeden W, Schreiner M (2006) Local multiscale modelling of geoid undulations from deflections of the vertical. J Geodesy 79:641–651

    Article  MATH  Google Scholar 

  • Freeden W, Schreiner M (2009) Spherical functions of mathematical geosciences: a scalar, vectorial, and tensorial setup. Springer, Berlin

    MATH  Google Scholar 

  • Freeden W, Wolf K (2009) Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik. Math Semesterber 56:53–77

    Article  MathSciNet  Google Scholar 

  • Freeden W, Gervens T, Schreiner M (1998) Constructive approximation on the sphere (with applications to geomathematics). Oxford Science Publications/Clarendon, Oxford

    MATH  Google Scholar 

  • Freeden W, Mayer C, Schreiner M (2003) Tree algorithms in wavelet approximations by Helmholtz potential operators. Numer Funct Anal Optim 24:747–782

    Article  MathSciNet  MATH  Google Scholar 

  • Freeden W, Fehlinger T, Klug M, Mathar D, Wolf K (2009) Classical globally reflected gravity field determination in modern locally oriented multiscale framework. J Geodesy 83:1171–1191

    Article  Google Scholar 

  • Gehringer M, Loksha V (2012) Handbook on planning and financing geothermal power generation. ESMAP (Energy Sector Management Assistence Programm), main findings and recommendations, The International Bank for Reconstruction and Development, Washington

    Google Scholar 

  • Georgsson LS, Friedleifsson IB (2009) Geothermal energy in the world from energy perspective. In: Short course IV on exploration for geothermal resources, Lake Naivasha, pp 1–22

    Google Scholar 

  • Geothermal Energy Association (2011) Annual US geothermal power production and development report. Technical report

    Google Scholar 

  • Gerhards C (2011) Spherical multiscale methods in terms of locally supported wavelets: theory and application to geomagnetic modeling. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Gerhards C (2012) Locally supported wavelets for the separation of spherical vector fields with respect to their sources. Int J Wavel Multires Inf Proc 10:1250034

    Article  MathSciNet  MATH  Google Scholar 

  • Gerhards C (2014) A multiscale power spectrum for the analysis of the lithospheric magnetic field. Int J Geomath. 5:63–79

    Article  MathSciNet  MATH  Google Scholar 

  • Ghassemi A (2003) A thermoelastic hydraulic fracture design tool for geothermal reservoir development. Technical report, Department of Geology & Geological Engineering, University of North Dakota

    Book  Google Scholar 

  • Ghassemi A, Tarasovs S (2004) Three-dimensional modeling of injection induced thermal stresses with an example from Coso. In: Proceedings, 29th workshop on geothermal reservoir engineering, Stanford University, Stanford

    Google Scholar 

  • Ghassemi A, Zhang Q (2004) Poro-thermoelastic mechanisms in wellbore stability and reservoir stimulation. In: Proceedings, 29th workshop on geothermal reservoir engineering, Stanford University, Stanford

    Google Scholar 

  • Ghassemi A, Tarasovs S, Cheng AHD (2003) An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rock. Int J Numer Anal Methods Geomech 27:989–1004

    Article  MATH  Google Scholar 

  • Golberg MA, Chen CS (1998) The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: Golberg MA (ed) Boundary integral methods – numerical and mathematical aspects. Computational mechanics publications. WIT, Southhampton, pp 103–176

    Google Scholar 

  • Gorenflo R, Mainardi F (1997) Fractional calculus: integral and differential equations of fractional order. In: Carpinteri A, Mainardi F (eds) Fractals and fractional calculus in continuum mechanics. Springer, Wien, pp 223–276

    Chapter  Google Scholar 

  • Hammons TJ (2011) Geothermal power generation: global perspectives, technology, direct uses, plants, drilling and sustainability worldwide. In: Electricity infrastructures in the global marketplace. InTech, pp 195–234

    Google Scholar 

  • Haney MM, Bartel LC, Aldridge DF, Symons NP (2005) Insight into the output of reverse-time migration: what do the amplitudes mean? In: Proceedings, SEG annual meeting, Houston

    Google Scholar 

  • Helmig R, Niessner J, Flemisch B, Wolff M, Fritz J (2014) Efficient modeling of flow and transport in porous media using multi-physics and multi-scale approaches. In: Freeden W, Nashed Z, Sonar T (eds) Handbook of geomathematics, 2nd edn. Springer, New York

    Google Scholar 

  • Heuer N, Küpper T, Windelberg D (1991) Mathematical model of a hot dry rock system. Geophys J Int 105:659–664

    Article  Google Scholar 

  • Hicks TW, Pine RJ, Willis-Richards J, Xu S, Jupe AJ, Rodrigues NEV (1996) A hydro-thermo-mechanical numerical model for HDR geothermal reservoir evaluation. Int J Rock Mech Min Sci 33:499–511

    Article  Google Scholar 

  • Hillis RR (2000) Pore pressure/stress coupling and its implications for seismicity. Explor Geophys 31:448–454

    Article  Google Scholar 

  • Hillis RR (2001) Coupled changes in pore pressure and stress in oil fields and sedimentary basins. Pet Geosci 7:419–425

    Article  Google Scholar 

  • Hillis RR (2003) Pore pressure/stress coupling and its implications for rock failure. In: Vanrensbergen P, Hillis RR, Maltman AJ, Morley CK (eds) Subsurface sediment mobilization. Geological Society of London, London, pp 359–368

    Google Scholar 

  • Ilyasov M (2011) A tree algorithm for Helmholtz potential wavelets on non-smooth surfaces: theoretical background and application to seismic data postprocessing. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • International Energy Agency (2010) Annual report. Technical report

    Google Scholar 

  • Itasca Consulting Group Inc (2000) UDEC user’s guide. Minnesota

    Google Scholar 

  • Jackson JD (1998) Classical electrodynamics. Wiley, New York

    MATH  Google Scholar 

  • Jacobs F, Meyer H (1992) Geophysik – Signale aus der Erde. Teubner, Stuttgart

    Book  Google Scholar 

  • Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics. Blackwell, Malden

    Google Scholar 

  • Jia X, Hu T (2006) Element-free precise integration method and its application in seismic modelling and imaging. Geophys J Int 166:349–372

    Article  Google Scholar 

  • Jing L, Hudson JA (2002) Numerical methods in rock mechanics. Int J Rock Mech Min Sci 39:409–427

    Article  Google Scholar 

  • Jing Z, Willis-Richards J, Watanabe K, Hashida T (2000) A three-dimensional stochastic rock mechanics model of engineered geothermal systems in fractured crystalline rock. J Geophys Res 105:23663–23679

    Article  Google Scholar 

  • Jing Z, Watanabe K, Willis-Richards J, Hashida T (2002) A 3-D water/rock chemical interaction model for prediction of HDR/HWR geothermal reservoir performance. Geothermics 31:1–28

    Article  Google Scholar 

  • Johansson BT, Lesnic D (2008) A method of fundamental solutions for transient heat conduction. Eng Anal Bound Elem 32:697–703

    Article  MATH  Google Scholar 

  • Johansson BT, Lesnic D, Reeve T (2011) A method of fundamental solutions for two-dimensional heat conduction. Int J Comput Math 88:1697–1713

    Article  MathSciNet  MATH  Google Scholar 

  • John V, Schmeyer E (2008) Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion. Comput Methods Appl Mech Eng 198:475–494

    Article  MathSciNet  MATH  Google Scholar 

  • John V, Kaya S, Layton W (2006) A two-level variational multiscale method for convection-dominated convection-diffusion equations. Comput Methods Appl Mech Eng 195:4594–4603

    Article  MathSciNet  MATH  Google Scholar 

  • Jung R (2007) Stand und Aussichten der Tiefengeothermie in Deutschland. Erdöl, Erdgas, Kohle 123:1–7

    Google Scholar 

  • Katsurada M (1989) A mathematical study of the charge simulation method II. J Fac Sci Univ Tokyo Sect IA Math 36:135–162

    MathSciNet  MATH  Google Scholar 

  • Katsurada M, Okamoto H (1996) The collocation points of the fundamental solution method for the potential problem. Comput Math Appl 31:123–137

    Article  MathSciNet  MATH  Google Scholar 

  • Kazemi H (1969) Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Soc Petrol Eng J 246:451–461

    Article  Google Scholar 

  • Kazemi H, Merril LS, Porterfield KL, Zeman PR (1976) Numerical simulation of water-oil flow in naturally fractured reservoirs. In: Proceedings, SPE-AIME 4th symposium on numerical simulation of reservoir performance, Los Angeles

    Google Scholar 

  • Kim I, Lindquist WB, Durham WB (2003) Fracture flow simulation using a finite-difference lattice Boltzmann method. Phys Rev E 67:046708

    Article  Google Scholar 

  • Kimura S, Masuda Y, Hayashi K (1992) Efficient numerical method based on double porosity model to analyze heat and fluid flows in fractured rock formations. JSME Int J Ser 2 35:395–399

    Google Scholar 

  • Kühn M (2009) Modelling feed-back of chemical reactions on flow fields in hydrothermal systems. Surv Geophys 30:233–251

    Article  Google Scholar 

  • Kühn M, Stöfen H (2005) A reactive flow model of the geothermal reservoir Waiwera, New Zealand. Hydrogeol J 13:606–626

    Article  Google Scholar 

  • Kupradze VD (1964) A method for the approximate solution of limiting problems in mathematical physics. USSR Comput Math Math Phys 4:199–205

    Article  MATH  Google Scholar 

  • Lai M, Krempl E, Ruben D (2010) Introduction to continuum mechanics. Butterworth-Heinemann, Burlington

    Google Scholar 

  • Landau LD, Pitaevskii LP, Lifshitz EM, Kosevich AM (1986) Theory of elasticity. Theoretical physics, vol 7, 3rd edn. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Lang U (1995) Simulation regionaler Strömungs- und Transportvorgänge in Karstaquifern mit Hilfe des Doppelkontinuum-Ansatzes: Methodenentwicklung und Parameteridentifikation. PhD thesis, University of Stuttgart

    Google Scholar 

  • Lang U, Helmig R (1995) Numerical modeling in fractured media – identification of measured field data. In: Herbert M, Kovar K (eds) Groundwater quality: remediation and protection. IAHS and University Karlova, Prague, pp 203–212

    Google Scholar 

  • Lee J, Choi SU, Cho W (1999) A comparative study of dual-porosity model and discrete fracture network model. KSCE J Civ Eng 3:171–180

    Article  Google Scholar 

  • Li X (2008a) Convergence of the method of fundamental solutions for Poisson’s equation on the unit sphere. Adv Comput Math 28:269–282

    Article  MathSciNet  MATH  Google Scholar 

  • Li X (2008b) Rate of convergence of the method of fundamental solutions and hyperinterpolation for modified Helmholtz equations on the unit ball. Adv Comput Math 29:393–413

    Article  MathSciNet  MATH  Google Scholar 

  • Lomize GM (1951) Seepage in fissured rocks. State Press, Moscow

    Google Scholar 

  • Long J, Remer J, Wilson C, Witherspoon P (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18:645–658

    Article  Google Scholar 

  • Luchko Y (2009) Maximum principle for the generalized time-fractional diffusion equation. J Math Anal Appl 351:218–223

    Article  MathSciNet  MATH  Google Scholar 

  • Luchko Y (2010) Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation. Comput Math Appl 59:1766–1772

    Article  MathSciNet  MATH  Google Scholar 

  • Luchko Y (2015) Fractional diffusion and wave propagation. In: Freeden W, Nashed M, Sonar T (Eds) Handbook of Geomathematics, 2nd Edn. Springer

    Google Scholar 

  • Luchko Y, Punzi A (2011) Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations. Int J Geomath 1:257–276

    Article  MathSciNet  MATH  Google Scholar 

  • Martin GS, Marfurt KJ, Larsen S (2002) Marmousi-2: an updated model for the investigation of AVO in structurally complex areas. In: Proceedings, SEG annual meeting, Salt Lake City

    Google Scholar 

  • Maryška J, Severýn O, Vohralík M (2004) Numerical simulation of fracture flow in mixed-hybrid FEM stochastic discrete fracture network model. Comput Geosci 8:217–234

    Article  MathSciNet  MATH  Google Scholar 

  • Masahi M, King P, Nurafza P (2007) Fast estimation of connectivity in fractured reservoirs using percolation theory. SPE J 12:167–178

    Article  Google Scholar 

  • Mayer C (2007) A wavelet approach to the Stokes problem. Habilitation thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Mayer C, Freeden W (2015) Stokes problem, layer potentials and regularizations, multiscale applications. In: Freeden W, Nashed Z, Sonar T (Eds) Handbook of Geomathematics, 2nd Edn. Springer

    Google Scholar 

  • McLean W, Mustapha K (2009) Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation. Numer Algorithms 52:69–88

    Article  MathSciNet  MATH  Google Scholar 

  • Menke W (1984) Geophysical data analysis: discrete inverse theory. Academic, Orlando

    MATH  Google Scholar 

  • Michel V (2002) A multiscale approximation for operator equations in separable Hilbert spaces – case study: reconstruction and description of the Earth’s interior. Habilitation thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Michel V, Fokas AS (2008) A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet based methods. Inverse Probl 24:045019

    Article  MathSciNet  MATH  Google Scholar 

  • Min KB, Jing L, Stephansson O (2004) Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: method and application to the field data from Sellafield, UK. Hydrogeol J 12:497–510

    Article  Google Scholar 

  • MIT (Massachusetts Institute of Technology) (2006) The future of geothermal energy. http://mitei.mit.edu/publications/reports-studies/future-geothermal-energy

  • Mo H, Bai M, Lin D, Roegiers JC (1998) Study of flow and transport in fracture network using percolation theory. Appl Math Model 22:277–291

    Article  Google Scholar 

  • Moeck I, Kwiatek G, Zimmermann G (2009) The in-situ stress field as a key issue for geothermal field development – a case study from the NE German Basin. In: Proceedings, 71st EAGE conference & exhibition, Amsterdam

    Google Scholar 

  • Möhringer S (2014) Decorrelation of gravimetric data. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Mongillo M (2011) International efforts to promote global sustainable geothermal development. In: GIA annual report executive summary, Singapore, pp 1–19

    Google Scholar 

  • Morgan WJ (1971) Convective plumes in the lower mantle. Nature 230:42–43

    Article  Google Scholar 

  • Müller C (1998) Analysis of spherical symmetries in euclidean spaces. Applied mathematical sciences, vol 129. Springer, Berlin

    Google Scholar 

  • Müller C, Kersten H (1980) Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung \(\bigtriangleup U + k^{2}U = 0\). Math Method Appl Sci 2:48–67

    Article  MATH  Google Scholar 

  • Nakao S, Ishido T (1998) Pressure-transient behavior during cold water injection into geothermal wells. Geothermics 27:401–413

    Article  Google Scholar 

  • Neuman S (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13:124–147

    Article  Google Scholar 

  • Neuman S, Depner J (1988) Use of variable-scale pressure test data to estimate the log hydraulic conductivity covariance and dispersivity of fractured granites near Oracle, Arizona. J Hydrol 102:475–501

    Article  Google Scholar 

  • Nolet G (2008) Seismic tomography: imaging the interior of the Earth and Sun. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Oden M, Niemi A (2006) From well-test data to input to stochastic continuum models: effect of the variable support scale of the hydraulic data. Hydrogeol J 14:1409–1422

    Article  Google Scholar 

  • Ödner H (1998) One-dimensional transient flow in a finite fractured aquifer system. Hydrol Sci J 43:243–265

    Article  Google Scholar 

  • Ostermann I (2011a) Modeling heat transport in deep geothermal systems by radial basis functions. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Ostermann I (2011b) Three-dimensional modeling of heat transport in deep hydrothermal reservoirs. Int J Geomath 2:37–68

    Article  MathSciNet  MATH  Google Scholar 

  • O’Sullivan MJ, Pruess K, Lippmann MJ (2001) State of the art of geothermal reservoir simulation. Geothermics 30:395–429

    Article  Google Scholar 

  • Ouenes A (2000) Practical application of fuzzy logic and neural networks to fractured reservoir characterization. Comput Geosci 26:953–962

    Article  Google Scholar 

  • Peters RR, Klavetter EA (1988) A continuum model for water movement in an unsaturated fractured rock mass. Water Resour Res 24:416–430

    Article  Google Scholar 

  • Phillips PJ (2005) Finite element method in linear poroelasticity: theoretical and computational results. PhD thesis, University of Texas, Austin

    Google Scholar 

  • Phillips PJ, Wheeler MF (2007) A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case. Comput Geosci 11:131–144

    Article  MathSciNet  MATH  Google Scholar 

  • Phillips WS, Rutledge JT, House LS, Fehler MC (2002) Induced microearthquake patterns in hydrocarbon and geothermal reservoirs: six case studies. Pure Appl Geophys 159:345–369

    Article  Google Scholar 

  • Podvin P, Lecomte I (1991) Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. Geophys J Int 105:271–284

    Article  Google Scholar 

  • Popov M (1982) A new method of computation of wave fields using Gaussian beams. Wave Motion 4:85–97

    Article  MathSciNet  MATH  Google Scholar 

  • Pruess K (1990) Modelling of geothermal reservoirs: fundamental processes, computer simulation and field applications. Geothermics 19:3–15

    Article  Google Scholar 

  • Pruess K, Narasimhan TN (1985) A practical method for modeling fluid and heat flow in fractured porous media. Soc Pet Eng J 25:14–26

    Article  Google Scholar 

  • Pruess K, Wang JSY, Tsang YW (1986) Effective continuum approximation for modeling fluid and heat flow in fractured porous tuff. Technical report, Sandia National Laboratories Report SAND86-7000, Albuquerque

    Google Scholar 

  • Reichenberger V, Jakobs H, Bastian P, Helmig R (2006) A mixed-dimensional finite volume method for two-phase flow in fractured porous media. Adv Water Resour 29:1020–1036

    Article  Google Scholar 

  • Renaut R, Fröhlich J (1996) A pseudospectral Chebychev method for 2D wave equation with domain stretching and absorbing boundary conditions. J Comput Phys 124:324–336

    Article  MathSciNet  MATH  Google Scholar 

  • Renner J, Steeb H (2015) Modeling of fluid transport in geothermal research. In: Freeden W, Nashed Z, Sonar T (Eds) Handbook of Geomathematics, 2nd Edn. Springer

    Google Scholar 

  • Rice JR, Cleary MP (1976) Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev Geophys Space Phys 14:227–241

    Article  Google Scholar 

  • Ritter JRR, Christensen UR (2007) Mantle plumes: a multidisciplinary approach. Springer, Berlin

    Book  Google Scholar 

  • Runge C (1885) Zur Theorie der eindeutigen analytischen Funktionen. Acta Math 6:229–234

    Article  MathSciNet  Google Scholar 

  • Rutqvist J, Stephansson O (2003) The role of hydromechanical coupling in fractured rock engineering. Hydrogeol J 11:7–40

    Article  Google Scholar 

  • Saemundsson K (2009) Geothermal systems in global perspective. In: Short course IV on exploration for geothermal resources, Lake Naivasha

    Google Scholar 

  • Sahimi M (1995) Flow and transport in porous media and fractured rock: from classical methods to modern approaches. VCH, Weinheim

    MATH  Google Scholar 

  • Sanyal SK (2005) Classification of geothermal systems – a possible scheme. In: Proceedings, 30th workshop on geothermal reservoir engineering, Stanford University, Stanford, SGP-TR-176, pp 85–92

    Google Scholar 

  • Sanyal SK, Butler SJ, Swenson D, Hardeman B (2000) Review of the state-of-the-art of numerical simulation of enhanced geothermal systems. In: Proceedings, world geothermal congress, Kyushu-Tohoku

    Google Scholar 

  • Schanz M (2001) Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids. Eng Anal Bound Elem 25:363–376

    Article  MATH  Google Scholar 

  • Schubert G, Turcotte DL, Olson P (2001) Mantle convection in the Earth and Planets. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Schulz R (2009) Aufbau eines geothermischen Informationssystems für Deutschland. Technical report, Leibniz-Institut für Angewandte Geophysik, Hannover

    Google Scholar 

  • Semtchenok NM, Popov MM, Verdel AR (2009) Gaussian beam tomography. In: Extended abstracts, 71st EAGE conference & exhibition, Amsterdam

    Google Scholar 

  • Showalter RE (2000) Diffusion in poro-elastic media. J Math Anal Appl 251:310–340

    Article  MathSciNet  MATH  Google Scholar 

  • Smyrlis Y-S (2009a) Applicability and applications of the method of fundamental solutions. Math Comput 78:1399–1434

    Article  MathSciNet  MATH  Google Scholar 

  • Smyrlis Y-S (2009b) Mathematical foundation of the MFS for certain elliptic systems in linear elasticity. Numer Math 112:319–340

    Article  MathSciNet  MATH  Google Scholar 

  • Smyrlis Y-S, Karageorghis A (2009) Efficient implementation of the MFS: the three scenarios. J Comput Appl Math 227:83–92

    Article  MathSciNet  MATH  Google Scholar 

  • Snieder R (2002) The perturbation method in elastic wave scattering and inverse scattering in pure and applied science. In: General theory of elastic wave. Academic, San Diego, pp 528–542

    Google Scholar 

  • Snow DT (1965) A parallel plate model of fractured permeable media. PhD thesis, University of California, Berkeley

    Google Scholar 

  • Stothoff S, Or D (2000) A discrete-fracture boundary integral approach to simulating coupled energy and moisture transport in a fractured porous medium. In: Faybishenko B, Witherspoon PA, Benson SM (eds) Dynamics of fluids in fractured rocks, concepts and recent advances. AGU geophysical monograph, vol 122. American Geophysical Union, Washington, DC, pp 269–279

    Google Scholar 

  • Sudicky EA, McLaren RG (1992) The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations. Water Resour Res 28:499–514

    Article  Google Scholar 

  • Symes WW (2003) Kinematics of reverse time S-G migration. Technical report, Rice University

    Google Scholar 

  • Symes WW (2007) Reverse time migration with optimal checkpointing. Geophysics 72:SM213–SM221

    Article  Google Scholar 

  • Takenaka H, Wang Y, Furumura T (1999) An efficient approach of the pseudospectral method for modelling of geometrical symmetric seismic wavefields. Earth Planets Space 51:73–79

    Article  Google Scholar 

  • Tang DH, Frind EO, Sudicky EA (1981) Contaminant transport in fractured porous media: analytical solution for a single fracture. Water Resour Res 17:555–564

    Article  Google Scholar 

  • Tran NH, Rahman SS (2006) Modelling discrete fracture networks using neuro-fractal-stochastic simulation. J Eng Appl Sci 1:154–160

    Google Scholar 

  • Travis BJ (1984) TRACR3D: a model of flow and transport in porous/fractured media. Technical report, Los Alamos National Laboratory LA-9667-MS, Los Alamos

    Google Scholar 

  • Trefftz E (1926) Ein Gegenstück zum Ritzschen Verfahren. In: Proceedings of the 2nd international congress for applied mechanics, Zürich

    Google Scholar 

  • Tsang Y, Tsang C (1987) Chanel flow model through fractured media. Water Resour Res 23:467–479

    Article  Google Scholar 

  • Tsang Y, Tsang C (1989) Flow chaneling in a single fracture as a two-dimensional strongly heterogeneous permeable medium. Water Resour Res 25:2076–2080

    Article  Google Scholar 

  • Tsang Y, Tsang C, Hale F, Dverstorp B (1996) Tracer transport in a stochastic continuum model of fractured media. Water Resour Res 32:3077–3092

    Article  Google Scholar 

  • Turcotte DL, Schubert G (2001) Geodynamics. Cambridge University Press, Cambridge

    Google Scholar 

  • Vidale J (1988) Finite-difference calculation of travel times. Bull Seismol Soc Am 78:2062–2076

    Google Scholar 

  • Walsh J (1929) The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions. Bull Am Math Soc 35:499–544

    Article  MathSciNet  MATH  Google Scholar 

  • Warren JE, Root PJ (1963) The behaviour of naturally fractured reservoirs. Soc Pet Eng J 228:245–255

    Article  Google Scholar 

  • Watanabe K, Takahashi T (1995) Fractal geometry characterization of geothermal reservoir fracture networks. J Geophys Res 100:521–528

    Article  Google Scholar 

  • Welding L (2007) GLITNIR geothermal research. In: United States geothermal energy market report, pp 1–37

    Google Scholar 

  • Wendland H (2005) Scattered data approximation. Cambridge monographs on applied and computational mathematics, vol 17. Cambridge University Press, Cambridge

    Google Scholar 

  • Wilson JT (1963) A possible origin of the Hawaiian island. Can J Phys 41:863–868

    Article  Google Scholar 

  • Wolf K (2009) Multiscale modeling of classical boundary value problems in physical geodesy by locally supported wavelets. PhD thesis, Geomathematics Group, University of Kaiserslautern

    Google Scholar 

  • Wu YS (2000) On the effective continuum method for modeling multiphase flow, multicomponent transport and heat transfer in fractured rock. In: Faybishenko B, Witherspoon PA, Benson SM (eds) Dynamics of fluids in fractured rocks, concepts and recent advances. American Geophysical Union, Washington, DC, pp 299–312

    Chapter  Google Scholar 

  • Wu YS, Pruess K (2005) A physically based numerical approach for modeling fracture-matrix interaction in fractured reservoirs. In: Proceedings, world geothermal congress 2005, Antalya

    Google Scholar 

  • Wu YS, Qin G (2009) A generalized numerical approach for modeling multiphase flow and transport in fractured porous media. Commun Comput Phys 6:85–108

    Article  MathSciNet  Google Scholar 

  • Wu X, Pope GA, Shook GM, Srinivasan S (2005) A semi-analytical model to calculate energy production in single fracture geothermal reservoirs. Geotherm Resour Counc Trans 29:665–669

    Google Scholar 

  • Wu RS, Xie XB, Wu XY (2006) One-way and one-return approximations (de Wolf approximation) for fast elastic wave modeling in complex media. Adv Geophys 48:265–322

    Article  Google Scholar 

  • Xie XB, Wu RS (2006) A depth migration method based on the full-wave reverse time calculation and local one-way propagation. In: Proceedings, SEG annual meeting, New Orleans

    Book  Google Scholar 

  • Yilmaz O (1987) Seismic data analysis: processing, inversion, and interpretation of seismic data. Society of Exploration Geophysicists, Tulsa

    Google Scholar 

  • Yin S (2008) Geomechanics-reservoir modeling by displacement discontinuity-finite element method. PhD thesis, University of Waterloo, Ontario

    Google Scholar 

  • Zhao C, Hobbs BE, Baxter K, Mühlhaus HB, Ord A (1999) A numerical study of pore-fluid, thermal and mass flow in fluid-saturated porous rock basins. Eng Comput 16:202–214

    Article  MATH  Google Scholar 

  • Zhou XX, Ghassemi A (2009) Three-dimensional poroelastic simulation of hydraulic and natural fractures using the displacement discontinuity method. In: Proceedings of the 34th workshop on geothermal reservoir engineering, Stanford

    Google Scholar 

  • Zubkov VV, Koshelev VF, Lin’kov AM (2007) Numerical modeling of hydraulic fracture initiation and development. J Min Sci 43:40–56

    Article  Google Scholar 

  • Zyvoloski G (1983) Finite element methods for geothermal reservoir simulation. Int J Numer Anal Methods Geomech 7:75–86

    Article  MATH  Google Scholar 

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Acknowledgements

The work of the Geomathematics Group Kaiserslautern and G.E.O.S Ingenieurgesellschaft mbH, Freiberg, is supported by the “Verbundprojekt GEOFÜND: Charakterisierung und Weiterentwicklung integrativer Untersuchungsmethoden zur Quantifizierung des Fündigkeitsrisikos” (PI: W. Freeden) Federal Ministry for Economic Affairs and Energy (BMWi) Germany. M. Augustin has been supported by a fellowship of the German National Academic Foundation (Studienstiftung des deutschen Volkes). C. Gerhards has been supported by a fellowship within the Postdoc-program of the German Academic Exchange Service (DAAD). S. Eberle is thankful for the support by the Rhineland-Palatinate Center of Excellence for Climate Change Impacts. M. Ilyasov, S. Möhringer, H. Nutz, I. Ostermann, and A. Punzi thank for the support by the Rhineland-Palatinate excellence research center “Center for Mathematical and Computational Modeling (CM)2” and the University of Kaiserslautern within the scope of the project “EGMS” (PI: W. Freeden).

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Authors and Affiliations

  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Matthias Augustin, Christian Blick, Sarah Eberle, Willi Freeden, Christian Gerhards Maxim Ilyasov, Matthias Klug, Sandra Möhringer, Helga Nutz & Alessandro Punzi

  2. CBM GmbH, Bexbach, Germany

    Mathias Bauer

  3. G.E.O.S. Ingenieurgesellschaft mbH, Freiberg, Germany

    René Kahnt

  4. Tiefe Geothermie Saar GmbH, Saarbrücken, Germany

    Thomas Neu

  5. Fraunhofer ITWM, Kaiserslautern, Germany

    Isabel Michel née Ostermann

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Correspondence to Matthias Augustin .

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  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

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Augustin, M. et al. (2015). Modeling Deep Geothermal Reservoirs: Recent Advances and Future Perspectives. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_22

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