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2014 | OriginalPaper | Buchkapitel

4. Mathematische Methoden

verfasst von: Prof. Dr. Willi Freeden, Helga Nutz

Erschienen in: Handbuch Tiefe Geothermie

Verlag: Springer Berlin Heidelberg

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Zusammenfassung

Aufgrund des gestiegenen Bedarfs an erneuerbaren Energien und den vielfältigen Produktionsmöglichkeiten ist die Modellierung von geothermischen Systemen ein zentrales Thema in der heutigen Ingenieurspraxis. Nach nunmehr bereits 40-jähriger Forschung wurden viele Modelle vorgeschlagen und weltweit an verschiedenen Standorten zum Einsatz gebracht. Inzwischen sind durch gestiegene Rechnerleistung und genauere Observations- und Messverfahren effizientere numerische Methoden und Simulationen realisierbar, die heutzutage wirklichkeitsnähere Modellumsetzungen als in der Vergangenheit ermöglichen.
Das Ziel des Beitrags ist es, die neuere Entwicklung im Bereich der Modellbildung für die Gebiete der Potentialmethoden, des seismischen Prozessing sowie der Simulation von Fluid- und Wärmeflüssen in porösen und geklüfteten unterirdischen Systemen darzustellen. Die üblicherweise im Bereich industrieller Energieexploration und -produktion eingesetzten Verfahren wie Gravimetrie, seismische Migration und Inversionsmethode in Kombination mit kontinuierlichen und diskreten Strömungsmodellen für die Kontrolle und das Management von Reservoiren werden aufgeführt und ihre Wirksamkeit in zwei- und dreidimensionalen Anwendungen erläutert. Darüber hinaus werden instruktive numerische Beispiele präsentiert, die auch Nichtmathematikern die große Bedeutung der Mathematik als eine Schlüsseltechnologie in der geothermischen Forschung vermitteln, ohne dass hierfür ein tieferes Verständnis des zugrunde liegenden mathematischen Apparates erforderlich ist. Abschließend werden zukünftige Forschungsfelder geothermischer Anwendung beschrieben sowie relevante Perspektiven und Herausforderungen diskutiert.
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Zurück zum Zitat Freeden, W., Reuter, R.: A constructive method for solving the displacement boundary–value problem of elastostatics by use of global basis systems. Math Meth Appl Sci 12, 105–128 (1990) Freeden, W., Reuter, R.: A constructive method for solving the displacement boundary–value problem of elastostatics by use of global basis systems. Math Meth Appl Sci 12, 105–128 (1990)
Zurück zum Zitat Freeden, W., Schreiner, M.: Local multiscale modelling of geoid undulations from deflections of the vertical. J Geodesy 79, 641–651 (2006) Freeden, W., Schreiner, M.: Local multiscale modelling of geoid undulations from deflections of the vertical. J Geodesy 79, 641–651 (2006)
Zurück zum Zitat Freeden, W., Wolf, K.: Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik. Math Semesterber 56, 53–77 (2009) Freeden, W., Wolf, K.: Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik. Math Semesterber 56, 53–77 (2009)
Zurück zum Zitat Gehringer, M., Loksha, V.: Handbook on planning and financing geothermal power generation. ESMAP (Energy Sector Management Assistence Programm), Main Findings and Recommandations. The International Bank for Reconstruction and Developement, Washington (2012) Gehringer, M., Loksha, V.: Handbook on planning and financing geothermal power generation. ESMAP (Energy Sector Management Assistence Programm), Main Findings and Recommandations. The International Bank for Reconstruction and Developement, Washington (2012)
Zurück zum Zitat Georgsson, L.S., Friedleifsson, I.B.: Geothermal energy in the world from energy perspective. In: Short Course IV on Exploration for Geothermal Resources, S. 1–22 (2009) Georgsson, L.S., Friedleifsson, I.B.: Geothermal energy in the world from energy perspective. In: Short Course IV on Exploration for Geothermal Resources, S. 1–22 (2009)
Zurück zum Zitat Geothermal Energy Association: Annual US geothermal power production and development report. Tech. rep. (2011) Geothermal Energy Association: Annual US geothermal power production and development report. Tech. rep. (2011)
Zurück zum Zitat Gerhards, C.: Spherical multiscale methods in terms of locally supported wavelets: Theory and application to geomagnetic modeling. Ph.D. thesis. Geomathematics Group, University of Kaiserslautern (2011) Gerhards, C.: Spherical multiscale methods in terms of locally supported wavelets: Theory and application to geomagnetic modeling. Ph.D. thesis. Geomathematics Group, University of Kaiserslautern (2011)
Zurück zum Zitat Gerhards, C.: A multiscale power spectrum for the analysis of the lithospheric magnetic field. Int J Geomath 5, 63–79 (2014) Gerhards, C.: A multiscale power spectrum for the analysis of the lithospheric magnetic field. Int J Geomath 5, 63–79 (2014)
Zurück zum Zitat Ghassemi, A.: A thermoelastic hydraulic fracture design tool for geothermal reservoir development. Tech. rep. Department of Geology & Geological Engineering, University of North Dakota (2003) Ghassemi, A.: A thermoelastic hydraulic fracture design tool for geothermal reservoir development. Tech. rep. Department of Geology & Geological Engineering, University of North Dakota (2003)
Zurück zum Zitat Ghassemi, A., Tarasovs, S., Cheng, A.H.D.: An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rock. Int J Numer Anal Meth Geomech 27, 989–1004 (2003) Ghassemi, A., Tarasovs, S., Cheng, A.H.D.: An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rock. Int J Numer Anal Meth Geomech 27, 989–1004 (2003)
Zurück zum Zitat Golberg, M.A., Chen, C.S.: The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: Golberg, M.A. (Hrsg.) Boundary Integral Methods – Numerical and Mathematical Aspects, S. 103–176. Computational Mechanics Publications, WIT Press, Southhampton (1998) Golberg, M.A., Chen, C.S.: The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: Golberg, M.A. (Hrsg.) Boundary Integral Methods – Numerical and Mathematical Aspects, S. 103–176. Computational Mechanics Publications, WIT Press, Southhampton (1998)
Zurück zum Zitat Gorenflo, R., Mainardi, F.: Fractional calculus: Integral and differential equations of fractional order. In: Carpinteri, A., Mainardi, F. (Hrsg.) Fractals and Fractional Calculus in Continuum Mechanics, S. 223–276. Springer, Wien (1997) Gorenflo, R., Mainardi, F.: Fractional calculus: Integral and differential equations of fractional order. In: Carpinteri, A., Mainardi, F. (Hrsg.) Fractals and Fractional Calculus in Continuum Mechanics, S. 223–276. Springer, Wien (1997)
Zurück zum Zitat Grasmair, M., Haltmeier, M., Scherzer, O.: Sparsity in inverse geophysical problems. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, S. 763–784. Springer, Berlin Heidelberg (2010) Grasmair, M., Haltmeier, M., Scherzer, O.: Sparsity in inverse geophysical problems. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, S. 763–784. Springer, Berlin Heidelberg (2010)
Zurück zum Zitat Haar, A.: Zur Theorie der orthogonalen Funktionsysteme. Math Ann 69, 331–371 (1910) Haar, A.: Zur Theorie der orthogonalen Funktionsysteme. Math Ann 69, 331–371 (1910)
Zurück zum Zitat Haney, M.M., Bartel, L.C., Aldridge, D.F., Symons, N.P.: Insight into the output of reverse-time migration: What do the amplitudes mean? In: Proceedings, SEG Annual Meeting. Internal Report, Houston (2005) Haney, M.M., Bartel, L.C., Aldridge, D.F., Symons, N.P.: Insight into the output of reverse-time migration: What do the amplitudes mean? In: Proceedings, SEG Annual Meeting. Internal Report, Houston (2005)
Zurück zum Zitat Helmig, R., Niessner, J., Flemisch, B., Wolff, M., Fritz, J.: Efficient modeling of flow and transport in porous media using multi-physics and multi-scale approaches. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, 2. Aufl. Springer, New York (2014). Accepted for publilcation Helmig, R., Niessner, J., Flemisch, B., Wolff, M., Fritz, J.: Efficient modeling of flow and transport in porous media using multi-physics and multi-scale approaches. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, 2. Aufl. Springer, New York (2014). Accepted for publilcation
Zurück zum Zitat Heuer, N., Küpper, T., Windelberg, D.: Mathematical model of a hot dry rock system. Geophys J Int 105, 659–664 (1991) Heuer, N., Küpper, T., Windelberg, D.: Mathematical model of a hot dry rock system. Geophys J Int 105, 659–664 (1991)
Zurück zum Zitat Hillis, R.R.: Pore pressure/stress coupling and its implications for seismicity. Explor Geophys 31, 448–454 (2000) Hillis, R.R.: Pore pressure/stress coupling and its implications for seismicity. Explor Geophys 31, 448–454 (2000)
Zurück zum Zitat Hillis, R.R.: Coupled changes in pore pressure and stress in oil fields and sedimentary basins. Pet Geosci 7, 419–425 (2001) Hillis, R.R.: Coupled changes in pore pressure and stress in oil fields and sedimentary basins. Pet Geosci 7, 419–425 (2001)
Zurück zum Zitat Hillis, R.R.: Pore pressure/stress coupling and its implications for rock failure. In: Vanrensbergen, P., Hillis, R.R., Maltman, A.J., Morley, C.K. (Hrsg.) Subsurface Sediment Mobilization, S. 359–368. Geological Society of London, London (2003) Hillis, R.R.: Pore pressure/stress coupling and its implications for rock failure. In: Vanrensbergen, P., Hillis, R.R., Maltman, A.J., Morley, C.K. (Hrsg.) Subsurface Sediment Mobilization, S. 359–368. Geological Society of London, London (2003)
Zurück zum Zitat Ilyasov, M.: A tree algorithm for Helmholtz potential wavelets on non-smooth surfaces: Theoretical background and application to seismic data postprocessing. Ph.D. thesis. Geomathematics Group, University of Kaiserslautern (2011) Ilyasov, M.: A tree algorithm for Helmholtz potential wavelets on non-smooth surfaces: Theoretical background and application to seismic data postprocessing. Ph.D. thesis. Geomathematics Group, University of Kaiserslautern (2011)
Zurück zum Zitat Jackson, J.D.: Classical electrodynamics. Wiley, New York (1998) Jackson, J.D.: Classical electrodynamics. Wiley, New York (1998)
Zurück zum Zitat Jacobs, F., Meyer, H.: Geophysik – Signale aus der Erde. Teubner, Stuttgart (1992) Jacobs, F., Meyer, H.: Geophysik – Signale aus der Erde. Teubner, Stuttgart (1992)
Zurück zum Zitat Jaeger, J.C., Cook, N.G.W., Zimmerman, R.W.: Fundamentals of rock mechanics. Blackwell Publishing, Malden (2007) Jaeger, J.C., Cook, N.G.W., Zimmerman, R.W.: Fundamentals of rock mechanics. Blackwell Publishing, Malden (2007)
Zurück zum Zitat Jia, X., Hu, T.: Element-free precise integration method and its application in seismic modelling and imaging. Geophys J Int 166, 349–372 (2006) Jia, X., Hu, T.: Element-free precise integration method and its application in seismic modelling and imaging. Geophys J Int 166, 349–372 (2006)
Zurück zum Zitat Jing, L., Hudson, J.A.: Numerical methods in rock mechanics. Int J Rock Mech Min Sci 39, 409–427 (2002) Jing, L., Hudson, J.A.: Numerical methods in rock mechanics. Int J Rock Mech Min Sci 39, 409–427 (2002)
Zurück zum Zitat Jing, Z., Watanabe, K., Willis-Richards, J., Hashida, T.: A 3-d water/rock chemical interaction model for prediction of HDR/HWR geothermal reservoir performance. Geothermics 31, 1–28 (2002) Jing, Z., Watanabe, K., Willis-Richards, J., Hashida, T.: A 3-d water/rock chemical interaction model for prediction of HDR/HWR geothermal reservoir performance. Geothermics 31, 1–28 (2002)
Zurück zum Zitat Jing, Z., Willis-Richards, J., Watanabe, K., Hashida, T.: A three-dimensional stochastic rock mechanics model of engineered geothermal systems in fractured crystalline rock. J Geophys Res 105(23), 663–623 (2000). 679 Jing, Z., Willis-Richards, J., Watanabe, K., Hashida, T.: A three-dimensional stochastic rock mechanics model of engineered geothermal systems in fractured crystalline rock. J Geophys Res 105(23), 663–623 (2000). 679
Zurück zum Zitat Johansson, B.T., Lesnic, D.: A method of fundamental solutions for transient heat conduction. Eng Anal Bound Elem 32, 697–703 (2008) Johansson, B.T., Lesnic, D.: A method of fundamental solutions for transient heat conduction. Eng Anal Bound Elem 32, 697–703 (2008)
Zurück zum Zitat Johansson, B.T., Lesnic, D., Reeve, T.: A method of fundamental solutions for two–dimensional heat conduction. Int J Comput Math 88, 1697–1713 (2011) Johansson, B.T., Lesnic, D., Reeve, T.: A method of fundamental solutions for two–dimensional heat conduction. Int J Comput Math 88, 1697–1713 (2011)
Zurück zum Zitat John, V., Kaya, S., Layton, W.: A two-level variational multiscale method for convection-dominated convection-diffusion equations. Comput Meth Appl Mech Eng 195, 4594–4603 (2006) John, V., Kaya, S., Layton, W.: A two-level variational multiscale method for convection-dominated convection-diffusion equations. Comput Meth Appl Mech Eng 195, 4594–4603 (2006)
Zurück zum Zitat John, V., Schmeyer, E.: Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion. Comput Meth Appl Mech Eng 198, 475–494 (2008) John, V., Schmeyer, E.: Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion. Comput Meth Appl Mech Eng 198, 475–494 (2008)
Zurück zum Zitat Jung, R.: Stand und Aussichten der Tiefengeothermie in Deutschland. Erdöl, Erdgas, Kohle 123, 1–7 (2007) Jung, R.: Stand und Aussichten der Tiefengeothermie in Deutschland. Erdöl, Erdgas, Kohle 123, 1–7 (2007)
Zurück zum Zitat Katsurada, M.: A mathematical study of the charge simulation method II. Journal of the Faculty of Science University of Tokyo Section IA Mathematics 36, 135–162 (1989) Katsurada, M.: A mathematical study of the charge simulation method II. Journal of the Faculty of Science University of Tokyo Section IA Mathematics 36, 135–162 (1989)
Zurück zum Zitat Katsurada, M., Okamoto, H.: The collocation points of the fundamental solution method for the potential problem. Comput Math Appl 31, 123–137 (1996) Katsurada, M., Okamoto, H.: The collocation points of the fundamental solution method for the potential problem. Comput Math Appl 31, 123–137 (1996)
Zurück zum Zitat Kazemi, H.: Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Soc Petrol Eng J 246, 451–461 (1969) Kazemi, H.: Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Soc Petrol Eng J 246, 451–461 (1969)
Zurück zum Zitat Kazemi, H., Merril, L.S., Porterfield, K.L., Zeman, P.R.: Numerical simulation of water-oil flow in naturally fractured reservoirs. In: Proceedings, SPE-AIME 4th Symposium on Numerical Simulation of Reservoir Performance Los Angeles, California (1976). SPE 5719 Kazemi, H., Merril, L.S., Porterfield, K.L., Zeman, P.R.: Numerical simulation of water-oil flow in naturally fractured reservoirs. In: Proceedings, SPE-AIME 4th Symposium on Numerical Simulation of Reservoir Performance Los Angeles, California (1976). SPE 5719
Zurück zum Zitat Kim, I., Lindquist, W.B., Durham, W.B.: Fracture flow simulation using a finite-difference lattice Boltzmann method. Phys Rev E 67(046), 708 (2003) Kim, I., Lindquist, W.B., Durham, W.B.: Fracture flow simulation using a finite-difference lattice Boltzmann method. Phys Rev E 67(046), 708 (2003)
Zurück zum Zitat Kimura, S., Masuda, Y., Hayashi, K.: 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 (1992) Kimura, S., Masuda, Y., Hayashi, K.: 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 (1992)
Zurück zum Zitat Kühn, M.: Modelling feed-back of chemical reactions on flow fields in hydrothermal systems. Surv Geophys 30, 233–251 (2009) Kühn, M.: Modelling feed-back of chemical reactions on flow fields in hydrothermal systems. Surv Geophys 30, 233–251 (2009)
Zurück zum Zitat Kühn, M., Stöfen, H.: A reactive flow model of the geothermal reservoir Waiwera, New Zealand. Hydrogeol J 13, 606–626 (2005) Kühn, M., Stöfen, H.: A reactive flow model of the geothermal reservoir Waiwera, New Zealand. Hydrogeol J 13, 606–626 (2005)
Zurück zum Zitat Kümmerer, B.: Mathematik. Campus, Spektrum der Wissenschaftsverlagsgesellschaft, Heidelberg, S. 1–15 (2002) Kümmerer, B.: Mathematik. Campus, Spektrum der Wissenschaftsverlagsgesellschaft, Heidelberg, S. 1–15 (2002)
Zurück zum Zitat Kupradze, V.D.: A method for the approximate solution of limiting problems in mathematical physics. USSR Comp Math Math Phys 4, 199–205 (1964) Kupradze, V.D.: A method for the approximate solution of limiting problems in mathematical physics. USSR Comp Math Math Phys 4, 199–205 (1964)
Zurück zum Zitat Lai, M., Krempl, E., Ruben, D.: Introduction to continuum mechanics. Butterworth-Heinemann, Burlington (2010) Lai, M., Krempl, E., Ruben, D.: Introduction to continuum mechanics. Butterworth-Heinemann, Burlington (2010)
Zurück zum Zitat Landau, L.D., Pitaevskii, L.P., Lifshitz, E.M., Kosevich, A.M.: Theory of elasticity, 3. Aufl. Theoretical Physics, Bd. 7. Butterworth-Heinemann, Oxford (1986) Landau, L.D., Pitaevskii, L.P., Lifshitz, E.M., Kosevich, A.M.: Theory of elasticity, 3. Aufl. Theoretical Physics, Bd. 7. Butterworth-Heinemann, Oxford (1986)
Zurück zum Zitat Lang, U.: Simulation regionaler Strömungs- und Transportvorgänge in Karstaquifern mit Hilfe des Doppelkontinuum-Ansatzes: Methodenentwicklung und Parameteridentifikation. Ph.D. thesis. University of Stuttgart (1995) Lang, U.: Simulation regionaler Strömungs- und Transportvorgänge in Karstaquifern mit Hilfe des Doppelkontinuum-Ansatzes: Methodenentwicklung und Parameteridentifikation. Ph.D. thesis. University of Stuttgart (1995)
Zurück zum Zitat Lang, U., Helmig, R.: Numerical modeling in fractured media – identification of measured field data. In: Herbert, M., Kovar, K. (Hrsg.) Groundwater Quality: Remediation and Protection, S. 203–212. IAHS and University Karlova, Prague (1995) Lang, U., Helmig, R.: Numerical modeling in fractured media – identification of measured field data. In: Herbert, M., Kovar, K. (Hrsg.) Groundwater Quality: Remediation and Protection, S. 203–212. IAHS and University Karlova, Prague (1995)
Zurück zum Zitat Lee, J., Choi, S.U., Cho, W.: A comparative study of dual-porosity model and discrete fracture network model. KSCE J Civ Eng 3, 171–180 (1999) Lee, J., Choi, S.U., Cho, W.: A comparative study of dual-porosity model and discrete fracture network model. KSCE J Civ Eng 3, 171–180 (1999)
Zurück zum Zitat Li, X.: Convergence of the method of fundamental solutions for Poisson’s equation on the unit sphere. Adv Comput Math 28, 269–282 (2008) Li, X.: Convergence of the method of fundamental solutions for Poisson’s equation on the unit sphere. Adv Comput Math 28, 269–282 (2008)
Zurück zum Zitat Li, X.: 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 (2008) Li, X.: 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 (2008)
Zurück zum Zitat Lomize, G.M.: Seepage in fissured rocks. State Press, Moscow (1951) Lomize, G.M.: Seepage in fissured rocks. State Press, Moscow (1951)
Zurück zum Zitat Long, J., Remer, J., Wilson, C., Witherspoon, P.: Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18, 645–658 (1982) Long, J., Remer, J., Wilson, C., Witherspoon, P.: Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18, 645–658 (1982)
Zurück zum Zitat Luchko, Y.: Maximum principle for the generalized time-fractional diffusion equation. J Math Anal Appl 351, 218–223 (2009) Luchko, Y.: Maximum principle for the generalized time-fractional diffusion equation. J Math Anal Appl 351, 218–223 (2009)
Zurück zum Zitat Luchko, Y.: Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation. Comput Math Appl 59, 1766–1772 (2010) Luchko, Y.: Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation. Comput Math Appl 59, 1766–1772 (2010)
Zurück zum Zitat Luchko, Y.: Fractional diffusion and wave propagation. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, 2. Aufl. Springer, New York (2014). Accepted for publication Luchko, Y.: Fractional diffusion and wave propagation. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, 2. Aufl. Springer, New York (2014). Accepted for publication
Zurück zum Zitat Luchko, Y., Punzi, A.: Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations. Int J Geomath 1, 257–276 (2011) Luchko, Y., Punzi, A.: Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations. Int J Geomath 1, 257–276 (2011)
Zurück zum Zitat Marks, D.: A family of approximations spanning the born and rytov scattering series. Optics Express 14, 8837–8848 (2006) Marks, D.: A family of approximations spanning the born and rytov scattering series. Optics Express 14, 8837–8848 (2006)
Zurück zum Zitat Martin, G.S., Marfurt, K.J., Larsen, S.: Marmousi-2: An updated model for the investigation of AVO in structurally complex areas. In: Proceedings, SEG Annual Meeting Salt Lake City (2002) Martin, G.S., Marfurt, K.J., Larsen, S.: Marmousi-2: An updated model for the investigation of AVO in structurally complex areas. In: Proceedings, SEG Annual Meeting Salt Lake City (2002)
Zurück zum Zitat Maryška, J., Severýn, O., Vohralík, M.: Numerical simulation of fracture flow in mixed-hybrid FEM stochastic discrete fracture network model. Comput Geosci 8, 217–234 (2004) Maryška, J., Severýn, O., Vohralík, M.: Numerical simulation of fracture flow in mixed-hybrid FEM stochastic discrete fracture network model. Comput Geosci 8, 217–234 (2004)
Zurück zum Zitat Masahi, M., King, P., Nurafza, P.: Fast estimation of connectivity in fractured reservoirs using percolation theory. SPE Journal 12, 167–178 (2007) Masahi, M., King, P., Nurafza, P.: Fast estimation of connectivity in fractured reservoirs using percolation theory. SPE Journal 12, 167–178 (2007)
Zurück zum Zitat Mayer, C.: A wavelet approach to the stokes problem. Habilitation thesis, University of Kaiserslautern, Geomathematics Group (2007) Mayer, C.: A wavelet approach to the stokes problem. Habilitation thesis, University of Kaiserslautern, Geomathematics Group (2007)
Zurück zum Zitat Mayer, C., Freeden, W.: Stokes problem, layer potentials and regularizations, multiscale applications. In: Freeden, W., Nashed, Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, 2. Aufl. Springer, New York (2014). Accepted for publication Mayer, C., Freeden, W.: Stokes problem, layer potentials and regularizations, multiscale applications. In: Freeden, W., Nashed, Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, 2. Aufl. Springer, New York (2014). Accepted for publication
Zurück zum Zitat McLean, W., Mustapha, K.: Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation. Numer Algorithms 52, 69–88 (2009) McLean, W., Mustapha, K.: Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation. Numer Algorithms 52, 69–88 (2009)
Zurück zum Zitat Menke, W.: Geophysical data analysis: Discrete inverse theory. Academic Press, Orlando (1984) Menke, W.: Geophysical data analysis: Discrete inverse theory. Academic Press, Orlando (1984)
Zurück zum Zitat Michel, V.: A multiscale approximation for operator equations in separable Hilbert spaces – case study: Reconstruction and description of the Earth’s interior. Habilitation thesis, University of Kaiserslautern, Geomathematics Group (2002) Michel, V.: A multiscale approximation for operator equations in separable Hilbert spaces – case study: Reconstruction and description of the Earth’s interior. Habilitation thesis, University of Kaiserslautern, Geomathematics Group (2002)
Zurück zum Zitat Michel, V., Fokas, A.S.: A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet based methods. Inverse Problems 24 (2008). doi:10.1088/0266-5611/24/4/04519 Michel, V., Fokas, A.S.: A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet based methods. Inverse Problems 24 (2008). doi:10.1088/0266-5611/24/4/04519
Zurück zum Zitat Min, K.B., Jing, L., Stephansson, O.: 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 (2004) Min, K.B., Jing, L., Stephansson, O.: 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 (2004)
Zurück zum Zitat Mo, H., Bai, M., Lin, D., Roegiers, J.C.: Study of flow and transport in fracture network using percolation theory. Appl Math Model 22, 277–291 (1998) Mo, H., Bai, M., Lin, D., Roegiers, J.C.: Study of flow and transport in fracture network using percolation theory. Appl Math Model 22, 277–291 (1998)
Zurück zum Zitat Moeck, I., Kwiatek, G., Zimmermann, G.: The in-situ stress field as a dey issue for geothermal field development – a case study from the NE German basin. In: Proceedings, 71st EAGE Conference & Exhibition Amsterdam (2009) Moeck, I., Kwiatek, G., Zimmermann, G.: The in-situ stress field as a dey issue for geothermal field development – a case study from the NE German basin. In: Proceedings, 71st EAGE Conference & Exhibition Amsterdam (2009)
Zurück zum Zitat Möhringer, S.: Decorrelation of gravimetric data. Ph.D. thesis. AG Geomathematik, TU Kaiserslautern (2014) Möhringer, S.: Decorrelation of gravimetric data. Ph.D. thesis. AG Geomathematik, TU Kaiserslautern (2014)
Zurück zum Zitat Morgan, W.J.: Convective plumes in the lower mantle. Nature 230, 42–43 (1971) Morgan, W.J.: Convective plumes in the lower mantle. Nature 230, 42–43 (1971)
Zurück zum Zitat Müller, C.: Analysis of spherical symmetries in Euclidean spaces Applied Mathematical Sciences, Bd. 129. Springer, Berlin (1998) Müller, C.: Analysis of spherical symmetries in Euclidean spaces Applied Mathematical Sciences, Bd. 129. Springer, Berlin (1998)
Zurück zum Zitat Müller, C., Kersten, H.: Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung \(\bigtriangleup U+k^{{2}}U=0\). Math Meth Appl Sci 2, 48–67 (1980) Müller, C., Kersten, H.: Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung \(\bigtriangleup U+k^{{2}}U=0\). Math Meth Appl Sci 2, 48–67 (1980)
Zurück zum Zitat Nakao, S., Ishido, T.: Pressure-transient behavior during cold water injection into geothermal wells. Geothermics 27, 401–413 (1998) Nakao, S., Ishido, T.: Pressure-transient behavior during cold water injection into geothermal wells. Geothermics 27, 401–413 (1998)
Zurück zum Zitat Neuman, S.: Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13, 124–147 (2005) Neuman, S.: Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13, 124–147 (2005)
Zurück zum Zitat Neuman, S., Depner, J.: 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 (1988) Neuman, S., Depner, J.: 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 (1988)
Zurück zum Zitat Nolet, G.: A Breviary of Seismic tomography: Imaging the interior of the Earth and Sun. Cambridge University Press, New York (2008) Nolet, G.: A Breviary of Seismic tomography: Imaging the interior of the Earth and Sun. Cambridge University Press, New York (2008)
Zurück zum Zitat Oden, M., Niemi, A.: 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 (2006) Oden, M., Niemi, A.: 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 (2006)
Zurück zum Zitat Ödner, H.: One-dimensional transient flow in a finite fractured aquifer system. Hydrol Sci J 43, 243–265 (1998) Ödner, H.: One-dimensional transient flow in a finite fractured aquifer system. Hydrol Sci J 43, 243–265 (1998)
Zurück zum Zitat Ostermann, I.: Modeling heat transport in deep geothermal systems by radial basis functions. Ph.D. thesis. University of Kaiserslautern, Geomathematics Group (2011a) Ostermann, I.: Modeling heat transport in deep geothermal systems by radial basis functions. Ph.D. thesis. University of Kaiserslautern, Geomathematics Group (2011a)
Zurück zum Zitat Ostermann, I.: Three-dimensional modeling of heat transport in deep hydrothermal reservoirs. Int J Geomath 2, 37–68 (2011b) Ostermann, I.: Three-dimensional modeling of heat transport in deep hydrothermal reservoirs. Int J Geomath 2, 37–68 (2011b)
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Metadaten
Titel
Mathematische Methoden
verfasst von
Prof. Dr. Willi Freeden
Helga Nutz
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-54511-5_4