Holdings: Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media

Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media:

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Main Author:	Jänicke, Ralf (Author)
Format:	Thesis Book
Language:	English
Published:	Bochum 2015
Subjects:	Diffusionsprozess Homogenisierung > Mathematik Modellierung Poröser Stoff Hochschulschrift
Online Access:	Inhaltsverzeichnis
Physical Description:	v, 151 Seiten Illustrationen, Diagramme

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MARC


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adam_text	CONTENTS 1 INTRODUCTION 1 1.1 SEISMIC ATTENUATION: THE PHYSICAL PHENOMENON ........................................... 2 1.2 COMPUTATIONAL HOM OGENIZATION ...................................................................... 5 1.3 N O TATIO N .............................................................................................................. 8 2 THEORETICAL FOUNDATIONS 11 2.1 THEORY OF POROUS M E D IA .................................................................................. 12 2.1.1 THE CONCEPT OF VOLUME FRACTIONS .......................................................... 12 2.1.2 KINEMATICS IN THE THEORY OF POROUS M E D IA ......................................... 14 2.1.3 BALANCE RE LA TIO N S ................................................................................... 18 2.1.4 MASTER BALANCE RE LA TIO N S ...................................................................... 24 2.2 BIPHASIC M IXTURES............................................................................................... 27 2.2.1 BIOT*S EQUATIONS OF LINEAR CONSOLIDATION.............................................. 28 2.2.2 NUMERICAL S O LU TIO N ............................................................................... 33 2.3 COMPUTATIONAL HOM OGENIZATION ...................................................................... 33 2.3.1 THE MESOSCOPIC BOUNDARY VALUE P RO B LE M ............................................ 34 3 A VISCOELASTIC SUBSTITUTE MODEL FOR HETEROGENEOUS POROELASTIC MEDIA 39 3.1 BRIDGING THE S C A L E S ............................................................................................. 40 3.1.1 EXTENDED MACRO-HOMOGENEITY C RITE RIO N .............................................. 40 3.1.2 AVERAGING RULES AND CONSISTENT BOUNDARY CONDITIONS.............................42 3.2 STUDY: INFLUENCE OF BOUNDARY CONDITIONS ON THE APPARENT ATTENUATION . . . 45 3.3 MODEL ORDER R E D U C TIO N ...................................................................................... 53 3.3.1 VARIATIONAL FORM OF THE HOMOGENIZATION P RO B LEM ................................... 53 3.3.2 APPROXIMATION OF MESOSCOPIC FIELD Q UANTITIES ......................................... 55 3.3.3 EVOLUTION OF INTERNAL VARIABLES.............................................................. 57 3.3.4 MODE IDENTIFICATION................................................................................ 59 3.4 STUDY: ID LAYERED POROELASTIC M E D IU M ........................................................... 60 3.5 STUDY: 2D PATCHY SATURATED POROELASTIC M EDIUM ............................................... 64 3.6 C ONCLUSIONS......................................................................................................... 68 4 V ISCOELASTIC SUBSTITUTE M ODELS FOR FLUID-SATURATED FRACTURED MEDIA 71 4.1 POROELASTIC FRACTURES IN AN IMPERMEABLE BACKGROUND RO C K ............................. 73 4.1.1 COMPUTATIONAL HOM OGENIZATION .......................................................... 75 4.1.2 MODEL ORDER RE D U C TIO N .......................................................................... 78 4.1.3 EVOLUTION OF THE INTERNAL VARIABLES ....................................................... 79 4.2 STUDY: A SIMPLE POROELASTIC FRACTURE NETW ORK ................................................. 80 4.3 A HYBRID-DIMENSIONAL A P P RO A C H ....................................................................... 87 4.3.1 MESO-SCALE M O D E LIN G ............................................................................. 88 4.3.2 COMPUTATIONAL HOM OGENIZATION .......................................................... 93 4.3.3 APPROXIMATION OF THE MESOSCOPIC FIELD QUANTITIES...................................99 4.3.4 EVOLUTION OF THE INTERNAL VARIABLES....................................................... 101 4.4 STUDY: A SIMPLE HYBRID-DIMENSIONAL FRACTURE N E TW O RK .................................... 102 4.5 C ONCLUSIONS....................................................................................................... .109 5 POROVISCOELASTICITY: IDENTIFICATION BY HOMOGENIZATION 111 5.1 COMPUTATIONAL HOMOGENIZATION USING PRESSURE B C .......................................... 114 5.2 MODEL ORDER REDUCTION USING PRESSURE B C ......................................................... 117 5.3 PHYSICAL IN TERP RETATIO N ........................................................................................122 5.4 COMPUTATIONAL HOMOGENIZATION USING FLUX B C ................................................ 123 5.5 MODEL ORDER REDUCTION USING FLUX B C ............................................................... 126 5.6 STUDY: COMPARISON OF PUBC AND F U B C ......................................................... 129 5.7 C ONCLUSIONS.......................................................................................................... 133 6 RESUM E AND OUTLOOK 135 A ALGORITHMIC TANGENT STIFFNESS OPERATOR 137 BIBLIOGRAPHY 140
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spelling	Jänicke, Ralf Verfasser (DE-588)14400626X aut Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media vorgelegt von Ralf Jänicke Bochum 2015 v, 151 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Habilitationsschrift Ruhr-Universität Bochum 2015 Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Homogenisierung Mathematik (DE-588)4403079-4 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Poröser Stoff (DE-588)4046811-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Poröser Stoff (DE-588)4046811-2 s Diffusionsprozess (DE-588)4274463-5 s Homogenisierung Mathematik (DE-588)4403079-4 s DE-604 Modellierung (DE-588)4170297-9 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029637217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Jänicke, Ralf Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media Diffusionsprozess (DE-588)4274463-5 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd Modellierung (DE-588)4170297-9 gnd Poröser Stoff (DE-588)4046811-2 gnd
subject_GND	(DE-588)4274463-5 (DE-588)4403079-4 (DE-588)4170297-9 (DE-588)4046811-2 (DE-588)4113937-9
title	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media
title_auth	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media
title_exact_search	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media
title_full	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media vorgelegt von Ralf Jänicke
title_fullStr	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media vorgelegt von Ralf Jänicke
title_full_unstemmed	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media vorgelegt von Ralf Jänicke
title_short	Computational homogenization and reduced order modeling of diffusion processes in fluid-saturated porous media
title_sort	computational homogenization and reduced order modeling of diffusion processes in fluid saturated porous media
topic	Diffusionsprozess (DE-588)4274463-5 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd Modellierung (DE-588)4170297-9 gnd Poröser Stoff (DE-588)4046811-2 gnd
topic_facet	Diffusionsprozess Homogenisierung Mathematik Modellierung Poröser Stoff Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029637217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT janickeralf computationalhomogenizationandreducedordermodelingofdiffusionprocessesinfluidsaturatedporousmedia

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