Thermo-Hydro-Mechanical-Chemical Processes in Porous Media Benchmark
The book comprises an assembly of benchmarks and examples for porous media mechanics collected over the last twenty years. Analysis of thermo-hydro-mechanical-chemical (THMC) processes is essential to many applications in environmental engineering, such a
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¨ Olaf Kolditz • Uwe-Jens Gorke Hua Shao • Wenqing Wang Editors
Thermo-Hydro-MechanicalChemical Processes in Fractured Porous Media Benchmarks and Examples
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Editors Olaf Kolditz Uwe-Jens G¨orke Wenqing Wang Helmholtz Centre for Environmental Research UFZ Technische Universit¨at Dresden (TUD) Leipzig Germany
Hua Shao Federal Institute for Geosciences and Natural Resources Hannover Germany
ISSN 1439-7358 ISBN 978-3-642-27176-2 e-ISBN 978-3-642-27177-9 DOI 10.1007/978-3-642-27177-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2012934370 Mathematics Subject Classification (2010): 35Mxx, 35Qxx, 35G61, 65M60, 68Uxx, 76S05, 76T10, 86-08, 92E20 c Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover illustration: The cover image represents a snapshot in time during a numerical simulation, illustrating fluid and heat flow pathways in a deep geothermal reservoir exhibiting several large hydraulic fractures. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents 1 Introduction
1
1.1
Scope of This Book . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
Application Areas . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Part I - Theory and Numerics
7
2 Theory
9
2.1
Continuum Mechanics . . . . . . . . . . . . . . . . . . . . . . . .
10
2.2
Porous Medium
. . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.3
Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.4
Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.5
Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . .
41
2.6
Porous Medium Properties
54
. . . . . . . . . . . . . . . . . . . . .
3 Numerical Methods
61
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3.2
Object-Orientation in Finite Element Analysis . . . . . . . . . .
63
3.3
General Finite Element Formulations
. . . . . . . . . . . . . . .
69
3.4
Element Objects: ELE . . . . . . . . . . . . . . . . . . . . . . . .
71
3.5
Parallel Computing and Automatic Control for Ti
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