Characterization and sensitivity analysis of tracer breakthrough curves with respect to multi continuum modeling [Elektronische Ressource] / vorgelegt von Thomas Vogel
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Characterization and sensitivity analysis of tracer breakthrough curves with respect to multi continuum modeling [Elektronische Ressource] / vorgelegt von Thomas Vogel

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281 pages
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"Characterization and Sensitivity Analysis ofTracer Breakthrough Curves with respect toMulti Continuum Modeling"Von der Fakult t f r Bauingenieurwesender Rheinisch-Westf lischen Technischen Hochschule Aachenzur Erlangung des akademischen Grades eines Doktorsder Ingenieurwissenschaftengenehmigte Dissertationvorgelegt vonThomas VogelausMettmannBerichter:Universit tsprofessor Dr.-Ing. J rgen K ngeterProfessor Dr.-Ing. Rainer HelmigTag der m ndlichen Pr fung: 14.01.2005 Diese Dissertation ist auf den Internetseiten derHochschulbibliothek online verf gbar . Acknowledgements IIIAcknowledgementsThe work presented in this thesis is based on my research within theAquifer Analogue Project (2001-2003) funded by the German researchfoundation (Deutsche Forschungsgemeinschaft, Ko 1573/2-4). Majorparts of my thesis were developed during my stay at the Universityof Waterloo (Department of Earth Sciences, Professor Sudicky), nan-cially supported by the Government of Canada Award.I would like to thank my advisor, Professor Dr.-Ing. J rgen K ngeter,for his valuable scienti c and administrative support in the past veyears as researcher at the Institute of Hydraulic Engineering andWater Resources Management (IWW) of the RWTH Aachen. Specialthanks go to Professor Dr.-Ing. Rainer Helmig, Universit t Stuttgart,for his encouragement, his suggestions and for the co-supervision ofmy thesis.

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Publié par
Publié le 01 janvier 2005
Nombre de lectures 4
Langue English
Poids de l'ouvrage 19 Mo

Extrait

"Characterization and Sensitivity Analysis of
Tracer Breakthrough Curves with respect to
Multi Continuum Modeling"
Von der Fakult t f r Bauingenieurwesen
der Rheinisch-Westf lischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines Doktors
der Ingenieurwissenschaften
genehmigte Dissertation
vorgelegt von
Thomas Vogel
aus
Mettmann
Berichter:
Universit tsprofessor Dr.-Ing. J rgen K ngeter
Professor Dr.-Ing. Rainer Helmig
Tag der m ndlichen Pr fung: 14.01.2005
Diese Dissertation ist auf den Internetseiten der
Hochschulbibliothek online verf gbar . Acknowledgements III
Acknowledgements
The work presented in this thesis is based on my research within the
Aquifer Analogue Project (2001-2003) funded by the German research
foundation (Deutsche Forschungsgemeinschaft, Ko 1573/2-4). Major
parts of my thesis were developed during my stay at the University
of Waterloo (Department of Earth Sciences, Professor Sudicky), nan-
cially supported by the Government of Canada Award.
I would like to thank my advisor, Professor Dr.-Ing. J rgen K ngeter,
for his valuable scienti c and administrative support in the past ve
years as researcher at the Institute of Hydraulic Engineering and
Water Resources Management (IWW) of the RWTH Aachen. Special
thanks go to Professor Dr.-Ing. Rainer Helmig, Universit t Stuttgart,
for his encouragement, his suggestions and for the co-supervision of
my thesis.
I highly appreciate the contributions of all colleagues of the IWW,
special thanks to Dipl.-Ing. Anke Hauschild, Dipl.-Ing. Daniel Bach-
mann, Dipl.-Ing. Andreas van Linn and Dr.-Ing. Vincent Lagendijk
for their support, the review of the manuscript and the inspiring dis-
cussions. Furthermore, I would like to express my gratitude to Kata-
rina Pintar, Waterloo, and my brother, Dr. jur. Christian Vogel, who
did a fabulous job at editing and proof-reading my thesis.
Finally, I would like to thank Svenja for her continuing support and
patience.
Aachen, February 2005
Thomas Vogel Abstract V
Abstract
In order to support a sustainable use of water resources in hard rock
aquifers, appropriate experimental and modeling techniques are es-
sential. Multi continuum modeling as a compromise between de-
tailed discrete modeling and rough estimations by analytical solu-
tions, considers different hydraulic properties yet neglects discrete
effects.
In the scope of this work, characterization techniques are investigated
in order to support the choice of an appropriate multi continuum
model. Furthermore, sensitivity analyses for multi continuum models
are developed to identify the relevant parameters and to explain the
dominant ow and transport processes. In order to assess the trans-
ferability of insights gained from gas tracer experiments as performed
within the Aquifer Analogue Project to water-saturated conditions,
both numerical investigations for the water- and the gas-saturated
case are analyzed.
A double continuum model of the sandstone block investigated in the
scope of the Aquifer Analogue Project is developed. The applicability
of the approach to identify an appropriate model type for a system
by means of key- gures to the two-dimensional case is investigated.
By of the sensitivity analyses carried out in the scope of this
thesis, the in uence of different components of a porous medium is
quanti ed and conclusions concerning the characteristic key- gures
are drawn. Contents VII
Contents
Acknowledgements III
Abstract V
List of Figures XI
List of Tables XXI
Nomenclature XXIII
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Discussion of the Relevant Fluid Properties for Tracer Transport 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Flow Through Fractured Porous Media . . . . . . . . . 8
2.2.1 Flow Velocity and Permeability . . . . . . . . . . 8
2.2.2 Compressibility . . . . . . . . . . . . . . . . . . . 12
2.3 Tracer Transport . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 Advection and Hydrodynamic Dispersion . . . 16
2.4 Signi cance of the Differences in Flow and Transport
Processes for Tracer Experiments . . . . . . . . . . . . . 18
2.5 The Role of Sensitivities . . . . . . . . . . . . . . . . . . 22
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Fundamentals of Sensitivity Analysis and Fields of Application 26
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Finite Differences . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Basic Principles . . . . . . . . . . . . . . . . . . . 27VIII Contents
3.2.2 Sources of Error . . . . . . . . . . . . . . . . . . . 28
3.2.3 Advantages and Disadvantages . . . . . . . . . 28
3.2.4 Implementation of Finite Differences . . . . . . . 30
3.3 Automatic Differentiation . . . . . . . . . . . . . . . . . 32
3.3.1 Basic Principles . . . . . . . . . . . . . . . . . . . 32
3.3.2 Methods of Automatic Differentiation . . . . . . 32
3.3.3 Advantages and Disadvantages . . . . . . . . . 33
3.3.4 Implementation by ADIFOR . . . . . . . . . . . . 33
3.4 Fields of Application of Sensitivity Analysis . . . . . . . 34
3.4.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.2 Interpretation of Sensitivities . . . . . . . . . . . 35
3.4.3 Model Calibration . . . . . . . . . . . . . . . . . 35
3.4.4 Uncertainty Analysis . . . . . . . . . . . . . . . . 39
3.4.5 Sampling Design . . . . . . . . . . . . . . . . . . 41
3.4.6 Optimization of Measures . . . . . . . . . . . . . 48
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Conceptual Model to Obtain Different Types of Tracer Breakthrough
Curves 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Description of the Conceptual Model . . . . . . . . . . . 51
4.3 Properties of the Conceptualized Aquifer . . . . . . . . 52
4.4 Discussion of Model Results - Basic Con guration . . . 54
4.5 Variation of Parameters . . . . . . . . . . . . . . 58
4.5.1 Single Continuum Model (SPSP) . . . . . . . . . 58
4.5.2 Double (DPDP) . . . . . . . . 58
4.5.3 Triple Model (TPTP) . . . . . . . . . 58
4.6 Resulting Tracer Breakthrough Curves . . . . . . . . . . 59
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Characterization Methods of Tracer Breakthrough Curves 62
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Existing Approaches to Characterize Tracer Break-
through Curves . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 63
5.2.2 Identi cation of Multi Continuum Models . . . 64
5.2.3 Motivation of the Further Development of Criteria . . . . . . . . . . . . . . . 64Contents IX
5.3 Characterization by Key Figures . . . . . . . . . . . . . 66
5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . 66
5.3.2 Description of Key Figures . . . . . . . . . . . . 67
5.3.3 Analysis of Correlation of Key Figures . . . . . . 71
5.3.4 Sensitivity Analysis of Key Figures . . . . . . . . 72
5.3.5 Dicussion of the Signi cance of Identi cation
by Key Figures . . . . . . . . . . . . . . . . . . . 72
5.3.6 Summary of Characterization by Key Figures . . 76
5.4 Characterization by Analyzing the Center of Gravity . 79
5.4.1 Description of the Method . . . . . . . . . . . . . 79
5.4.2 Application to Simulation Results . . . . . . . . 81
5.5 Discussion of Characterization Criteria . . . . . . . . . . 84
6 Sensitivity Analysis with Respect to Multi Continuum Model Para-
meters 85
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Sensitivity Analysis of Key Figures . . . . . . . . . . . . 86
6.2.1 Automatic Differentiation . . . . . . . . . . . . . 87
6.2.2 Implementation of Sensitivity Calculation of
Key Figures . . . . . . . . . . . . . . . . . . . . . 87
6.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . 89
6.3.1 General Remarks . . . . . . . . . . . . . . . . . . 89
6.3.2 Remarks on the In uence of Time Discretization 92
6.3.3 on the of Initial Parameter
Values and the Standardization of Sensitivities . 98
6.3.4 Water-saturated Case . . . . . . . . . . . . . . . . 104
6.3.5 Gas-saturated Case in Comparison to the
Water-saturated Case . . . . . . . . . . . . . . . . 120
6.3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . 145
7 Development of a Multi Continuum Model for the Field Block Scale 148
7.1 The Modeling Process . . . . . . . . . . . . . . . . . . . 148
7.2 Characterization of the Sandstone Block . . . . . . . . . 150
7.2.1 The Sandstone Block . . . . . . . . . . . . . . . . 150
7.2.2 Gas Flow Experiments . . . . . . . . . . . . . . . 153
7.2.3 Gas Tracer Tests . . . . . . . . . . . . . . . . . . . 156
7.3 Choice of an Appropriate Model Type to Represent the
Sandstone Block . . . . . . . . . . . . . . . . . . . . . . . 161X Contents
7.4 Determination of the Equivalent Parameters . . . . . . 165
7.4.1 Equivalent Permeability . . . . . . . . . . . . . . 165
7.4.2 Porosity . . . . . . . .

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