Upscaling and Inverse Modeling of Groundwater Flow and Mass ...

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150 CHAPTER 6. GROUNDWATER FLOW INVERSE MODELING . . . Table 6.2: Definition of scenarios Scenario Parallel flow Radial flow Well (111) Well (32) Correct Prior Wrong Prior NS-EnKF L-NS-EnKF 1 √ √ 2 √ √ 3 √ √ √ √ 4 √ √ √ 5 √ √ √ √ 6 √ √ √ 7 √ √ 8 √ √ 9 √ √ √ √ 10 √ √ √ 11 √ √ √ √ 12 √ √ √ 13 √ √ √ √ 14 √ √ √ √ α √ √ √ √ α indicates the localized NS-EnKF. boundary (West), prescribed flux boundary (East) and impermeable boundaries (North and South); (ii) boundary conditions inducing radial flow (Figure 6.3B), with impermeable boundaries and a set of injection/extraction wells in a typical configuration for contaminant remediation or for reservoir exploitation. For both boundary conditions, groundwater flow is simulated for a period of 500 days starting with an initial head equal to zero everywhere. The simulation time is discretized into 100 time steps, the sizes of which follow a geometric series with a ratio of 1.05. The specific storage is assumed constant and equal to 0.003 m −1 . The MODFLOW 2000 code (Harbaugh et al., 2000) is used to solve the transient flow equation (6.1). The head data are sampled at the first 60 time steps (approximately 67.7 days) and will be used as the conditioning data in the NS-EnKF. The spatial distribution of the sampling wells is shown in Figure 6.3. Although the sampled head data are error-free since they are taken from the “true” field, in the following data assimilation procedures it was assumed that they have a normalized measurement error with a mean of zero and a standard deviation of 0.05 m. 6.3.2 Scenarios Fourteen scenarios are analyzed with the characteristics indicated in the Table 6.2. The impact of the prior model, the use of a localization function and the different boundary conditions is tested with help of fourteen scenarios (Table 6.2). The scenarios are organized to show how the characterization of the hydraulic conductivities evolves starting from an unconditional ensemble of realizations as piezometric heads are incorporated, and then when localization
CHAPTER 6. GROUNDWATER FLOW INVERSE MODELING . . . 151 (A) 240 Constant Head (h=0) No Flow 0 No Flow 300 (B) 240 No Flow Q=-125 Q=100 No Flow Q=-125 Q=100 Q=100 Q=-125 Q=100 Q=100 Q=-125 0 No Flow 300 No Flow 3 Q=-4.0 m /d 3 Q=-90.0 m /d 3 Q=-11.0 m /d 3 Q=-150.0 m /d 3 Q=-15. 5 m /d Figure 6.3: Spatial distribution of sampled head data and flow configurations: (A) boundary conditions A (B) boundary conditions B (the unit of flow in wells: m 3 /d).
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Upscaling and Inverse Modeling of G
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c⃝ Copyright by Liangping Li 2011
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Abstract The need to reduce the com
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improved as more data is assimilate
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Resumen La necesidad de reducir el
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Por último, en el tercer bloque, e
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Resum La necessitat de reduir el co
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flux i el transport (conductivitat
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Acknowledgements I want to thank my
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xx CONTENTS 3 Transport Upscaling U
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xxii CONTENTS
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xxiv LIST OF FIGURES 2.7 Flow compa
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xxvi LIST OF FIGURES 4.4 Reference
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xxviii LIST OF FIGURES
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1.1 Motivation and Objectives 1 Int
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CHAPTER 1. INTRODUCTION 3 Chapter 2
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6 CHAPTER 2. A COMPARATIVE STUDY OF
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10 CHAPTER 2. A COMPARATIVE STUDY O
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38 BIBLIOGRAPHY Berkowitz, B., Sche
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40 BIBLIOGRAPHY Gómez-Hernández,
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42 BIBLIOGRAPHY Salamon, P., Fernà
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44 CHAPTER 3. TRANSPORT UPSCALING U
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70 BIBLIOGRAPHY Dagan, G., 1994. Up
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72 BIBLIOGRAPHY Lawrence, A. E., Sa
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74 BIBLIOGRAPHY Zhang, Y., 2004. Up
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76 CHAPTER 4. MODELING TRANSIENT GR
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Page 132 and 133: 100 CHAPTER 4. MODELING TRANSIENT G
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