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

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84 CHAPTER 4. MODELING TRANSIENT GROUNDWATER . . . (A) �� -3.0 -4.0 �� -5.0 -6.0 �� -7.0 �� Figure 4.1: (A) Reference lnK field overlaid with the discretization of the numerical model at the coarse scale. (B) Conditioning lnK data. 100 conductivity data are sampled at the locations shown in Figure 4.1B. These data will be used for conditioning. The forward transient groundwater flow model is run in the reference realization with the boundary conditions shown in Figure 4.2 and initial heads equal to zero everywhere. The total simulation time is 500 days, discretized into 100 time steps following a geometric sequence of ratio 1.05. The aquifer is confined. Specific storage is assumed constant and equal to 0.003 m −1 . The simulated piezometric heads at the end of time step 60 (67.7 days) are displayed in Figure 4.4. Piezometric heads at locations W1 to W9 in Figure 4.2 are sampled for the first 60 time steps to be used as conditioning data. The simulated heads at locations W10 to W13 will be used as validation data. 4.3.2 Hydraulic Conductivity Upscaling For the reasons explained by Zhou et al. (2010); Li et al. (2010), the fine scale realizations must be slightly larger than the aquifer domain in order to apply the Laplacian-with-skin upscaling approach. We assume that the aquifer of interest is comprised by the inner 320 by 320 cell domain for all realizations. Each one of these realizations is upscaled onto a 32 by 32 square-block model implying an order-of-two magnitude reduction in the discretization of the aquifer after upscaling. After several tests, the skin selected for the upscaling procedure has a width of 10 m, since it is the one that gives best results in the reproduction of the interblock specific discharges when compared to those computed on the fine scale underlying realizations. Since the upscaling is applied to the interblock volume straddling between adjacent block centers, there are 32 by 31 column-to-column interblock tensors (K b,c ) plus 31 by 32 row- ��
CHAPTER 4. MODELING TRANSIENT GROUNDWATER . . . 85 320 m H(0,y)=0 m 0 Y ∂h ∂y Y=320 =0 W1 W2 W3 W4 W5 W6 W7 W10 W11 W12 W13 ∂h ∂y W8 Y=0 =0 W9 Q(320,y)=-45m /d 320 m X Figure 4.2: Sketch of the flow problem with boundary conditions, observation and prediction wells. Empty squares correspond to the piezometric head observation wells (W1-W9); filled squares correspond to the control wells (W10- W13). 3
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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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Page 70 and 71: 38 BIBLIOGRAPHY Berkowitz, B., Sche
Page 72 and 73: 40 BIBLIOGRAPHY Gómez-Hernández,
Page 74 and 75: 42 BIBLIOGRAPHY Salamon, P., Fernà
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Page 102 and 103: 70 BIBLIOGRAPHY Dagan, G., 1994. Up
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Page 106 and 107: 74 BIBLIOGRAPHY Zhang, Y., 2004. Up
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Page 134 and 135: 102 BIBLIOGRAPHY Durlofsky, L. J.,
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134 CHAPTER 5. JOINTLY MAPPING HYDR
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136 BIBLIOGRAPHY Chen, Y., Zhang, D
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138 BIBLIOGRAPHY Journel, A., 1974.
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140 BIBLIOGRAPHY Wen, X., Deutsch,
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142 CHAPTER 6. GROUNDWATER FLOW INV
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170 BIBLIOGRAPHY Deutsch, C. V., Jo
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172 BIBLIOGRAPHY Lee, S., Carle, S.
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174 BIBLIOGRAPHY Yeh, W., 1986. Rev
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176 CHAPTER 7. CONCLUSIONS travels
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178 CHAPTER 7. CONCLUSIONS predicti
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180 APPENDIX A. FLOWXYZ3D - A THREE
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182 APPENDIX A. FLOWXYZ3D - A THREE
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