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

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28 CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . not due just to having almost twice as many blocks, but to the fact, that these many more blocks are located in the zones where the variability of velocity is the highest. The message to take away is that it is advantageous to use a non-uniform coarse grid and that the definition of this grid is very important to achieve the best upscaling results. Other authors have investigated along these lines and have proposed the use of flexible grids which maintain a given topology (basically keeping constant the number of rows, columns and layers) but which are deformed so as to reduce the variability of the specific discharge vector within each coarse block (i.e, Garcia et al., 1992; Wen and Gómez- Hernández, 1998). Normalized Mass 1 0.1 0.01 0.001 0 50 100 150 200 250 Downstream Distance [m] Mass distribution t=27 days Realization #26 Uniform coarsening Nonuniform coarsening Figure 2.10: Longitudinal mass distribution profiles of the tritium plume from the fine scale reference realization, and predictions on uniform and nonuniform coarse scale grids, for t = 328 days. Figure 2.11 compares the mass longitudinal profile of the upscaling approaches in Figures 2.9A (uniform grid, simple-Laplacian, block-centered), 2.9B (uniform grid, simple-Laplacian, interblock-centered) and 2.9D (uniform grid, Laplacian-with-skin, interblock-centered) with the reference profile at day 328. The improvement in the reproduction of the reference values by the difference upscaling techniques shows a similar progression as the improvement seen in the reproduction of the fluxes in Figure 2.9. Comparing these curves to any of the curves in Figure 2.8, which were obtained with simple averaging upscaling rules, it is clear that any upscaling approach based on a local solution of the flow equation provides a better representation of the hydraulic conductivity distribution and yields better transport predictions. The
CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . 29 Normalized Mass 1 0.1 0.01 0.001 0 50 100 150 200 250 Downstream Distance [m] Mass distribution t=27 days Realization #26 Laplacian with skin (interblock) Simple Laplacian (interblock) Simple Laplacian (block) Figure 2.11: Longitudinal mass distribution profiles of the tritium plume from the fine scale reference realization, and predictions by some Laplacian-based upscaling approaches at the coarse scale, for t = 328 days. two interblock-aimed upscaling approaches are able to capture both the peak concentration near the source and the downstream spreading. Figure 2.10 shows the mass longitudinal profile of the upscaling approaches in Figures 2.9D (uniform grid, Laplacian-with-skin, interblock-centered) and 2.9F (non-uniform grid, Laplacian-with-skin, interblock-centered). It is evident that the non-uniform coarsening gives again the best results: up to a downstream distance of 200 m, the reproduction is almost perfect, and the very low concentrations for distances farther than 200 m are adequately reproduced. A final comparison of the different approaches can be performed by analyzing the spatial distribution of the contaminant plume, both in plan view (depth integrated) and lateral view (integrated along the x-axis). Figure 2.12 shows the contaminant plume in the reference fine-scale conductivity realization. Figures 2.13, 2.14, and 2.15 show the corresponding distributions for the mass transport simulation in the upscaled fields using a block-centered, simple- Laplacian upscaling approach, an interblock-centered, Laplacian-with-skin approach, and the non-uniform coarsening, interblock-centered, Laplacian-withskin approach, respectively. It is evident that the block-centered approach is not capable to produce a field in which the solute travels as far downstream as in the reference field, while the most elaborated upscaling approach of Figure 2.15 gives results which quite closely resemble the reference values.
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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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Page 22 and 23: xx CONTENTS 3 Transport Upscaling U
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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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78 CHAPTER 4. MODELING TRANSIENT GR
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100 CHAPTER 4. MODELING TRANSIENT G
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102 BIBLIOGRAPHY Durlofsky, L. J.,
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104 BIBLIOGRAPHY Tran, T., 1996. Th
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106 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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