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

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34 CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . heterogeneity that had to be taken into account in the transport simulation at the coarse scale. Can the findings from this work be extrapolated to other case studies? We believe that, regarding flow upscaling, yes they can. In fact, the findings from this paper are in agreement with similar works in other case studies. However, regarding transport upscaling, they can be extrapolated only under the same conditions considered here, that is, using coarse blocks smaller than the correlation range, and, using a non-uniform grid with smaller blocks in the areas with highest velocities and in the areas through which the plume will travel. The final point of discussion is why we have worked trying to reproduce flow and transport on a realization from Salamon et al. (2007) instead of trying to reproduce the available experimental data. This paper did not try to perform a calibration exercise of the MADE site, but rather to help in performing such a calibration in the future. With the work in this paper we show that a coarse scale model, obtained by careful upscaling of a fine scale one, can reproduce the type of transport behavior observed at the MADE site simply using the advection dispersion equation. Trying to calibrate a two-million cell model as obtained by Salamon et al. (2007) is not an easy task, it would require running many times the flow and transport models in many realizations of the site; but those runs would be possible on the coarse models used in our work. The next step in this direction would be to develop a calibration approach that would account for the upscaling step needed to reduce the numerical modeling effort. In its application of such an approach, considering heterogeneity in porosity may also help in obtaining the best calibration; something not needed in our upscaling exercise, since we assume constant porosity attached to the reference conductivity realization. 2.6 Summary and Conclusions In this paper, we have presented a detailed analysis of the impact of different upscaling techniques on the reproduction of solute transport at the MADE site. We use as a reference a fine scale realization taken from the work by Salamon et al. (2007) that is able to reproduce the contaminant spreading observed in the experiment using an advection-dispersion model. The techniques analyzed span from simple averaging to the estimation of block tensors by local flow models. We have also analyzed the impact that non-uniform coarsening may have in the quality of the results. This work has three main and important conclusions: 1. In complex environments, such as the MADE site, with hydraulic conductivities which vary over many orders of magnitude, and display an
CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . 35 intricate spatial variability, carefully choosing the upscaling technique is very important. The hydraulic conductivity full tensors obtained using the interblock-centered Laplacian-with-skin upscaling technique with a skin size of half block performs best among the different upscaling methods analyzed, although, at the MADE site, the superiority of the fulltensor upscaling over diagonal tensors upscaling is very limited. This can be explained by the fact that the principal directions of hydraulic conductivity are parallel with the reference axes. 2. A non-uniform coarsening focused in the refinement of the regions through which the solute plume travels can further improve the results. 3. Modeling of flow and transport at the MADE site has been the object of debate for many years, and many complex transport models have been proposed to reproduce the plume spreading observed. We show that the advection-dispersion model can be used on a coarse model to explain the plume migration in the highly heterogeneous MADE site if careful modeling/upscaling of the flow field is performed, as long as the block size remains smaller than the correlation ranges of the underlying fine scale conductivities.
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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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Page 22 and 23: xx CONTENTS 3 Transport Upscaling U
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Page 70 and 71: 38 BIBLIOGRAPHY Berkowitz, B., Sche
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Page 74 and 75: 42 BIBLIOGRAPHY Salamon, P., Fernà
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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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