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

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8 CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . testing the use of a full tensor representation of conductivities in the upscaled model, our group had to develop a computer code (Li et al., 2010), which has been placed on the public domain, specifically designed to solve the finitedifference approximation of the groundwater flow equation without assuming that the principal directions of the hydraulic conductivity tensors are aligned to the reference axes. The remaining of this paper is organized as follows. First, in section 2.2, we summarize the findings by Salamon et al. (2007) who used a hole-effect variogram model to describe the spatial variability of lnK and, thus, were able to reproduce the non-Fickian solute spreading observed in the field. Out of the several realizations analyzed by Salamon et al. (2007), we select the one with the best reproduction of the solute spreading. This realization will be used as the reference to test different upscaling approaches. Second, in section 2.3, simple average, simple-Laplacian, Laplacian-with-skin and nonuniform coarsening upscaling methods are revisited from the perspective of their numerical implementation. Third, in section 2.4, the flow and transport numerical models are discussed, and the benefits/limitations of using different upscaling methods at the MADE site are quantified and evaluated. Next, in section 2.5, there is a general discussion. Finally, in section 2.6, we summarize the main results and conclusions of this paper. 2.2 Modeling transport at the MADE site In this work, we focus on the tritium data collected in the second MADE experiment. An extensive discussion of the main geological features and hydrogeological characterization of the site has been given by Boggs et al. (1992), Adams and Gelhar (1992), Rehfeldt et al. (1992), and Boggs and Adams (1992). Salamon et al. (2007) found that the non-Fickian solute spreading observed in the field could be reproduced using the standard advection-dispersion model as long as the spatial variability of hydraulic conductivity is properly characterized at the fine scale. For the sake of completeness, next we briefly comment the results by Salamon et al. (2007). The geostatistical analysis of the 2 495 flowmeter-derived hydraulic conductivity measurements obtained at 62 boreholes (see Figure 2.1) indicates that the spatial variability of lnK shows a pseudo-periodic behavior in the direction of flow (Figure 2.2). This behavior is modeled using a hole-effect variogram, which is nested with a nugget effect and a spherical variogram as given by: γ(h) = c0 + c1 · Sph ( ∥ hx ax1 , hy , ay1 hz ∥ az1 ) [ + c2· 1 − cos ( ∥ hx , ax2 hy , ay2 hz ∥π az2 )] (2.1)
CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . 9 Y [m] 280 260 240 220 200 180 160 140 120 100 80 60 40 20 10 30 50 70 90 110 X [m] Principal Direction of Transport Figure 2.1: Plan view of model domain. Open circles denote multilevel sampler wells. Triangles indicate the tracer injection wells. Solid circles correspond to flowmeter well locations.
Page 1: Upscaling and Inverse Modeling of G
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Page 7 and 8: Abstract The need to reduce the com
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Page 11 and 12: Resumen La necesidad de reducir el
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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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58 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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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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