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

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54 CHAPTER 3. TRANSPORT UPSCALING USING MULTI- . . . At the fine scale, the five-point block-centered finite-difference groundwater flow model MODFLOW 2000 (Harbaugh et al., 2000) was employed to solve the flow equation (3.1). The interface velocities were calculated, and then utilized in the random walk particle tracking code RW3D (Fernàndez- Garcia et al., 2005; Salamon et al., 2006b), which was used to solve the fine scale transport equation (3.2). In this approach, the evolution in time of each particle is comprised of a deterministic component, which depends only on the local velocity field, and a superposed Brownian motion responsible for dispersion. A hybrid scheme is used for the velocity interpolation which provides local as well as global divergence-free velocity fields within the solution domain. Meanwhile, a continuous dispersion tensor field provides good mass balance at grid interfaces of adjacent cells with contrasting hydraulic conductivities (LaBolle et al., 1996; Salamon et al., 2006b). Furthermore, in contrast to the common constant-time scheme used in random walk modeling, a constant-displacement scheme (Wen and Gómez-Hernández, 1996a), which modifies automatically the time step size for each particle according to the local velocity, is employed in order to decrease computational effort. At the coarse scale, the nineteen-point block-centered finite-difference groundwater model FLOWXYZ (Li et al., 2010b) was employed to solve the flow equation (3.4). The most remarkable characteristic of this forward flow simulator is the capacity to deal with full conductivity tensors defined at block interfaces. Hydraulic conductivity tensors are defined at the block interfaces eliminating the need to average conductivity tensors at adjacent blocks to approximate their values at the interfaces. This scheme has been shown to perform better than the MODFLOW LVDA package (Li et al., 2010b), and has been successfully applied in other studies (e.g., Zhou et al., 2010; Li et al., 2010a). Again, the RW3D was used to solve the coarse scale multi-rate transport equation (3.5) based on the methodology presented by Salamon et al. (2006a). Mass transfer processes are efficiently incorporated into the particle tracking algorithm by switching the state of the particle between mobile/immobile states according to appropriate transition probabilities. For the sake of simplicity, we neglect dispersion, and only consider advection, at the fine scale, i.e., Dm = 0 and αi = 0. A total of 20000 particles (a number that we have tested yields stable transport predictions for this specific case) randomly distributed in a rectangular-shaped area of 60 m width and 30 m height located orthogonal to the principal flow direction in the plane at x = 20 m were released at time t = 0. The variable time step was computed on the basis of a grid Courant number of 0.01. A unit mass was assigned to each particle. Control planes are located within the aquifer to measure the mass arrival at 10 m intervals (see Figure 3.2).
CHAPTER 3. TRANSPORT UPSCALING USING MULTI- . . . 55 50 Z [m] 0 0 50 Y [m] 100 200 150 100 X [m] 50 0 lnK[m/d] 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 Figure 3.1: A realization of reference lnK field (σ2 lnK =4.0) overlaid with the discretization of the numerical model at the coarse scale. 50 Z [m] 0 0 Source 50 Y [m] 100 200 150 100 X [m] 50 0 Control Planes Figure 3.2: Sketch of transport simulations. The shaded rectangle located in the upstream zone delineates the initial particle injection zone. Control planes are also shown for measuring the mass fluxes.
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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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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 134 and 135: 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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