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

Recommendations

Info

18 CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . Figure 2.6: An example of four boundary condition sets that could be used in 2D for the local flow models when performing the Laplacian-with-skin upscaling. The white area is the block being upscaled, and the gray area is the skin region; the arrows indicate the (negative) mean head gradient induced by the prescribed head boundary conditions, and the shapes on the sides of the block indicate the magnitude of the prescribed heads given by tilting planes with gradients opposite to the arrows.
CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . 19 2.3.4 Non-uniform coarsening Prior to upscaling, the fine-scale realization has to be overlain with the coarsescale discretization that will be used in the numerical model. Each block in the coarse discretization must be assigned an upscaled conductivity value on the basis of the conductivity values in the fine-scale realization. Initially, all studies on hydraulic conductivity upscaling assumed that the coarse scale discretization was uniform, that is, all coarse blocks were of the same shape and size, until Durlofsky et al. (1997) introduced the concept of non-uniform coarsening. The rationale was simple, if upscaling induces smoothing, and the petroleum engineer is most interested in the water cut (the early breakthrough at the production wells when petroleum is being displaced by injected water) it is important to smooth the least the areas of high displacement velocities, whereas the smoothing in the areas of low velocities is less relevant. For this purpose, Durlofsky et al. (1997) suggest the following steps: (1) identify the underlying high velocity regions using a fine-scale single-phase flow simulation; (2) on the basis of this simulation define a discretization with small blocks in high-velocity areas and large ones elsewhere; and (3) apply the Laplacianwith-skin upscaling technique to calculate the block conductivity tensors of the coarse (non-uniform) blocks. In a hydrogeological context, we can also use a non-uniform coarsening aimed to preserve small blocks in: (1) high flow velocity zones; (2) regions where hydraulic gradients change substantially over short distances, such as near pumping or injection wells (Wen and Gómez-Hernández, 1998); (3) areas near contaminant spills within a regional aquifer where accurate simulation of plume movement is of interest; and (4) in zones requiring a detailed representation of heterogeneity, for instance to capture channels or fractures (Durlofsky et al., 1997; Wen et al., 2003; Flodin et al., 2004). 2.4 Coarse model and simulation results In this section, we first present the governing equation and the solution procedures for the flow and transport models, and then we discuss the results obtained applying the different upscaling techniques described in the previous section. All of these techniques are applied to realization #26 of the MADE aquifer in Salamon et al. (2007). 2.4.1 Coarse Flow and Transport Equations Under steady-state flow conditions and in the absence of sinks and sources, the flow equation of an incompressible or slightly compressible fluid in saturated porous media can be expressed by combining Darcy’s Law and the continuity
Page 1: Upscaling and Inverse Modeling of G
Page 4 and 5: c⃝ Copyright by Liangping Li 2011
Page 7 and 8: Abstract The need to reduce the com
Page 9 and 10: improved as more data is assimilate
Page 11 and 12: Resumen La necesidad de reducir el
Page 13 and 14: Por último, en el tercer bloque, e
Page 15 and 16: Resum La necessitat de reduir el co
Page 17 and 18: flux i el transport (conductivitat
Page 19: Acknowledgements I want to thank my
Page 22 and 23: xx CONTENTS 3 Transport Upscaling U
Page 24 and 25: xxii CONTENTS
Page 26 and 27: xxiv LIST OF FIGURES 2.7 Flow compa
Page 28 and 29: xxvi LIST OF FIGURES 4.4 Reference
Page 30 and 31: xxviii LIST OF FIGURES
Page 33 and 34: 1.1 Motivation and Objectives 1 Int
Page 35: CHAPTER 1. INTRODUCTION 3 Chapter 2
Page 38 and 39: 6 CHAPTER 2. A COMPARATIVE STUDY OF
Page 40 and 41: 8 CHAPTER 2. A COMPARATIVE STUDY OF
Page 42 and 43: 10 CHAPTER 2. A COMPARATIVE STUDY O
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
Page 76 and 77: 44 CHAPTER 3. TRANSPORT UPSCALING U
Page 100 and 101:
68 CHAPTER 3. TRANSPORT UPSCALING U
Page 102 and 103:
70 BIBLIOGRAPHY Dagan, G., 1994. Up
Page 104 and 105:
72 BIBLIOGRAPHY Lawrence, A. E., Sa
Page 106 and 107:
74 BIBLIOGRAPHY Zhang, Y., 2004. Up
Page 108 and 109:
76 CHAPTER 4. MODELING TRANSIENT GR
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
100 CHAPTER 4. MODELING TRANSIENT G
Page 134 and 135:
102 BIBLIOGRAPHY Durlofsky, L. J.,
Page 136 and 137:
104 BIBLIOGRAPHY Tran, T., 1996. Th
Page 138 and 139:
106 CHAPTER 5. JOINTLY MAPPING HYDR
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
136 BIBLIOGRAPHY Chen, Y., Zhang, D
Page 170 and 171:
138 BIBLIOGRAPHY Journel, A., 1974.
Page 172 and 173:
140 BIBLIOGRAPHY Wen, X., Deutsch,
Page 174 and 175:
142 CHAPTER 6. GROUNDWATER FLOW INV
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
170 BIBLIOGRAPHY Deutsch, C. V., Jo
Page 204 and 205:
172 BIBLIOGRAPHY Lee, S., Carle, S.
Page 206 and 207:
174 BIBLIOGRAPHY Yeh, W., 1986. Rev
Page 208 and 209:
176 CHAPTER 7. CONCLUSIONS travels
Page 210 and 211:
178 CHAPTER 7. CONCLUSIONS predicti
Page 212 and 213:
180 APPENDIX A. FLOWXYZ3D - A THREE
Page 214:
182 APPENDIX A. FLOWXYZ3D - A THREE
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?