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

xx CONTENTS
3 Transport Upscaling Using Multi-Rate Mass Transfer in Three-
Dimensional Highly Heterogeneous Media (published in Advances in
Water Resources) 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.2 Hydraulic conductivity upscaling using the Laplacianwith-skin
method . . . . . . . . . . . . . . . . . . . . . . 49
3.2.3 Transport upscaling using mass transfer . . . . . . . . . 51
3.3 Numerical Evaluation . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 Model Configuration . . . . . . . . . . . . . . . . . . . . 53
3.3.2 Flow upscaling results . . . . . . . . . . . . . . . . . . . 56
3.3.3 Transport upscaling results . . . . . . . . . . . . . . . . 58
3.3.4 Propagation of Uncertainty . . . . . . . . . . . . . . . . 62
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 67
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 Modeling Transient Groundwater Flow by Coupling Ensemble
Kalman Filtering and Upscaling (submitted to Water Resources
Research) 75
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.1 Generation of the Ensemble of Fine Scale Conductivities 78
4.2.2 Upscaling . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.3 The EnKF with Hydraulic Conductivity Tensors . . . . 80
4.3 Application Example . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.1 Reference Field . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.2 Hydraulic Conductivity Upscaling . . . . . . . . . . . . 84
4.3.3 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.4 Performance Measurements . . . . . . . . . . . . . . . . 88
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4.1 The EnKF Coupled with Upscaling . . . . . . . . . . . . 90
4.4.2 Worth of Data . . . . . . . . . . . . . . . . . . . . . . . 96
4.4.3 Other Issues . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Jointly Mapping Hydraulic Conductivity and Porosity by Assimilating
Concentration Data via Ensemble Kalman Filter
(submitted to Journal of Hydrology) 105
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106