Modeling Density-Driven Flow in Porous Media: Principles, Numerics, Software

ISBN-13: 9783642637193 / Angielski / Miękka / 2012 / 286 str.

Ekkehard O. Holzbecher

Opis

Modeling of flow and transport in groundwater has become an important focus of scientific research in recent years. Most contributions to this subject deal with flow situations, where density and viscosity changes in the fluid are neglected. This restriction may not always be justified. The models presented in the book demonstrate immpressingly that the flow pattern may be completely different when density changes are taken into account. The main applications of the models are: thermal and saline convection, geothermal flow, saltwater intrusion, flow through salt formations etc. This book not only presents basic theory, but the reader can also test his knowledge by applying the included software and can set up own models.

Spis treści

1 Introduction.- 1.1 Density-Driven Flow.- 1.2 Modeling.- 1.3 Modeling Density-driven Flow in Porous Media.- 1.4 FAST-C(2D) Modeling Software.- 2 Density and Other Water Properties.- 2.1 Dependence on Temperature.- 2.1.1 Density.- 2.1.2 Thermal Expansion Coefficient.- 2.1.3 Viscosity.- 2.1.4 Specific Heat Capacity.- 2.1.5 Thermal Conductivity.- 2.1.6 Diffusivity.- 2.2 Dependence on Salinity.- 2.2.1 Density.- 2.2.2 Viscosity.- 2.3 Dependence on Pressure.- 2.3.1 Density.- 2.3.2 Compressibility.- 3 Analytical Description.- 3.1 Basic Principles.- 3.2 Oberbeck-Boussinesq Assumption.- 3.3 Hydraulic Head Formulation.- 3.4 Streamfunction Formulation.- 3.5 Vorticity Equation.- 3.6 Extended Oberbeck-Boussinesq Assumption.- 3.7 Dimensionless Formulation.- 3.8 Boundary Layer Formulation.- 3.9 Heat and Mass Transfer.- 4 Numerical Modeling (Fast-C(2D)).- 4.1 Spatial Discretization.- 4.2 Temporal Discretization.- 4.3 Boundary Conditions.- 4.4 Initial Conditions and RESTART.- 4.5 Solution of the Nonlinear System.- 4.5.1 Newton Method and Variations.- 4.5.2 Picard Iterations.- 4.6 Solution of Linear Systems.- 4.6.1 Conjugate Gradients.- 4.7 Postprocessing.- 5 Steady Convection.- 5.1 Bénard Experiments in Porous Medium.- 5.2 Linear Analysis.- 5.2.1 Isotropic Porous Medium.- 5.2.2 Anisotropic Porous Medium.- 5.3 Bifurcation Analysis.- 5.4 Numerical Experiments.- 5.4.1 Isotropic Porous Medium.- 5.4.2 Anisotropic Porous Medium.- 6 Special Topics in Convection.- 6.1 Thermal Convection in Slender Boxes.- 6.1.1 Analytical Studies.- 6.1.2 Numerical Experiments.- 6.2 Variable Viscosity Effects on Convection.- 6.2.1 Introduction.- 6.2.2 Onset of Convection.- 6.2.3 Heat Transfer.- 6.3 Convection in Cold Groundwater.- 6.3.1 Streamfunction Formulation.- 6.3.2 Onset of Convection.- 6.3.3 Flow Patterns.- 6.4 Relevance of Convection in Natural Systems.- 7 Oscillatory Convection.- 7.1 Hopf Bifurcation.- 7.2 Simulation.- 7.3 Influence of Numerical Parameters.- 8 Horizontal Heat and Mass Transfer.- 8.1 Analytical Approximations and Solutions.- 8.1.1 Convection.- 8.1.2 Conduction.- 8.2 Numerical Experiments.- 8.2.1 Conduction.- 8.2.2 Convection.- 9 Elder Experiment.- 9.1 Laboratory Experiment.- 9.2 Numerical Experiments.- 9.2.1 Elder’s Model.- 9.2.2 FAST-C(2D) Model.- 9.2.3 Further Models.- 9.3 Related Problems.- 10 Geothermal Flow (Yusa’s Example).- 10.1 Hypothetical Situation and Analytical Description.- 10.2 Flow Pattern Characterization.- 10.3 Sensitivity Analysis.- 10.4 Other Geothermal Systems.- 11 Saltwater Intrusion (Henry’s Example).- 11.1 Problem Description.- 11.2 Sharp Interface Approach.- 11.3 Henry’s Example.- 11.4 Modeling Saltwater Intrusion.- 11.4.1 Henry’s Example.- 11.4.2 Parameter Variation.- 11.4.3 Layered Aquifers.- 12 Saltwater Upconing.- 12.1 Problem Description.- 12.2 Modeling Saltwater Upconing.- 12.2.1 Sharp Interface Approach.- 12.2.2 Miscible Displacement.- 12.2.3 Variable Density Effects.- 12.3 Case Study.- 13 Flow Across a Salt-Dome.- 13.1 Salt Formations and Scenarios.- 13.2 HYDROCOIN Test-Case.- 13.3 Modeling the HYDROCOIN Test-Case.- 13.4 FAST-C(2D) Model.- 14 Desert Sedimentary Basins.- 14.1 System Description.- 14.2 Numerical Modeling.- Concluding Remark.- References.- Appendix I: Fast-C(2D) Input- and Output-Files.- Input-File for FAST-C(2D).- Output-Files.