One important precondition for modeling multiphase flow and transport processes in the hydrosystem "subsurface" is the general formulation of a model. The objective of this book is to present a consistent, easily accessible formulation of the fundamental phenomena and concepts, to give a uniform description of mathematical and numerical modeling, and to show the latest developments in the field of simulation of multiphase processes, especially in porous and heterogeneous media. Some general aspects which affect the selection of the relevant processes and the corresponding parameters as well as…mehr
One important precondition for modeling multiphase flow and transport processes in the hydrosystem "subsurface" is the general formulation of a model. The objective of this book is to present a consistent, easily accessible formulation of the fundamental phenomena and concepts, to give a uniform description of mathematical and numerical modeling, and to show the latest developments in the field of simulation of multiphase processes, especially in porous and heterogeneous media. Some general aspects which affect the selection of the relevant processes and the corresponding parameters as well as the mathematical and numerical model concepts are discussed in detail.
1. Introduction.- 1.1 Problem classification.- 1.2 Problem formulation and exact definition of the subject.- 2. Fundamental principles of conceptual modeling.- 2.1 Preliminary remarks.- 2.2 System properties.- 2.3 Phase state, phase transition, phase change.- 2.4 Capillarity.- 2.5 Hysteresis.- 2.6 Definition of different saturations.- 2.7 Relative permeability.- 2.8 Pressure and temperature dependence of porosity.- Mathematical modeling.- 3.1 General balance equation.- 3.2 Continuity equation per phase.- 3.3 Momentum equation and Darcy's law.- 3.4 General form of the multiphase flow equation.- 3.5 Transport equation.- 3.5.4 Multicomponent transport processes in the gas phase.- 3.6 Energy equation.- 3.7 Multiphase/multicomponent system.- 4. Numerical modeling.- 4.1 Classification.- 4.2 Finite element and finite volume methods.- 4.3 Linearization of the multiphase problem.- 4.4 Discussion of the instationary hyperbolic (convective) transport equation.- 4.5 Special discretization methods.- 5. Comparison of the different discretization methods.- 5.1 Discretization.- 5.2 Boundedness principle - discussion of a monotonic solution.- 5.3 Comparative study of the different methods in homogeneous porous media.- 5.4 Heterogeneity effects.- 5.5 Comparative study of the methods for flow in heterogeneous porous media.- 5.6 Five-spot waterflood problem.- 6. Test problems - applications.- 6.1 DNAPL-Infiltration.- 6.2 LNAPL-Infiltration.- 6.3 Non-isothermal multiphase/multicomponent flow.- 7. Final remarks.
1. Introduction.- 1.1 Problem classification.- 1.2 Problem formulation and exact definition of the subject.- 2. Fundamental principles of conceptual modeling.- 2.1 Preliminary remarks.- 2.2 System properties.- 2.3 Phase state, phase transition, phase change.- 2.4 Capillarity.- 2.5 Hysteresis.- 2.6 Definition of different saturations.- 2.7 Relative permeability.- 2.8 Pressure and temperature dependence of porosity.- Mathematical modeling.- 3.1 General balance equation.- 3.2 Continuity equation per phase.- 3.3 Momentum equation and Darcy's law.- 3.4 General form of the multiphase flow equation.- 3.5 Transport equation.- 3.5.4 Multicomponent transport processes in the gas phase.- 3.6 Energy equation.- 3.7 Multiphase/multicomponent system.- 4. Numerical modeling.- 4.1 Classification.- 4.2 Finite element and finite volume methods.- 4.3 Linearization of the multiphase problem.- 4.4 Discussion of the instationary hyperbolic (convective) transport equation.- 4.5 Special discretization methods.- 5. Comparison of the different discretization methods.- 5.1 Discretization.- 5.2 Boundedness principle - discussion of a monotonic solution.- 5.3 Comparative study of the different methods in homogeneous porous media.- 5.4 Heterogeneity effects.- 5.5 Comparative study of the methods for flow in heterogeneous porous media.- 5.6 Five-spot waterflood problem.- 6. Test problems - applications.- 6.1 DNAPL-Infiltration.- 6.2 LNAPL-Infiltration.- 6.3 Non-isothermal multiphase/multicomponent flow.- 7. Final remarks.
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