Author: Rainer Helmig
Translator: P. Schulz.
Series: Environmental Science and Engineering / Environmental Engineering.
Length: 367 pages.
Publisher: Springer; 1 edition (October 16, 1997).
Language: English.
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.Table of Contents:
1. Introduction.
- 1.1 Problem classification.
- 1.2 Problem formulation and exact definition of the subject.
- 1.2.1 Application of the different models.
- 1.2.2 Remarks on the term model.
- 1.2.3 Objective and structure of this book.
2. Fundamental principles of conceptual modeling.
- 2.1 Preliminary remarks.
- 2.1.1 General remarks.
- 2.1.2 Definitions and fundamental terms.
- 2.2 System properties.
- 2.2.1 Mass and mole fractions.
- 2.2.2 Density.
- 2.2.3 Viscosity.
- 2.2.4 Specific enthalpy, specific internal energy.
- 2.2.5 Surface tension.
- 2.2.6 Specific heat capacity.
- 2.3 Phase state, phase transition, phase change.
- 2.3.1 Phase state.
- 2.3.2 Phase transition, phase change.
- 2.4 Capillarity.
- 2.4.1 Microscopic capillarity.
- 2.4.2 Macroscopic capillarity.
- 2.4.3 Capillarity in fractures.
- 2.5 Hysteresis.
- 2.6 Definition of different saturations.
- 2.7 Relative permeability.
- 2.7.1 Permeability.
- 2.7.2 Relative permeability at the micro scale.
- 2.7.3 Relative permeability at the macro scale.
- 2.7.4 Relative permeability-saturation relation in fractures.
- 2.7.5 Fracture-matrix interaction.
- 2.8 Pressure and temperature dependence of porosity.
3. Mathematical modeling.
- 3.1 General balance equation.
- 3.1.1 Preconditions and assumptions.
- 3.1.2 The Reynolds transport theorem in integral form.
- 3.1.3 Derivation of the general balance equation.
- 3.1.4 Initial and boundary conditions.
- 3.1.5 Choice of the primary variables.
- 3.2 Continuity equation per phase.
- 3.2.1 Time derivative.
- 3.3 Momentum equation and Darcy’s law.
- 3.3.1 General remarks.
- 3.3.2 Darcy’s law of single-phase flow.
- 3.3.3 Generalization of Darcy’s law for multiphase flow.
- 3.4 General form of the multiphase flow equation.
- 3.4.1 Pressure formulation.
- 3.4.2 Pressure-saturation formulation.
- 3.4.3 Saturation formulation.
- 3.4.4 Mathematical modeling for three-phase infiltration and remobilization processes.
- 3.5 Transport equation.
- 3.5.1 Basic transport equation.
- 3.5.2 Transport in a multiphase system.
- 3.5.3 Description of the mass transfer between phases.
- 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.
- 4.1.1 Problem and special solution methods.
- 4.1.2 Fundamentals of discretization.
- 4.1.3 Conservative discretization.
- 4.1.4 Weighted residual method.
- 4.2 Finite element and finite volume methods.
- 4.2.1 Spatial discretization.
- 4.2.2 Choice of element types.
- 4.2.3 Galerkin finite element method.
- 4.2.4 Sub domain collocation — finite volume method.
- 4.2.5 Time discretization.
- 4.3 Linearization of the multiphase problem.
- 4.3.1 Weak nonlinearities.
- 4.3.2 Strong nonlinearities.
- 4.3.3 Handling of the nonlinearities.
- 4.3.4 Example: Linearized two-phase equation.
- 4.4 Discussion of the instationary hyperbolic (convective) transport equation.
- 4.4.1 Classification of hyperbolic differential equations.
- 4.4.2 A linear hyperbolic transport equation.
- 4.4.3 A quasilinear hyperbolic transport equation - Buckley-Levereit equation.
- 4.4.4 Analytical solutions for the Buckley-Lev ereit problem.
- 4.5 Special discretization methods.
- 4.5.1 Motivation.
- 4.5.2 Upwind method — finite difference method.
- 4.5.3 Explicit upwind method of first order — Fully Upwind.
- 4.5.4 Multidimensional upwind method of first order.
- 4.5.5 Explicit upwind method of higher order — TVD techniques.
- 4.5.6 Implicit upwind method of first order — Fully Upwind.
- 4.5.7 Petrov-Galerkin finite element method.
- 4.5.8 Additional remarks on conservative discretization.
- 4.5.9 Flux-corrected method.
- 4.5.10 Mixed-hybrid finite element methods.
5. Comparison of the different discretization methods.
- 5.1 Discretization.
- 5.1.1 Finite element Galerkin method.
- 5.1.2 Sub domain collocation finite volume method (box method).
- 5.2 Boundedness principle — discussion of a monotonic solution.
- 5.3 Comparative study of the different methods in homogeneous porous media.
- 5.3.1 Multiphase flow without capillary pressure effects — Buckley-Lev ereit problem.
- 5.3.2 Multiphase flow with capillary pressure effects — McWhorter problem.
- 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.
- 6.3.1 Heat pipe.
- 6.3.2 Study of bench-scale experiments.
7. Final remarks.
