Multiphase Flow and Transport Processes in the Subsurface

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.