Multiphase Flow and Transport Processes in the Subsurface - Helmig, Rainer

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Biographie:
Tobias K?ppl is an applied mathematician. He received his PhD in 2015 at the Technical University of Munich. From 2014 to 2018, he was a postdoctoral researcher at the Department for Hydromechanics and Modelling of Hydrosystems of the University of Stuttgart. In December 2020, Dr. Tobias K?ppl successfully completed his habilitation at the University of Stuttgart. At the moment he is working as a reseacher at the University of Hasselt. Prof. Dr. Rainer Helmig since the year 2000, Rainer Helmig is the head of the Department of Hydromechanics and Moeling of Hydrosystems at the Institute for Modelling Hydraulic and Environmental Systems (IWS) of the University of Stuttgart. His research is focused on developing numerical methods for coupling hydrosystem compartments and complex flow and transport processes as well as integrating data and hydrosystem models. Rainer Helmig is author of numerous articles and books....

Sommaire:
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.