Optimal Control of Soil Venting: Mathematical Modeling and Applications

1 Introduction.- 1.1 Background and Problem.- 1.2 Objectives.- 2 Modeling Soil Venting.- 2.1 Physical Basis of the Venting Technique.- 2.2 Simulation Models.- 3 Stationary Problem and Optimal Control.- 3.1 Basic and State Equations, Objective Function.- 3.2 Mathematical Analysis, Simplifications.- 4 Well-Posedness and Optimality.- 4.1 Air Flow in a Domain with Holes.- 4.2 Air Flow with Dirac-Type Sinks.- 4.3 Non-smooth Transmissivity at Active Wells.- 4.4 Contaminant Transport in a Domain with Holes.- 4.5 Differentiation of the Transport Equations.- 5 Optimization of Simple Well Configurations.- 5.1 One Single Active Well.- 5.2 Two Active Wells.- 5.3 Configurations with a Few Wells.- 6 Estimating the Coefficients.- 6.1 Pedotransfer Model.- 6.2 Spatial Variability and Uncertainties.- 6.3 Ordinary Kriging.- 6.4 Generation of a Random Field.- 6.5 Parameter Identification of Kertess.- 7 Numerical Methods and Optimization.- 7.1 Gas Flow Field.- 8 Applications.- 8.1 Kertess.- 8.2 Kirchweyhe.- 9 Stochastic Optimization.- 9.1 Monte Carlo Optimization.- 9.2 Sensitivity Analysis.- 10 Discussions and Conclusions.- 10.1 Time Dependent Problem.- 10.2 Optimization of Well Positions in Large Scale Applications.- 10.3 Further Aspects of Stochastic Optimization.