A description of the latest and most appropriate mathematical and numerical methods for optimizing soil venting. The monograph considers mathematical, numerical, and technical aspects as well as their practical significance. This book will be of interest to applied mathematicians, geophysicists, geoecologists, soil physicists, and environmental engineers.
1 Introduction.- 1.1 Background and Problem.- 1.2 Objectives.- 1.2.1 Mathematical and Numerical Objectives.- 1.2.2 Objectives of the Optimization.- 2 Modeling Soil Venting.- 2.1 Physical Basis of the Venting Technique.- 2.2 Simulation Models.- 2.2.1 Soil Gas Transport Models.- 2.2.2 Phase Mass Transfer Models.- 2.2.3 Multi-phase Permeability Models.- 2.2.4 Biological Decay.- 2.2.5 Measurement Configuration.- 2.2.6 Heterogeneous Media.- 2.2.7 Structured Soil.- 2.2.8 Mathematical Aspects.- 2.2.9 Remarks on Preferential Gas Flow in Structured Soils.- 3 Stationary Problem and Optimal Control.- 3.1 Basic and State Equations, Objective Function.- 3.1.1 Air Flow.- 3.1.2 Contaminant Transport.- 3.1.3 Optimal Control.- 3.2 Mathematical Analysis, Simplifications.- 3.2.1 Dimensionless Form.- 3.2.2 Approximation of Sinks by Dirac Functions.- 3.2.3 Justification of a Leakage Term.- 3.2.4 Streamline Method.- 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.- 5.1.1 Constant Volatilization on a Disk.- 5.1.2 Bell-Shaped Volatilization.- 5.2 Two Active Wells.- 5.3 Configurations with a Few Wells.- 6 Estimating the Coefficients.- 6.1 Pedotransfer Model.- 6.1.1 Grouping of Soil Substrates.- 6.1.2 Grouping of the Texture of the Fine Soil Material (equivalent grain diameter smaller than 2 mm).- 6.1.3 Estimation of the Cumulative Particle-Size Distribution.- 6.1.4 Graphical Interpretation of the Particle-Size Distribution.- 6.1.5 Estimation of the Hydraulic Conductivity at Pore Water Saturation.- 6.1.6 Permeability of the Refilled and Rubble Material.- 6.1.7 Analytical Interpretation of the Particle-Size Distribution.- 6.1.8 Residual Water Saturation.- 6.1.9 Hydraulic Parameter Functions.- 6.1.10 Relative Permeability, Saturation-Pressure, and Relative Permeability Relations.- 6.1.11 Pedotransfer Functions, Pressure-Saturation Relations.- 6.1.12 Discussion.- 6.2 Spatial Variability and Uncertainties.- 6.3 Ordinary Kriging.- 6.4 Generation of a Random Field.- 6.5 Parameter Identification of Kertess.- 6.5.1 Calibration of the Transmissivity T, the Leakage L and the Boundary Leakage 1.- 6.5.2 Second Calibration of the Transmissivity T.- 6.5.3 Results of the Calibration of the Air Flow Parameters.- 6.5.4 Calibration of the Volatilization Coefficient V.- 6.5.5 Numerical Minimization Method.- 6.5.6 Results of the Calibration of the Volatilization Coefficient.- 7 Numerical Methods and Optimization.- 7.1 Gas Flow Field.- 7.1.1 Linearity of the Flow Field w.r.t. the Control Variable.- 7.1.2 Mixed Variational Formulation.- 7.1.3 Discrete Variational Formulation.- 7.2 Contaminant Transport.- 7.3 Integrating the Extraction Rate.- 7.4 Optimization Algorithm.- 7.5 Programming Aspects.- 8 Applications.- 8.1 Kertess.- 8.1.1 Optimizing the Extraction Rates.- 8.2 Kirchweyhe.- 8.2.1 Optimizing the Extraction Rates.- 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.- 10.3.1 Solution Strategies.- 10.3.2 Solution Strategies.
