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Stochastic Methods in Subsurface Contaminant Hydrology, 2002
- Contents
- 1 Preliminary Concepts in Stochastic Processes [Go to Page]
- The Case for Stochastic Approaches
- Preliminary Concepts of Random Fields
- Scope of This Book
- References
- 2 Perturbation Theories for the Estimation of Macrodispersivities in Heterogeneous Aquifers [Go to Page]
- Introduction
- Statistical Characterization of Random Fields
- Flow in a Heterogeneous Porous Medium and the Spectrum of Specific Discharge Variations
- Solute Transport in Heterogeneous Aquifers [Go to Page]
- Eulerian Approach
- Lagrangian Approach
- Unified View of Eulerian and Lagrangian Approaches and Some Illustrative Results
- Influence of the Plume Size on Macrodispersion
- Comparison of Dispersivity Predictions Against Field Data an dNumerical Simulations
- Summary and Concluding Remarks
- References
- 3 Concentration Fluctuations, Dilution, and Risk Assessment: Role of Local Dispersion and Heterogeneity [Go to Page]
- Introduction [Go to Page]
- Background
- Objective
- Fundamentals [Go to Page]
- Seepage Velocity
- Local Dispersion
- Solute Transport Equation
- Enhanced Spreading Due to Heterogeneity [Go to Page]
- Field Observations
- Macrodispersion
- Stochastic Model [Go to Page]
- Flow in a Random Hydraulic Conductivity Field
- Solute Transport Simulation
- Disconnect Between Dilution and Spreading [Go to Page]
- Dilution-Spreading-Local Dispersion Characteristics
- Cape Cod Bromide Tracer Data
- Volume Occupied by Solute
- Concentration Fluctuations and Risk [Go to Page]
- Irregularity of Concentration Distributions
- Rise and Fall of the Concentration Coefficient of Variation
- Conclusion
- Acknowledgments
- References
- 4 Stochastic Analysis of Reactive Transport Processes in Heterogeneous Porous Media [Go to Page]
- Introduction
- Subsurface Contaminants and Their Sources
- Physical and Chemical Concepts in Reactive Transport Modeling [Go to Page]
- Mass Transport in Saturated and Unsaturated Porous Media
- Mass Transfer Processes: Sorption
- Mass Transfer Processes: Transformation
- Reactive Contaminant Transport: Field Observations
- Stochastic Analysis of Reactive Contaminant Transport [Go to Page]
- Spatially Variable Linear Equilibrium Assumption Sorption in One-Dimensional Media with Homogeneous Hydraulic Conductivity
- Spatially Variable Linear Sorption in Heterogeneous Media with No Local Dispersion (Lagrangian Analysis)
- Spatially Variable Linear Sorption and Degradation in Heterogeneous Media with Local Dispersion (Eulerian Analysis)
- Nonlinear Sorption and Kinetic Processes in Heterogeneous Media
- Stochastic Analysis of Contaminant Breakthrough Curves [Go to Page]
- The Breakthrough Curve Concept in Heterogeneous Porous Media
- Nonreactive Solute Travel Time
- Reactive Solute Travel Time
- Travel Time Moments for Nonequilibrium Sorption and Degradation
- Reactive Contaminant Transport in the Vadose Zone
- Conclusion
- Acknowledgments
- Table of Notation
- References
- 5 Streamtube Ensemble Techniques for Subsurface Multicomponent Reactive Transport [Go to Page]
- Introduction [Go to Page]
- Multicomponent Reaction Systems
- Reaction Systems in Convective-Dispersive Transport
- Overview of Streamtube Ensemble Scaling Approach
- Streamtube Ensemble Formulation [Go to Page]
- Assumptions
- From General to Streamtube Coordinates
- From Streamtube to Projection-Streamtube Coordinates
- Travel-Time Formulations, the Constant Velocity Ensemble, and Streamtube Invariance
- Stochastic-Convective Averaging [Go to Page]
- Convolution Forms: Use and Limitations
- Streamtube Invariance: Use and Limitations
- Chemical/Biologic Heterogeneity in Immobile Species
- Travel-Time Distribution Function Estimation [Go to Page]
- Parametric Approaches
- Nonparametric Approaches
- Error Bounds
- A Computational Example [Go to Page]
- A Four-Component Nonlinear, Nonlocal-in-Time, Reaction System
- A Finite Ensemble of Effective Streamtubes
- Computing a Travel-Time Distribution from the Breakthrough of Chloride
- Simulation of Breakthroughs By Means of Streamtube Ensemble Averages
- Summary
- Acknowledgments
- References
- 6 Theory and Applications of Time Moment Analysis to Study the Fate of Reactive Solutes in Soil [Go to Page]
- Introduction
- Definition of Time Moments and Associated Functions [Go to Page]
- Background
- Moments and Characteristic Function
- Relationship Between p[sub(x)](x) and Concentration of Solute in a Porous Medium
- Transfer Function and Resident Time Distribution Function
- Cumulants and Related Concepts
- Approaches of Time Moment Analysis [Go to Page]
- Derivation of Theoretical Time Moments
- Computing Time Moments from Experimental Data
- Applications of the Method of Moments [Go to Page]
- Estimating Parameters of the Transport Equation
- Estimating Effective Transport Parameters in Spatially Variable Porous Media
- Estimating Breakthrough Curves from Moments
- Gaining Physical Insight into Solute Transport Processes
- Conclusions
- References
- 7 Conservation Equations for Solute Transport by Unsteady and Steady Flows in Heterogeneous Aquifers: The Cumulant Expansion/Lie Operator Methodology [Go to Page]
- Introduction
- Cumulants And Cumulant Expansion
- Use of Cumulant Expansions, Time-Ordered Exponential Operators, and Lie Operators in Developing Ensemble Average Forms of Transport Conservation Equations [Go to Page]
- Conservation Equations of Transport by Unsteady Flow
- Conservation Equations of Transport by Steady, Spatially Nonstationary Flow
- Application and Validation of the Developed Theory
- Discussion and Conclusions
- Acknowledgments
- References
- 8 Semigroup and Decomposition Methods in Solving Stochastic Subsurface Contamination Problems [Go to Page]
- Introduction
- Semigroup Operators in Subsurface Contaminant Hydrology
- Analytical Decomposition Methods in Subsurface Contaminant Hydrology
- Applications to Convection Dispersion Models
- Applications to Scale-Dependent Transport Models
- Decomposition Theory of Non-Fickian Transport
- The Form of the Field Dispersion Coefficient According to Decomposition
- Applications to Nonpoint Sources and Spills Originated in the Unsaturated Zone
- Conclusion and Recommendations
- Acknowledgments
- References
- 9 Estimation and Prediction of Hydrogeochemical Parameters Using Extended Kalman Filtering [Go to Page]
- Introduction
- General Formulation of Extended Kalman Filtering Equations [Go to Page]
- State, Parameter, and Measurement Equations
- State and Parameter Moment Propagation Equations
- State and Parameter Moment Update Equations
- Comments on Filter Form and Behavior
- Application of the Extended Kalman Filter to Field-Scale Subsurface Flow and Transport Problems
- Estimating Head, Transmissivity, and Recharge in the Floridan Aquifer [Go to Page]
- Application to Predicting Solute Transport in the Borden Tracer Experiment
- Application to Estimating Residual Non-Aqueous Phase Liquid (NAPL) Distribution at Hill Air Force Base, Ogden, Utah
- Conclusions
- References
- 10 Anomalous Dispersion of Conservative Tracers: Theory and Three-Dimensional Particle Tracking Velocimetry Experiments [Go to Page]
- Introduction
- Self-Dispersion (Wave-Vector Representation)
- Self-Dispersion (Real-Space Representation)
- Wave-Vector Expansions for Material Coefficients
- Dispersion of Nonreacting Species
- Statistical Mechanical Setting: Equilibrium
- Statistical Mechanical Setting: Local Equilibrium
- Three-Dimensional Particle Tracking Velocimetry Experimental Set-up
- Image Processing
- Experimental Results and Discussion
- Conclusion
- Acknowledgments
- References
- Index [Go to Page]
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Y
- Z [Go to Page]