Ebook: Non-fickian Solute Transport in Porous Media: A Mechanistic and Stochastic Theory
Author: Don Kulasiri (auth.)
- Tags: Geophysics/Geodesy, Fluid- and Aerodynamics, Mathematical Modeling and Industrial Mathematics
- Series: Advances in Geophysical and Environmental Mechanics and Mathematics
- Year: 2013
- Publisher: Springer Berlin Heidelberg
- Language: English
- pdf
The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.
The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.
Content:
Front Matter....Pages i-ix
Non-fickian Solute Transport....Pages 1-27
Stochastic Differential Equations and Related Inverse Problems....Pages 29-74
A Stochastic Model for Hydrodynamic Dispersion....Pages 75-126
A Generalized Mathematical Model in One-Dimension....Pages 127-165
Theories of Fluctuations and Dissipation....Pages 167-181
Multiscale, Generalised Stochastic Solute Transport Model in One Dimension....Pages 183-200
The Stochastic Solute Transport Model in 2-Dimensions....Pages 201-218
Multiscale Dispersion in Two Dimensions....Pages 219-224
Back Matter....Pages 225-227
The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.
Content:
Front Matter....Pages i-ix
Non-fickian Solute Transport....Pages 1-27
Stochastic Differential Equations and Related Inverse Problems....Pages 29-74
A Stochastic Model for Hydrodynamic Dispersion....Pages 75-126
A Generalized Mathematical Model in One-Dimension....Pages 127-165
Theories of Fluctuations and Dissipation....Pages 167-181
Multiscale, Generalised Stochastic Solute Transport Model in One Dimension....Pages 183-200
The Stochastic Solute Transport Model in 2-Dimensions....Pages 201-218
Multiscale Dispersion in Two Dimensions....Pages 219-224
Back Matter....Pages 225-227
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