Percolation Theory for Flow in Porous Media

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This monograph presents, for the first time, a unified and comprehensive introduction to some of the basic transport properties of porous media, such as electrical and hydraulic conductivity, air permeability and diffusion. The approach is based on critical path analysis and the scaling of transport properties, which are individually described as functions of saturation.
At the same time, the book supplies a tutorial on percolation theory for hydrologists, providing them with the tools for solving actual problems. In turn, a separate chapter serves to introduce physicists to some of the language and complications of groundwater hydrology necessary for successful modeling. The end-of-chapter problems often indicate open questions, which young researchers entering the field can readily start working on. This significantly revised and expanded third edition includes in particular two new chapters: one on advanced fractal-based models, and one devoted to the discussion of various open issues such as the role of diffusion vs. advection, preferential flow vs. critical path, universal vs. non-universal exponents for conduction, and last but not least, the overall influence of the experimental apparatus in data collection and theory validation. «The book is suitable for advanced graduate courses, with selected problems and questions appearing at the end of each chapter.

Author(s): Allen Hunt, Robert Ewing, Behzad Ghanbarian (auth.)
Series: Lecture Notes in Physics 880
Edition: 1
Publisher: Springer International Publishing
Year: 2014

Language: English
Pages: 447
Tags: Hydrogeology; Statistical Physics, Dynamical Systems and Complexity; Geoengineering, Foundations, Hydraulics; Numerical and Computational Physics

Front Matter....Pages I-XXIV
Percolation Theory: Topology and Structure....Pages 1-35
Properties Relevant for Transport and Transport Applications....Pages 37-57
Porous Media Primer for Physicists....Pages 59-101
Fractal Models of Porous Media....Pages 103-129
Specific Examples of Critical Path Analysis....Pages 131-156
Hydraulic and Electrical Conductivity: Conductivity Exponents and Critical Path Analysis....Pages 157-217
Other Transport Properties of Porous Media....Pages 219-272
Pressure Saturation Curves and the Critical Volume Fraction for Percolation: Accessibility Function of Percolation Theory....Pages 273-296
Applications of the Correlation Length: Scale Effects on Flow....Pages 297-312
Applications of the Cluster Statistics....Pages 313-331
Properties Based on Tortuosity....Pages 333-408
Effects of Multi-scale Heterogeneity....Pages 409-428
Misconceptions....Pages 429-434
Back Matter....Pages 435-447