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This book provides theoretical concepts and applications of
fractals and multifractals to a broad range of audiences from
various scientific communities, such as petroleum, chemical, civil
and environmental engineering, atmospheric research, and hydrology.
In the first chapter, we introduce fractals and multifractals from
physics and math viewpoints. We then discuss theory and practical
applications in detail. In what follows, in chapter 2,
fragmentation process is modeled using fractals. Fragmentation is
the breaking of aggregates into smaller pieces or fragments, a
typical phenomenon in nature. In chapter 3, the advantages and
disadvantages of two- and three-phase fractal models are discussed
in detail. These two kinds of approach have been widely applied in
the literature to model different characteristics of natural
phenomena. In chapter 4, two- and three-phase fractal techniques
are used to develop capillary pressure curve models, which
characterize pore-size distribution of porous media. Percolation
theory provides a theoretical framework to model flow and transport
in disordered networks and systems. Therefore, following chapter 4,
in chapter 5 the fractal basis of percolation theory and its
applications in surface and subsurface hydrology are discussed. In
chapter 6, fracture networks are shown to be modeled using fractal
approaches. Chapter 7 provides different applications of fractals
and multifractals to petrophysics and relevant area in petroleum
engineering. In chapter 8, we introduce the practical advantages of
fractals and multifractals in geostatistics at large scales, which
have broad applications in stochastic hydrology and hydrogeology.
Multifractals have been also widely applied to model atmospheric
characteristics, such as precipitation, temperature, and cloud
shape. In chapter 9, these kinds of properties are addressed using
multifractals. At watershed scales, river networks have been shown
to follow fractal behavior. Therefore, the applications of fractals
are addressed in chapter 10. Time series analysis has been under
investigations for several decades in physics, hydrology,
atmospheric research, civil engineering, and water resources. In
chapter 11, we therefore, provide fractal, multifractal,
multifractal detrended fluctuation analyses, which can be used to
study temporal characterization of a phenomenon, such as flow
discharge at a specific location of a river. Chapter 12 addresses
signals and again time series using a novel fractal Fourier
analysis. In chapter 13, we discuss constructal theory, which has a
perspective opposite to fractal theories, and is based on
optimizationof diffusive exchange. In the case of river drainages,
for example, the constructal approach begins at the divide and
generates headwater streams first, rather than starting from the
fundamental drainage pattern.
This book provides theoretical concepts and applications of
fractals and multifractals to a broad range of audiences from
various scientific communities, such as petroleum, chemical, civil
and environmental engineering, atmospheric research, and hydrology.
In the first chapter, we introduce fractals and multifractals from
physics and math viewpoints. We then discuss theory and practical
applications in detail. In what follows, in chapter 2,
fragmentation process is modeled using fractals. Fragmentation is
the breaking of aggregates into smaller pieces or fragments, a
typical phenomenon in nature. In chapter 3, the advantages and
disadvantages of two- and three-phase fractal models are discussed
in detail. These two kinds of approach have been widely applied in
the literature to model different characteristics of natural
phenomena. In chapter 4, two- and three-phase fractal techniques
are used to develop capillary pressure curve models, which
characterize pore-size distribution of porous media. Percolation
theory provides a theoretical framework to model flow and transport
in disordered networks and systems. Therefore, following chapter 4,
in chapter 5 the fractal basis of percolation theory and its
applications in surface and subsurface hydrology are discussed. In
chapter 6, fracture networks are shown to be modeled using fractal
approaches. Chapter 7 provides different applications of fractals
and multifractals to petrophysics and relevant area in petroleum
engineering. In chapter 8, we introduce the practical advantages of
fractals and multifractals in geostatistics at large scales, which
have broad applications in stochastic hydrology and hydrogeology.
Multifractals have been also widely applied to model atmospheric
characteristics, such as precipitation, temperature, and cloud
shape. In chapter 9, these kinds of properties are addressed using
multifractals. At watershed scales, river networks have been shown
to follow fractal behavior. Therefore, the applications of fractals
are addressed in chapter 10. Time series analysis has been under
investigations for several decades in physics, hydrology,
atmospheric research, civil engineering, and water resources. In
chapter 11, we therefore, provide fractal, multifractal,
multifractal detrended fluctuation analyses, which can be used to
study temporal characterization of a phenomenon, such as flow
discharge at a specific location of a river. Chapter 12 addresses
signals and again time series using a novel fractal Fourier
analysis. In chapter 13, we discuss constructal theory, which has a
perspective opposite to fractal theories, and is based on
optimizationof diffusive exchange. In the case of river drainages,
for example, the constructal approach begins at the divide and
generates headwater streams first, rather than starting from the
fundamental drainage pattern.
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. [...] I think the book is an important work that
will guide soil scientists, hydrologists, and physicists to gain a
better qualitative and quantitative understanding of multitransport
properties of soils." (Marcel G. Schaap, Soil Science Society of
America Journal, May-June, 2006)
Physics of Fluid Flow and Transport in Unconventional Reservoir
Rocks Understanding and predicting fluid flow in hydrocarbon shale
and other non-conventional reservoir rocks Oil and natural gas
reservoirs found in shale and other tight and ultra-tight porous
rocks have become increasingly important sources of energy in both
North America and East Asia. As a result, extensive research in
recent decades has focused on the mechanisms of fluid transfer
within these reservoirs, which have complex pore networks at
multiple scales. Continued research into these important energy
sources requires detailed knowledge of the emerging theoretical and
computational developments in this field. Following a
multidisciplinary approach that combines engineering, geosciences
and rock physics, Physics of Fluid Flow and Transport in
Unconventional Reservoir Rocks provides both academic and
industrial readers with a thorough grounding in this cutting-edge
area of rock geology, combining an explanation of the underlying
theories and models with practical applications in the field.
Readers will also find: An introduction to the digital modeling of
rocks Detailed treatment of digital rock physics, including decline
curve analysis and non-Darcy flow Solutions for
difficult-to-acquire measurements of key petrophysical
characteristics such as shale wettability, effective permeability,
stress sensitivity, and sweet spots Physics of Fluid Flow and
Transport in Unconventional Reservoir Rocks is a fundamental
resource for academic and industrial researchers in hydrocarbon
exploration, fluid flow, and rock physics, as well as professionals
in related fields.
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