Fluid Dynamics in Complex Fractured-Porous Systems

Fluid Dynamics in Complex Fractured-Porous Systems

Author: Boris Faybishenko

Publisher: John Wiley & Sons

Published: 2015-07-07

Total Pages: 262

ISBN-13: 1118877209

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Despite of many years of studies, predicting fluid flow, heat, and chemical transport in fractured-porous media remains a challenge for scientists and engineers worldwide. This monograph is the third in a series on the dynamics of fluids and transport in fractured rock published by the American Geophysical Union (Geophysical Monograph Series, Vol. 162, 2005; and Geophysical Monograph, No. 122, 2000). This monograph is dedicated to the late Dr. Paul Witherspoon for his seminal influence on the development of ideas and methodologies and the birth of contemporary fractured rock hydrogeology, including such fundamental and applied problems as environmental remediation; exploitation of oil, gas, and geothermal resources; disposal of spent nuclear fuel; and geotechnical engineering. This monograph addresses fundamental and applied scientific questions and is intended to assist scientists and practitioners bridge gaps in the current scientific knowledge in the areas of theoretical fluids dynamics, field measurements, and experiments for different practical applications. Readers of this book will include researchers, engineers, and professionals within academia, Federal agencies, and industry, as well as graduate/undergraduate students involved in theoretical, experimental, and numerical modeling studies of fluid dynamics and reactive chemical transport in the unsaturated and saturated zones, including studies pertaining to petroleum and geothermal reservoirs, environmental management and remediation, mining, gas storage, and radioactive waste isolation in underground repositories. Volume highlights include discussions of the following: Fundamentals of using a complex systems approach to describe flow and transport in fractured-porous media. Methods of Field Measurements and Experiments Collective behavior and emergent properties of complex fractured rock systems Connection to the surrounding environment Multi-disciplinary research for different applications


Book Synopsis Fluid Dynamics in Complex Fractured-Porous Systems by : Boris Faybishenko

Download or read book Fluid Dynamics in Complex Fractured-Porous Systems written by Boris Faybishenko and published by John Wiley & Sons. This book was released on 2015-07-07 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite of many years of studies, predicting fluid flow, heat, and chemical transport in fractured-porous media remains a challenge for scientists and engineers worldwide. This monograph is the third in a series on the dynamics of fluids and transport in fractured rock published by the American Geophysical Union (Geophysical Monograph Series, Vol. 162, 2005; and Geophysical Monograph, No. 122, 2000). This monograph is dedicated to the late Dr. Paul Witherspoon for his seminal influence on the development of ideas and methodologies and the birth of contemporary fractured rock hydrogeology, including such fundamental and applied problems as environmental remediation; exploitation of oil, gas, and geothermal resources; disposal of spent nuclear fuel; and geotechnical engineering. This monograph addresses fundamental and applied scientific questions and is intended to assist scientists and practitioners bridge gaps in the current scientific knowledge in the areas of theoretical fluids dynamics, field measurements, and experiments for different practical applications. Readers of this book will include researchers, engineers, and professionals within academia, Federal agencies, and industry, as well as graduate/undergraduate students involved in theoretical, experimental, and numerical modeling studies of fluid dynamics and reactive chemical transport in the unsaturated and saturated zones, including studies pertaining to petroleum and geothermal reservoirs, environmental management and remediation, mining, gas storage, and radioactive waste isolation in underground repositories. Volume highlights include discussions of the following: Fundamentals of using a complex systems approach to describe flow and transport in fractured-porous media. Methods of Field Measurements and Experiments Collective behavior and emergent properties of complex fractured rock systems Connection to the surrounding environment Multi-disciplinary research for different applications

Multiphase Fluid Flow in Porous and Fractured Reservoirs

Multiphase Fluid Flow in Porous and Fractured Reservoirs

Author: Yu-Shu Wu

Publisher: Gulf Professional Publishing

Published: 2015-09-23

Total Pages: 418

ISBN-13: 0128039116

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Multiphase Fluid Flow in Porous and Fractured Reservoirs discusses the process of modeling fluid flow in petroleum and natural gas reservoirs, a practice that has become increasingly complex thanks to multiple fractures in horizontal drilling and the discovery of more unconventional reservoirs and resources. The book updates the reservoir engineer of today with the latest developments in reservoir simulation by combining a powerhouse of theory, analytical, and numerical methods to create stronger verification and validation modeling methods, ultimately improving recovery in stagnant and complex reservoirs. Going beyond the standard topics in past literature, coverage includes well treatment, Non-Newtonian fluids and rheological models, multiphase fluid coupled with geomechanics in reservoirs, and modeling applications for unconventional petroleum resources. The book equips today’s reservoir engineer and modeler with the most relevant tools and knowledge to establish and solidify stronger oil and gas recovery. Delivers updates on recent developments in reservoir simulation such as modeling approaches for multiphase flow simulation of fractured media and unconventional reservoirs Explains analytical solutions and approaches as well as applications to modeling verification for today’s reservoir problems, such as evaluating saturation and pressure profiles and recovery factors or displacement efficiency Utilize practical codes and programs featured from online companion website


Book Synopsis Multiphase Fluid Flow in Porous and Fractured Reservoirs by : Yu-Shu Wu

Download or read book Multiphase Fluid Flow in Porous and Fractured Reservoirs written by Yu-Shu Wu and published by Gulf Professional Publishing. This book was released on 2015-09-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiphase Fluid Flow in Porous and Fractured Reservoirs discusses the process of modeling fluid flow in petroleum and natural gas reservoirs, a practice that has become increasingly complex thanks to multiple fractures in horizontal drilling and the discovery of more unconventional reservoirs and resources. The book updates the reservoir engineer of today with the latest developments in reservoir simulation by combining a powerhouse of theory, analytical, and numerical methods to create stronger verification and validation modeling methods, ultimately improving recovery in stagnant and complex reservoirs. Going beyond the standard topics in past literature, coverage includes well treatment, Non-Newtonian fluids and rheological models, multiphase fluid coupled with geomechanics in reservoirs, and modeling applications for unconventional petroleum resources. The book equips today’s reservoir engineer and modeler with the most relevant tools and knowledge to establish and solidify stronger oil and gas recovery. Delivers updates on recent developments in reservoir simulation such as modeling approaches for multiphase flow simulation of fractured media and unconventional reservoirs Explains analytical solutions and approaches as well as applications to modeling verification for today’s reservoir problems, such as evaluating saturation and pressure profiles and recovery factors or displacement efficiency Utilize practical codes and programs featured from online companion website

Fluid Dynamics in Complex Fractured-Porous Systems

Fluid Dynamics in Complex Fractured-Porous Systems

Author: Boris Faybishenko

Publisher: John Wiley & Sons

Published: 2015-06-04

Total Pages: 264

ISBN-13: 1118877284

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Despite of many years of studies, predicting fluid flow, heat, and chemical transport in fractured-porous media remains a challenge for scientists and engineers worldwide. This monograph is the third in a series on the dynamics of fluids and transport in fractured rock published by the American Geophysical Union (Geophysical Monograph Series, Vol. 162, 2005; and Geophysical Monograph, No. 122, 2000). This monograph is dedicated to the late Dr. Paul Witherspoon for his seminal influence on the development of ideas and methodologies and the birth of contemporary fractured rock hydrogeology, including such fundamental and applied problems as environmental remediation; exploitation of oil, gas, and geothermal resources; disposal of spent nuclear fuel; and geotechnical engineering. This monograph addresses fundamental and applied scientific questions and is intended to assist scientists and practitioners bridge gaps in the current scientific knowledge in the areas of theoretical fluids dynamics, field measurements, and experiments for different practical applications. Readers of this book will include researchers, engineers, and professionals within academia, Federal agencies, and industry, as well as graduate/undergraduate students involved in theoretical, experimental, and numerical modeling studies of fluid dynamics and reactive chemical transport in the unsaturated and saturated zones, including studies pertaining to petroleum and geothermal reservoirs, environmental management and remediation, mining, gas storage, and radioactive waste isolation in underground repositories. Volume highlights include discussions of the following: Fundamentals of using a complex systems approach to describe flow and transport in fractured-porous media. Methods of Field Measurements and Experiments Collective behavior and emergent properties of complex fractured rock systems Connection to the surrounding environment Multi-disciplinary research for different applications


Book Synopsis Fluid Dynamics in Complex Fractured-Porous Systems by : Boris Faybishenko

Download or read book Fluid Dynamics in Complex Fractured-Porous Systems written by Boris Faybishenko and published by John Wiley & Sons. This book was released on 2015-06-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite of many years of studies, predicting fluid flow, heat, and chemical transport in fractured-porous media remains a challenge for scientists and engineers worldwide. This monograph is the third in a series on the dynamics of fluids and transport in fractured rock published by the American Geophysical Union (Geophysical Monograph Series, Vol. 162, 2005; and Geophysical Monograph, No. 122, 2000). This monograph is dedicated to the late Dr. Paul Witherspoon for his seminal influence on the development of ideas and methodologies and the birth of contemporary fractured rock hydrogeology, including such fundamental and applied problems as environmental remediation; exploitation of oil, gas, and geothermal resources; disposal of spent nuclear fuel; and geotechnical engineering. This monograph addresses fundamental and applied scientific questions and is intended to assist scientists and practitioners bridge gaps in the current scientific knowledge in the areas of theoretical fluids dynamics, field measurements, and experiments for different practical applications. Readers of this book will include researchers, engineers, and professionals within academia, Federal agencies, and industry, as well as graduate/undergraduate students involved in theoretical, experimental, and numerical modeling studies of fluid dynamics and reactive chemical transport in the unsaturated and saturated zones, including studies pertaining to petroleum and geothermal reservoirs, environmental management and remediation, mining, gas storage, and radioactive waste isolation in underground repositories. Volume highlights include discussions of the following: Fundamentals of using a complex systems approach to describe flow and transport in fractured-porous media. Methods of Field Measurements and Experiments Collective behavior and emergent properties of complex fractured rock systems Connection to the surrounding environment Multi-disciplinary research for different applications

Fluid Flow In Porous Media: Fundamentals And Applications

Fluid Flow In Porous Media: Fundamentals And Applications

Author: Liang Xue

Publisher: World Scientific

Published: 2020-09-24

Total Pages: 408

ISBN-13: 9811219540

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Processes of flow and displacement of multiphase fluids through porous media occur in many subsurface systems and have found wide applications in many scientific, technical, and engineering fields. This book focuses on the fundamental theory of fluid flow in porous media, covering fluid flow theory in classical and complex porous media, such as fractured porous media and physicochemical fluid flow theory. Key concepts are introduced concisely and derivations of equations are presented logically. Solutions of some practical problems are given so that the reader can understand how to apply these abstract equations to real world situations. The content has been extended to cover fluid flow in unconventional reservoirs. This book is suitable for senior undergraduate and graduate students as a textbook in petroleum engineering, hydrogeology, groundwater hydrology, soil sciences, and other related engineering fields.


Book Synopsis Fluid Flow In Porous Media: Fundamentals And Applications by : Liang Xue

Download or read book Fluid Flow In Porous Media: Fundamentals And Applications written by Liang Xue and published by World Scientific. This book was released on 2020-09-24 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processes of flow and displacement of multiphase fluids through porous media occur in many subsurface systems and have found wide applications in many scientific, technical, and engineering fields. This book focuses on the fundamental theory of fluid flow in porous media, covering fluid flow theory in classical and complex porous media, such as fractured porous media and physicochemical fluid flow theory. Key concepts are introduced concisely and derivations of equations are presented logically. Solutions of some practical problems are given so that the reader can understand how to apply these abstract equations to real world situations. The content has been extended to cover fluid flow in unconventional reservoirs. This book is suitable for senior undergraduate and graduate students as a textbook in petroleum engineering, hydrogeology, groundwater hydrology, soil sciences, and other related engineering fields.

Rock Fractures and Fluid Flow

Rock Fractures and Fluid Flow

Author: National Research Council

Publisher: National Academies Press

Published: 1996-08-27

Total Pages: 568

ISBN-13: 0309049962

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Scientific understanding of fluid flow in rock fracturesâ€"a process underlying contemporary earth science problems from the search for petroleum to the controversy over nuclear waste storageâ€"has grown significantly in the past 20 years. This volume presents a comprehensive report on the state of the field, with an interdisciplinary viewpoint, case studies of fracture sites, illustrations, conclusions, and research recommendations. The book addresses these questions: How can fractures that are significant hydraulic conductors be identified, located, and characterized? How do flow and transport occur in fracture systems? How can changes in fracture systems be predicted and controlled? Among other topics, the committee provides a geomechanical understanding of fracture formation, reviews methods for detecting subsurface fractures, and looks at the use of hydraulic and tracer tests to investigate fluid flow. The volume examines the state of conceptual and mathematical modeling, and it provides a useful framework for understanding the complexity of fracture changes that occur during fluid pumping and other engineering practices. With a practical and multidisciplinary outlook, this volume will be welcomed by geologists, petroleum geologists, geoengineers, geophysicists, hydrologists, researchers, educators and students in these fields, and public officials involved in geological projects.


Book Synopsis Rock Fractures and Fluid Flow by : National Research Council

Download or read book Rock Fractures and Fluid Flow written by National Research Council and published by National Academies Press. This book was released on 1996-08-27 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific understanding of fluid flow in rock fracturesâ€"a process underlying contemporary earth science problems from the search for petroleum to the controversy over nuclear waste storageâ€"has grown significantly in the past 20 years. This volume presents a comprehensive report on the state of the field, with an interdisciplinary viewpoint, case studies of fracture sites, illustrations, conclusions, and research recommendations. The book addresses these questions: How can fractures that are significant hydraulic conductors be identified, located, and characterized? How do flow and transport occur in fracture systems? How can changes in fracture systems be predicted and controlled? Among other topics, the committee provides a geomechanical understanding of fracture formation, reviews methods for detecting subsurface fractures, and looks at the use of hydraulic and tracer tests to investigate fluid flow. The volume examines the state of conceptual and mathematical modeling, and it provides a useful framework for understanding the complexity of fracture changes that occur during fluid pumping and other engineering practices. With a practical and multidisciplinary outlook, this volume will be welcomed by geologists, petroleum geologists, geoengineers, geophysicists, hydrologists, researchers, educators and students in these fields, and public officials involved in geological projects.

Fractured Porous Media

Fractured Porous Media

Author: Pierre M. Adler

Publisher: Oxford University Press

Published: 2013

Total Pages: 184

ISBN-13: 0199666512

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This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.


Book Synopsis Fractured Porous Media by : Pierre M. Adler

Download or read book Fractured Porous Media written by Pierre M. Adler and published by Oxford University Press. This book was released on 2013 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.

Fluid Flow in Fractured Porous Media

Fluid Flow in Fractured Porous Media

Author: Yujing Jiang

Publisher: MDPI

Published: 2019-09-30

Total Pages: 492

ISBN-13: 303921473X

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The fluid flow in fracture porous media plays a significant role in the assessment of deep underground reservoirs, such as through CO2 sequestration, enhanced oil recovery, and geothermal energy development. Many methods have been employed—from laboratory experimentation to theoretical analysis and numerical simulations—and allowed for many useful conclusions. This Special Issue aims to report on the current advances related to this topic. This collection of 58 papers represents a wide variety of topics, including on granite permeability investigation, grouting, coal mining, roadway, and concrete, to name but a few. We sincerely hope that the papers published in this Special Issue will be an invaluable resource for our readers.


Book Synopsis Fluid Flow in Fractured Porous Media by : Yujing Jiang

Download or read book Fluid Flow in Fractured Porous Media written by Yujing Jiang and published by MDPI. This book was released on 2019-09-30 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fluid flow in fracture porous media plays a significant role in the assessment of deep underground reservoirs, such as through CO2 sequestration, enhanced oil recovery, and geothermal energy development. Many methods have been employed—from laboratory experimentation to theoretical analysis and numerical simulations—and allowed for many useful conclusions. This Special Issue aims to report on the current advances related to this topic. This collection of 58 papers represents a wide variety of topics, including on granite permeability investigation, grouting, coal mining, roadway, and concrete, to name but a few. We sincerely hope that the papers published in this Special Issue will be an invaluable resource for our readers.

Fractured Vuggy Carbonate Reservoir Simulation

Fractured Vuggy Carbonate Reservoir Simulation

Author: Jun Yao

Publisher: Springer

Published: 2017-08-08

Total Pages: 245

ISBN-13: 3662550326

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This book solves the open problems in fluid flow modeling through the fractured vuggy carbonate reservoirs. Fractured vuggy carbonate reservoirs usually have complex pore structures, which contain not only matrix and fractures but also the vugs and cavities. Since the vugs and cavities are irregular in shape and vary in diameter from millimeters to meters, modeling fluid flow through fractured vuggy porous media is still a challenge. The existing modeling theory and methods are not suitable for such reservoir. It starts from the concept of discrete fracture and fracture-vug networks model, and then develops the corresponding mathematical models and numerical methods, including discrete fracture model, discrete fracture-vug model, hybrid model and multiscale models. Based on these discrete porous media models, some equivalent medium models and methods are also discussed. All the modeling and methods shared in this book offer the key recent solutions into this area.


Book Synopsis Fractured Vuggy Carbonate Reservoir Simulation by : Jun Yao

Download or read book Fractured Vuggy Carbonate Reservoir Simulation written by Jun Yao and published by Springer. This book was released on 2017-08-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book solves the open problems in fluid flow modeling through the fractured vuggy carbonate reservoirs. Fractured vuggy carbonate reservoirs usually have complex pore structures, which contain not only matrix and fractures but also the vugs and cavities. Since the vugs and cavities are irregular in shape and vary in diameter from millimeters to meters, modeling fluid flow through fractured vuggy porous media is still a challenge. The existing modeling theory and methods are not suitable for such reservoir. It starts from the concept of discrete fracture and fracture-vug networks model, and then develops the corresponding mathematical models and numerical methods, including discrete fracture model, discrete fracture-vug model, hybrid model and multiscale models. Based on these discrete porous media models, some equivalent medium models and methods are also discussed. All the modeling and methods shared in this book offer the key recent solutions into this area.

Modelling of Flow and Transport in Fractal Porous Media

Modelling of Flow and Transport in Fractal Porous Media

Author: Jianchao Cai

Publisher: Elsevier

Published: 2020-11-05

Total Pages: 274

ISBN-13: 0128177985

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This important resource explores recent theoretical advances and modelling on fluids transport in fractal porous systems and presents a systematic understanding of the characterization of complex microstructure and transport mechanism in fractal porous media. Modelling of Flow and Transport in Fractal Porous Media shows how fractal theory and technology, combined with other modern experiments and numerical simulation methods, will assist researchers and practitioners in modelling of transport properties of fractal porous media, such as fluid flow, heat and mass transfer, mechanical characteristics, and electrical conductivity. Presents the main methods and technologies for transport characterization of fractal porous media, including soils, reservoirs and artificial materials Provides the most recent theoretical advances in modelling of fractal porous media, including gas and vapor transport in fibrous materials, nonlinear seepage flow in hydrocarbon reservoirs, mass transfer of porous nanofibers, and fractal mechanics of unsaturated soils Includes multidisciplinary examples of applications of fractal theory to aid researchers and practitioners in characterizing various porous media structures


Book Synopsis Modelling of Flow and Transport in Fractal Porous Media by : Jianchao Cai

Download or read book Modelling of Flow and Transport in Fractal Porous Media written by Jianchao Cai and published by Elsevier. This book was released on 2020-11-05 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important resource explores recent theoretical advances and modelling on fluids transport in fractal porous systems and presents a systematic understanding of the characterization of complex microstructure and transport mechanism in fractal porous media. Modelling of Flow and Transport in Fractal Porous Media shows how fractal theory and technology, combined with other modern experiments and numerical simulation methods, will assist researchers and practitioners in modelling of transport properties of fractal porous media, such as fluid flow, heat and mass transfer, mechanical characteristics, and electrical conductivity. Presents the main methods and technologies for transport characterization of fractal porous media, including soils, reservoirs and artificial materials Provides the most recent theoretical advances in modelling of fractal porous media, including gas and vapor transport in fibrous materials, nonlinear seepage flow in hydrocarbon reservoirs, mass transfer of porous nanofibers, and fractal mechanics of unsaturated soils Includes multidisciplinary examples of applications of fractal theory to aid researchers and practitioners in characterizing various porous media structures

Numerical Modelling and Analysis of Fluid Flow and Deformation of Fractured Rock Masses

Numerical Modelling and Analysis of Fluid Flow and Deformation of Fractured Rock Masses

Author: Xing Zhang

Publisher: Elsevier

Published: 2002-05-14

Total Pages: 300

ISBN-13: 9780080537863

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Our understanding of the subsurface system of the earth is becoming increasingly more sophisticated both at the level of the behaviour of its components (solid, liquid and gas) as well as their variations in space and time. The implementation of coupled models is essential for the understanding of an increasing number of natural phenomena and in predicting human impact on these. The growing interest in the relation between fluid flow and deformation in subsurface rock systems that characterise the upper crust has led to increasingly specialized knowledge in many branches of earth sciences and engineering. A multidisciplinary subject dealing with deformation and fluid flow in the subsurface system is emerging. While research in the subject area of faulting, fracturing and fluid flow has led to significant progress in many different areas, the approach has tended to be "reductionist", i.e. involving the isolation and simplification of phenomena so that they may be treated as single physical processes. The reality is that many processes operate together within subsurface systems, and this is particularly true for fluid flow and deformation of fractured rock masses. The aim of this book is to begin to explore how advances in numerical modelling can be applied to understanding the complex phenomena observed in such systems. Although mainly based on original research, the book also includes the fundamental principles and practical methods of numerical modelling, in particular distinct element methods. This volume explores the principles of numerical modelling and the methodologies for some of the most important problems, in addition to providing practical models with detailed discussions on various topics.


Book Synopsis Numerical Modelling and Analysis of Fluid Flow and Deformation of Fractured Rock Masses by : Xing Zhang

Download or read book Numerical Modelling and Analysis of Fluid Flow and Deformation of Fractured Rock Masses written by Xing Zhang and published by Elsevier. This book was released on 2002-05-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the subsurface system of the earth is becoming increasingly more sophisticated both at the level of the behaviour of its components (solid, liquid and gas) as well as their variations in space and time. The implementation of coupled models is essential for the understanding of an increasing number of natural phenomena and in predicting human impact on these. The growing interest in the relation between fluid flow and deformation in subsurface rock systems that characterise the upper crust has led to increasingly specialized knowledge in many branches of earth sciences and engineering. A multidisciplinary subject dealing with deformation and fluid flow in the subsurface system is emerging. While research in the subject area of faulting, fracturing and fluid flow has led to significant progress in many different areas, the approach has tended to be "reductionist", i.e. involving the isolation and simplification of phenomena so that they may be treated as single physical processes. The reality is that many processes operate together within subsurface systems, and this is particularly true for fluid flow and deformation of fractured rock masses. The aim of this book is to begin to explore how advances in numerical modelling can be applied to understanding the complex phenomena observed in such systems. Although mainly based on original research, the book also includes the fundamental principles and practical methods of numerical modelling, in particular distinct element methods. This volume explores the principles of numerical modelling and the methodologies for some of the most important problems, in addition to providing practical models with detailed discussions on various topics.