Why would we wish to start a 2nd edition of “Percolation theory for ?ow in porous media” only two years after the ?rst one was ?nished? There are essentially three reasons: 1) Reviews in the soil physics community have pointed out that the introductory material on percolation theory could have been more accessible. Our additional experience in teaching this material led us to believe that we could improve this aspect of the book. In the context of rewriting the ?rst chapter, however, we also expanded the discussion of Bethe lattices and their relevance for “classical” - ponents of percolation theory, thus giving more of a basis for the discussion of the relevance of hyperscaling. This addition, though it will not tend to make the book more accessible to hydrologists, was useful in making it a more complete reference, and these sections have been marked as being possible to omit in a ?rst reading. It also forced a division of the ?rst chapter into two. We hope that physicists without a background in percolation theory will now also ?nd the - troductory material somewhat more satisfactory. 2) We have done considerable further work on problems of electrical conductivity, thermal conductivity, and electromechanical coupling.

This book discusses various aspects of percolation mechanics. It starts with the driving forces and driving modes and then examines in detail the steady state percolation of single-phase incompressible fluids, percolation law of natural gas and percolation of non-Newtonian fluids. Progressing from simple to complex concepts, it also analyzes Darcy’s law, providing a basis for the study of reservoir engineering, oil recovery engineering and reservoir numerical simulation. It serves as a textbook for undergraduate students majoring in petroleum engineering, petroleum geology and groundwater engineering, and offers a valuable reference guide for graduate students, researchers and technical engineers engaged in oil and gas exploration and development.

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

A comprehensive, stepwise introduction to the basic terminology, methods and theory of the physics of flow in porous media.

In this standard reference of the field, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are considered. Two different approaches are discussed and contrasted with each other. The first approach is based on the classical equations of flow and transport, called 'continuum models'. The second approach is based on modern methods of statistical physics of disordered media; that is, on 'discrete models', which have become increasingly popular over the past 15 years. The book is unique in its scope, since (1) there is currently no book that compares the two approaches, and covers all important aspects of porous media problems; and (2) includes discussion of fractured rocks, which so far has been treated as a separate subject. Portions of the book would be suitable for an advanced undergraduate course. The book will be ideal for graduate courses on the subject, and can be used by chemical, petroleum, civil, environmental engineers, and geologists, as well as physicists, applied physicist and allied scientists that deal with various porous media problems.

The present 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 treatment 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 introduces physicists to some of the language and complications of groundwater hydrology necessary for succesful modelling.

It is an honour and pleasure to write a foreword to this useful and interesting book. Authors are very well known researchers who pioneered percolation modelling of transport in porous media in Russia from the early 80-th till nowadays. The main scope of the work presented in the book was developed when bright papers by A. Aharony, H.T. Davis, F.A.L. Dullien, A.A. Heiba, R.G. Larson, R. Lenormand, M.Sahimi, L.E. Scriven, D. Stauffer, M. Yanuka, Y.C.Yortsos were not available at the "other" side of the Iron Curtain. Nowadays hundreds of works and papers with the "percolation" keywords ap pear in petroleum and related applied research areas. The book will take a re markable place in the "petroleum percolation" bibliography. There are two important features of novelty in the monograph presented. First of all the authors developed a generalization of percolation clusters theory for grids with varying conductivity. Technique of representation of an infinite cluster as an hierarchial set of trees (so called r-chain model) allows to present conductivity of a stochastic grid in a closed form of explicit formulae. This method differs from those known in the West, such as effective media theory, solutions for the Bethe-lattice, etc. It has his own area of successful appli cations.

Over the past two decades percolation theory has been used to explain and model a wide variety of phenomena that are of industrial and scientific importance. Examples include characterization of porous materials and reservoir rocks, fracture patterns and earthquakes in rocks, calculation of effective transport properties of porous media permeability, conductivity, diffusivity, etc., groundwater flow, polymerization and gelation, biological evolution, galactic formation in the universe, spread of knowledge, and many others. Most of such applications have resulted in qualitative as well as quantitative predictions for the system of interest. This book attempts to describe in simple terms some of these applications, outline the results obtained so far, and provide further references for future reading.

This book aims to develop the ideas from fundamentals of percolation theory to practical reservoir engineering applications. Through a focus on field scale applications of percolation concepts to reservoir engineering problems, it offers an approximation method to determine many important reservoir parameters, such as effective permeability and reservoir connectivity and the physical analysis of some reservoir engineering properties. Starring with the concept of percolation theory, it then develops into methods to simple geological systems like sand-bodies and fractures. The accuracy and efficiency of the percolation concept for these is explained and further extended to more complex realistic models.Percolation Theory in Reservoir Engineering primarily focuses on larger reservoir scale flow and demonstrates methods that can be used to estimate large scale properties and their uncertainty, crucial for major development and investment decisions in hydrocarbon recovery.

The first edition of this book was published in 1994. Since then considerable progress has been made in both theoretical developments of percolation theory, and in its applications. The 2nd edition of this book is a response to such developments. Not only have all of the chapters of the 1st edition been completely rewritten, reorganized, and updated all the way to 2022, but also 8 new chapters have been added that describe extensive new applications, including biological materials, networks and graphs, directed percolation, earthquakes, geochemical processes, and large-scale real world problems, from spread of technology to ad-hoc mobile networks.