By Muhammad Sahimi
During this commonplace reference of the sphere, theoretical and experimental methods to circulation, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are thought of. varied techniques are mentioned and contrasted with one another. the 1st procedure relies at the classical equations of circulate and shipping, referred to as 'continuum models'. the second one procedure is predicated on sleek equipment of statistical physics of disordered media; that's, on 'discrete models', that have develop into more and more well known during the last 15 years. The publication is exclusive in its scope, seeing that (1) there's at present no booklet that compares the 2 methods, and covers all vital features of porous media difficulties; and (2) contains dialogue of fractured rocks, which thus far has been taken care of as a separate subject.
parts of the ebook will be appropriate for a complicated undergraduate path. The e-book may be excellent for graduate classes at the topic, and will be utilized by chemical, petroleum, civil, environmental engineers, and geologists, in addition to physicists, utilized physicist and allied scientists that take care of numerous porous media difficulties.
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Additional info for Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches
The connectivity exponents and the fractal dimension Df for 2D systems as well as all the quantities for Bethe lattices are exact. 7 The Signiﬁcance of Power Laws If two physical phenomena in disordered media, and in particular porous media, that contain percolation-type disorder (those in which the connectivity of the media’s microscopic elements is important to their macroscopic properties) are described by two distinct sets of critical exponents, then the physical laws governing the two phenomena must be fundamentally different.
In their original paper, Broadbent and Hammersley focused on two problems: 1. Bond percolation in which the bonds of a network are either occupied or open (to passage of a ﬂuid) randomly and independently of each other with probability p, or they are vacant or closed (to passage of a ﬂuid) with probability 1 p . For a large network, the probability p is equivalent to a random fraction p of all the bonds being open or intact. 3 shows a square network in which a fraction p of the bonds are intact or open.
20) to estimate ζ and, thus, δ D ζ ν. 10 Random Networks and Continuum Models Although percolation in regular networks – those in which the coordination number Z is the same everywhere – has been extensively invoked for studying ﬂow and transport in disordered porous media, percolation in continua and in topologicallyrandom networks – those in which the coordination number varies from site to site – are of great interest since, in almost any practical situation, one must work with such irregular and continuous systems.