Flow and Transport in Porous Media and Fractured Rock by Muhammad Sahimi

By Muhammad Sahimi

During this common reference of the sphere, theoretical and experimental techniques to circulation, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are thought of. varied ways are mentioned and contrasted with one another. the 1st technique is predicated at the classical equations of stream and shipping, referred to as 'continuum models'. the second one process relies on sleek equipment of statistical physics of disordered media; that's, on 'discrete models', that have develop into more and more renowned during the last 15 years. The e-book is exclusive in its scope, for the reason that (1) there's at the moment no ebook that compares the 2 ways, and covers all very important facets of porous media difficulties; and (2) comprises dialogue of fractured rocks, which up to now has been taken care of as a separate subject.Portions of the ebook will be appropriate for a sophisticated undergraduate direction. The publication could 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 a number of porous media difficulties.

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Example text

Clearly, then, no 1D material can be bicontinuous, as its 2, any (bond or site) percolation threshold p c is one. For spatial dimensions d system possessing phase-inversion symmetry is bicontinuous for p c < p < 1 p c (where p c is either the site or bond percolation threshold), provided that p c < 1/2. 1 can be bicontinuous in either bond or site percolation. For 3D networks, however, neither p c < 1/2 nor phase-inversion symmetry is a necessary condition for the bicontinuity. Two-dimensional porous media are much more difficult to be made bicontinuous.

The conditions under which µ p ¤ e will be described below. The power law that characterizes the behavior of the effective diffusivity De (p ) near p c is derived from that of g e (p ). According to Einstein’s relation, g e / De , where is the density of the carriers. Although a diffusing species (carrier) can move on all the clusters, above p c , only diffusion on the sample-spanning cluster contributes significantly to De so that / X A (p ). Hence, g e (p ) / X A (p )De(p ) and, therefore, De (p ) (p p c)µp β .

Holes” formed by the closed bonds. Thus, there must be a well-defined value of p, which we denote by p cb , at which a transition occurs in the macroscopic connectivity of the network: For p cb , there is no sample-spanning cluster of open bonds that connects two opposing faces of the network, while for p cb C , such a cluster exists, where ! 0. p cb is called the bond percolation threshold of the network. Physically, p cb is the largest fraction of the open bonds below ) there is no sample-spanning cluster of such bonds.

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