By Muhammad Sahimi
During this usual reference of the sector, theoretical and experimental ways to move, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are thought of. various techniques are mentioned and contrasted with one another. the 1st process relies at the classical equations of circulation and delivery, referred to as 'continuum models'. the second one procedure relies on smooth tools of statistical physics of disordered media; that's, on 'discrete models', that have develop into more and more renowned over the last 15 years. The ebook is exclusive in its scope, seeing that (1) there's at present no publication that compares the 2 techniques, and covers all vital elements of porous media difficulties; and (2) contains dialogue of fractured rocks, which to date has been handled as a separate subject.
parts of the e-book will be compatible for a sophisticated undergraduate path. The booklet 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 care for a variety of porous media difficulties.
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During this general reference of the sphere, theoretical and experimental ways to stream, 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 process relies at the classical equations of movement and delivery, known as 'continuum models'.
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Extra resources for Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches
Sample text
At points on the edges and at corner points, all spheres must be considered that would be tangent, were the edge or corner infinitesimally rounded. The loci of the centers of two-point-of-contact-spheres define continuous strips that are edged and ended by curves defined by the centers of three-point-of-contactspheres. Such strips run throughout in the void space and share its connectivity and, therefore, its topology. Moreover, a stripwork (that is, a network of strips) can be reduced to a set of curves by shrinking it along the geodesic normal to its boundaries.
The derivation of the exact values of p cb and p cs is an extremely difficult problem. 1) where Z is the coordination number of the network, that is, the number of bonds connected to the same site, and for many two-dimensional (2D) networks. 1. 1 Percolation thresholds and Bc D Z p cb for some common 2D and 3D networks. 199 BCC FCC a Exact result. org/wiki/Percolation_threshold (accessed 23 March 2010). 21 22 3 Characterization of Pore Space Connectivity: Percolation Theory depending only on the dimensionality d of the network, with Bc ' d d 1 .
The exponents µ p and e are mostly universal. 2, the most accurate estimates of the critical exponents in 2D and 3D are compiled. 2 The critical exponents (and fractal dimensions) of percolation. 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.