By Muhammad Sahimi

During this typical reference of the sector, theoretical and experimental ways to circulate, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are thought of. diversified methods are mentioned and contrasted with one another. the 1st strategy relies at the classical equations of circulate and shipping, known as 'continuum models'. the second one strategy is predicated on smooth equipment of statistical physics of disordered media; that's, on 'discrete models', that have turn into more and more well known during the last 15 years. The ebook is exclusive in its scope, on account that (1) there's at present no e-book that compares the 2 methods, and covers all very important elements of porous media difficulties; and (2) comprises dialogue of fractured rocks, which to this point has been handled as a separate subject.Portions of the booklet will be appropriate for a sophisticated undergraduate path. The e-book might be perfect 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**

14) which is used heavily throughout this book. 3 The Diffusion and Convective-Diffusion Equations We consider a binary mixture of two miscible ﬂuids, one of which is the solvent, while the other one is the solute. Suppose that the concentration of the solute is C, and that the molecular diffusivity of the solute in the solvent is Dm . 15) where RA is the molar rate of reaction (if there is any) per unit volume, and J the total ﬂux of the solute, given by J D Cv Dm r C . 16) Therefore, the equation of continuity for the solute is given by @C C r (C v) D r (Dm r C ) C RA .

Even if the medium is not structurally anisotropic, the overall behavior of the transport of the solute in the solvent may be characterized by an effective diffusivity tensor. Dispersion phenomena that are studied in Chapters 11 and 12, and are also important to miscible displacements that are studied in Chapter 13, provide an example of a system in which there is a ﬂow-induced dynamical anisotropy and, thus, one needs more than one effective diffusivity to characterize the phenomena. 4 Fluid Flow in Porous Media The conservation equations must be supplemented by additional correlations by which one can calculate physical properties of the ﬂuids, for example, their viscosities, densities and diffusivities.

20) and in spherical coordinates one has 1 @ r D 2 r @r 2 Â @ r @r Ã 2 1 @ C 2 r sin θ @θ Â @ sin θ @θ Ã C 1 @2 . 21) If RA D 0 and the ﬂuids are stagnant, then we obtain the well-known diffusion equation @C D r (Dm r C ) . 22) More generally, instead of a single-valued diffusivity, one may have an effective diffusivity tensor. For example, if a porous medium is anisotropic, then each principal direction of the system is characterized by a distinct diffusivity. Even if the medium is not structurally anisotropic, the overall behavior of the transport of the solute in the solvent may be characterized by an effective diffusivity tensor.