By V.I. Selyakov
It is an honour and enjoyment to write down a foreword to this beneficial and fascinating e-book. Authors are rather well identified researchers who pioneered percolation modelling of delivery in porous media in Russia from the early 80-th until these days. the most scope of the paintings offered within the booklet used to be built while shiny papers by way of 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 weren't on hand on the "other" aspect of the Iron Curtain. these days countless numbers of works and papers with the "percolation" key phrases ap pear in petroleum and similar utilized learn components. The publication will take a re markable position within the "petroleum percolation" bibliography. There are vital positive factors of novelty within the monograph offered. to begin with the authors constructed a generalization of percolation clusters concept for grids with various conductivity. means of illustration of an unlimited cluster as an hierarchial set of timber (so known as r-chain version) permits to provide conductivity of a stochastic grid in a closed type of particular formulae. this technique differs from these identified within the West, similar to powerful media idea, ideas for the Bethe-lattice, and so forth. It has his personal quarter of winning appli cations.
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Additional info for Percolation Models for Transport in Porous Media: With Applications to Reservoir Engineering
41). al)/C)}. 41) define the values of the corresponding components of the permeability tensor. Similar relationships take place for the specific electric conductivity of the medium. The relationships presented allow to calculate the change of the coefficients of permeability in the medium given the distribution function of pore channels with respect to values of intrinsic conductivities. The problem of determining /(r) will be studied in detail in further sections of this book. 43) CHAPTER2. 0 Figure 11: Plots of the conductivity of the medium against its strained state where a* is the minimal radius of a conducting capillary.
108 Pais presented in fig. 11 (curve 1). KfK and SE/'E against pressure, measured experimentally for a sandstone core in  (curves 3 and 4). are also presented in this figure. ' fu' = 7 · 10-6 m, II = 0, other parameters the same. 11) for the case of anisotropic loading of a grained medium under constant pressure p = 200 · 105 Pa. 11 that a satisfactory agreement between theoretical and experimental data takes place for the given set of parameters of the model of a nonlinearly elastic porous medium.
16), v was set to equal!. 4 CONDUCTIVITY OF A FRACTURED MEDIUM Figure 9: tures 31 For determining the average number of intersections for circular frac- Consider a set of randomly distributed circular fractures in an infinite medium. Assume that the fractures are oriented isotropically and all have the same radius Tt and opening b. Assume also that the centers of the fractures are sites, and intersections of any two fractures form a bond between the sites. In this case the probability of bonds having a non-zero conductivity is determined from the ratio of two quantities, namely the number of intersections an arbitrary fracture has with other fractures and the number of its nearest neighbors (sites).