By Pierre M Adler; Jean-François Thovert; Valeri V Mourzenko
This booklet presents a scientific remedy of the geometrical and shipping houses of fractures, fracture networks, and fractured porous media.
It is split into significant elements. the 1st half bargains with geometry of person fractures and of fracture networks. using the dimensionless density rationalizes the implications for the percolation threshold of the networks. It offers the an important benefit of grouping the numerical information for numerous fracture shapes.
The moment half bargains as a rule with permeability less than regular stipulations of fractures, fracture networks, and fractured porous media. back the implications for varied kinds of networks might be rationalized by way of the dimensionless density. A bankruptcy is devoted to 2 section circulate in fractured porous media
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This ebook presents a scientific therapy of the geometrical and delivery homes of fractures, fracture networks, and fractured porous media. it truly is divided into significant components. the 1st half bargains with geometry of person fractures and of fracture networks. using the dimensionless density rationalizes the implications for the percolation threshold of the networks.
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This series of operations is repeated for a suﬃciently large number N of independent networks. Among these N networks, Np percolate. 7a) N Fig. 14 The connected and percolating components in a two-dimensional fracture network; the square is the unit cell of a 2D spatially periodic medium. The fractures are the random segments denoted as vi . The network consists of two connected components; 1 percolates through the cell, and 2 does not. Periodic conditions are used for component 1; v1 straddles the unit cell wall; it is connected to v3 in the left part of the unit cell and to v9 in the right.
Another question is the determination of the number of solid blocks which are cut in the matrix by the network. Of course, when the fracture density ρ is small, fractures are isolated and there is only one inﬁnite block which is the medium itself. When ρ increases, blocks are likely to become more and more numerous. The industrial requirements of these blocks depend on the application. In order to store nuclear waste in granite repositories, for example, blocks should be as large as possible. However, in an oil ﬁeld, the oil is mostly in the porous medium from which it ﬂows to the fractures and hopefully to the wells; in this case, the blocks should be as small as possible.
The intersections of all the fractures are determined and an intersection table can be ﬁlled. Then, the connected components of the fracture network are determined by a pseudo-diﬀusion algorithm which works as follows. Let us start with fracture 1; label it as fracture 1; look at the intersection table and give label 2 to all the fractures which intersect fracture 1; look at the intersection table of fractures with label 2 and give label 3 to all the fractures which intersect them; repeat this process until no new fracture is obtained.