Page 138 - Percolation Models for Transport in Porous Media With

132 CHAPTER 7. PARAMETERS OF FRACTURED ROCKS

Figure 50: Refers to the determination of the number of fracture traces that fell
completely inside the lateral surface of the core

these quantities, one can find the volumetric concentration and the average length
of the disk fractures. Finally, upon determining the concentration and the average
length of the disk fractures, one can estimate the coefficient of permeability of a
fractured medium, for example, for the model presented in the study [79].

7.2 Determination of Fracture Length Distribu-

tion from Fracture Traces on the Core

Length distribution of fractures is one of the important characteristic properties
of a fractured medium. Knowledge of this distribution is necessary both for the
calculation of conducting properties of the medium and for the description of its
destruction under the impulse loads (80].
In this section, a technique for processing the results obtained from the in-
vestigation of fracture traces on the core is proposed, which permits to obtain
information about the length distribution for the model of a medium with disk
fractures.
Assume that the medium contains disk fractures with arbitrarily distributed
centers. Fractures leave traces - line segments of length 2d 8 - on some cross-
section; distribution of these segments is determined by the function nd(d 8 , 9).
In this case nd(ds, 9)~ds~9 is the number of the centers of those fracture traces
on a unit area, whose half-lengths lie in the interval d 8 + d 8 + ~ds and which
are oriented at an angle from the interval 9 + 9 + ~9. Suppose that a circle of
radius R' corresponds to the surface of the core. Some of the fracture traces
with length 2da fall within this circle, with some traces lying completely inside
the circle and others intersecting with the boundary of the core. The length and
location of a fracture center is impossible to determine from the fracture trace