Page 142 - Percolation Models for Transport in Porous Media With

136 CHAPTER 7. PARAMETERS OF FRACTURED ROCKS

then the integral in (7.16} can be easily evaluated. The length distribution of
fractures in this case has the following form

where Ki(-) is Macdonald's function.

7.3 Determination of Fracture Parameters from
the Core

The techniques for the determination of the fracture parameters for different media
were tried on cores of a fractured rock extracted from Well 96 of the condensed gas
deposit in Orenburg. Cores were taken from the productive layer of the deposi-
tions constructed from organogenic and organogenic-fragmental limestones of the
Artine, Sakmarian, and Assel stages of the lower Permian. An interval of dense
limestones with low porosities (0.7-3.3%} and minor permeabilities (0.001·10- 15 -
0.8·10- 15 m 2 }, opened at a depth of 1379-1436.2 m, were chosen for investigations.
These are fractured reservoir rocks.
In the studied interval of 57 m thickness, 10 specimen of the core were chosen.
The specimen were "cubes" of dimensions 5 x 5 x 5.
The method described in [81] was used to detect traces on the lateral faces
of each cube. According to this technique, capillary saturation of the rocks with
a luminescent solid was carried out, after which they were photographed in the
ultra-violet to detect open fractures on the pictures of the faces. On each of the
pictures, a pattern with concentric circles R~ = 0.5; 1.5; 2.5 em was put and the
number of traces inside each of the circles was calculated. After averaging over
60 faces of the studied specimen, the quantities v:, average values of the number
of the fracture traces inside each circle of radius R~, were found. The constructed
histogram vHRi) (fig. 51} was processed according to the technique developed
based on the results obtained in §7.1. The equation (7.2} is rewritten in the form

(7.17}

By introducing the notations Y = nd'\ X= ds, ai = 4RUv;, bi = 1rR'~Jv:, the
system (7.17} can be represented in the form

(7.18}

Formally, this system must be solved by breaking it up in pairs of equations
and further averaging of the obtained results. In the averaging of the solutions
of the paired systems, their statistical weights determined by the radius R~ must