Geometrical Characterization of Blocks in Fractured Media

When fractures are sufficiently dense, they partition fractured media into blocks. The determination of the statistical properties of these blocks is important for the oil industry, for instance; the oil which is initially located in the porous medium may flow into the fractures and this transfer is controlled by the block geometry. Our first purpose is to determine the geometrical properties of these blocks; little is known about them except for infinite fractures.

Fractures of various shapes and of various densities are generated isotropically with random positions. The blocks are determined after the fractures are triangulated. Therefore, each solid block is limited by several triangulated plane faces. Then, the neighbors of a given triangle are identified. When this is done for all the triangles, the independent connected components of the triangles are identified by a pseudo-diffusion algorithm. Each independent component corresponds to a block. The block density corresponds to the number of blocks per unit volume.

Then, the volume, the surface and the number of faces are calculated for each block. The dimensionless density rho’ which is equal to the average number of intersections of a fracture with other fractures, varies between 1 to 150, for three shapes, namely squares, rectangles with an aspect ratio of 4 and 20-gons which are very close to disks.

Some of the results can be summarized as follows. The block density is proportional to rho’**4, independently of the fracture shape. The fraction of volume occupied by blocks follows a power law as well until it gets close to 1.

Unexpectedly, the mean block volume and the mean surface area of the blocks start increasing with rho’ and decrease for large rho’ where they follow the predictions for infinite fractures. The average number of faces of a block increases until it reaches 6 as predicted for infinite fractures.

Dimensionless relations which are convenient to apply, summarize the numerical findings.