As the aperture distribution becomes narrower, flow does not concentrate in a small portion of fractures: Most fractures play a roughly similar role in the flow, which means fewer fractures can be removed without significantly reducing the equivalent network permeability.
We compare the effective permeability of the sub-network with a portion of fractures eliminated from the original fracture network using these criteria.
Countless criteria can be used to decide which portion of fractures to remove, such as fracture length, aperture, [length × aperture], velocity, etc.
Figures 19 and 20 show the sub-network equivalent permeability after elimination of a portion of fractures, where the aperture is, respectively, proportional to and independent of the fracture length.
Thus, removing a portion of fractures which carry little flow does not greatly reduce the equivalent network permeability, as the fractures that play a more important role are still in the system.
As a result, when a portion of fractures is eliminated, the equivalent network permeability is strongly affected.
The results show that for all of the cases, a portion of fractures can be eliminated without significantly affecting the overall network permeability.
For all of the cases with a power-law aperture distribution, at least a portion of fractures can be eliminated without significantly affecting the effective network permeability.
As the aperture distribution becomes broader, the distribution of Q is also broader, and there is a small portion of fractures which carry much more flow than the others.
In this work, we define "the dominant sub-network" as the sub-network obtained by eliminating a portion of fractures while retaining 90% of the original network equivalent permeability.
