Abstract. It is well known that fracture networks display self-similarity in
many cases and the connectivity and flow behavior of such networks are
influenced by their respective fractal dimensions. In the past, the concept
of lacunarity, a parameter that quantifies spatial clustering, has been
implemented by one of the authors in order to demonstrate that a set of
seven nested natural fracture maps belonging to a single fractal system, but
of different visual appearances, have different clustering attributes. Any
scale-dependency in the clustering of fractures will also likely have
significant implications for flow processes that depend on fracture
connectivity. It is therefore important to address the question as to
whether the fractal dimension alone serves as a reasonable proxy for the
connectivity of a fractal-fracture network and hence, its flow response or,
if it is the lacunarity, a measure of scale-dependent clustering, that may
be used instead. The present study attempts to address this issue by
exploring possible relationships between the fractal dimension, lacunarity
and connectivity of fractal-fracture networks. It also endeavors to study
the relationship between lacunarity and fluid flow in such fractal-fracture
networks. A set of deterministic fractal-fracture models generated at
different iterations and, that have the same theoretical fractal dimension
are used for this purpose. The results indicate that such deterministic
synthetic fractal-fracture networks with the same theoretical fractal
dimension have differences in their connectivity and that the latter is
fairly correlated with lacunarity. Additionally, the flow simulation results
imply that lacunarity influences flow patterns in fracture networks.
Therefore, it may be concluded that at least in synthetic fractal-fracture
networks, rather than fractal dimension, it is the lacunarity or
scale-dependent clustering attribute that controls the connectivity and
hence the flow behavior.
Impact of scaling break and fracture orientation on effective permeability of fractal fracture network
