Complexity of fluid flow in a rough fracture is induced by the complex configurations of opening areas between the fracture planes. In this study, we model fluid flow in an evolvable real rock joint structure, which under certain normal load is sheared. In an experimental study, information regarding about apertures of the rock joint during consecutive 20 mm displacements and fluid flow (permeability) in different pressure heads have been recorded by a scanner laser. Our aim in this study is to simulate the fluid flow in the mentioned complex geometries using the lattice Boltzmann method (LBM), while the characteristics of the aperture field will be compared with the modeled fluid flow permeability To characterize the aperture, we use a new concept in the graph theory, namely: complex networks and motif analysis of the corresponding networks. In this approach, the similar aperture profile along the fluid flow direction is mapped in to a network space. The modeled permeability using the LBM shows good correlation with the experimental measured values. Furthermore, the two main characters of the obtained networks, i.e., characteristic length and number of edges show the same evolutionary trend with the modeled permeability values. Analysis of motifs through the obtained networks showed the most transient sub-graphs are much more frequent in residual stages. This coincides with nearly stable fluid flow and high permeability values.
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