A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks

We present a methodology that characterizes through the topology of a network the capability of flow conductivity in fractures associated to a reservoir under study. This strategy considers the fracture image as a graph, and is focused on two key aspects. The first is to identify communities or sets of nodes that are more conductive, and the second one is to find nodes that form the largest paths and have therefore more possibility of serving as flow channels. The methodology is divided into two stages, the first stage obtains the cross points from fracture networks. The second stage deepens on the community identification. This second stage carries out the process of identifying conductive nodes by using centrality measures (betweenness, eccentricity and closeness) for evaluating each node in the network. Then an optimization modularity method is applied in order to form communities using two different types of weights between cross points or nodes. Finally, each community is associated with the average value of each measure. In this way the maximum values in betweenness and eccentricity are selected for identifying communities with the most important nodes in the network. The results obtained allow us to show regions in the fracture network that are more conductive according to the topology. In addition, this general methodology can be applied to other fracture characteristics.