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

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Abstract

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.

Introduction

Many real world problems such as biological, social, metabolic, food, neural networks and pathological networks among others can be modeled and studied as complex networks (Kolaczyk, 2009, Cohen and Havlin, 2010, Estada, 2011). They are mathematically represented and topologically studied to uncover some structural properties. In the petroleum industry one issue of importance is the study and analysis of fluid flow in fractured rocks. In this paper we present a methodology for the characterization, through the topology of a network, of the capability of flow conductivity in fractures associated to a reservoir under study. Our methodology extracts from a fracture image a graph focusing on two key aspects. The first is to identify regions of fractures that are more conductive, and the second one is to find nodes that belong to the largest paths that have more possibility of serving as flow channels. This paper deals with real fracture networks derived from original hand-sample images. These images of rocks correspond to a Gulf of Mexico oil reservoir, and are used as test examples for identifying properties related to the fluid flow from a topological perspective. This methodology assumes that the fractures in the image have all being identified as conductive. Then it determines qualitatively different conductive regions in the fracture network through the analysis of the cross points of the fractures, and quantifies the connectivity among these cross points and their topological function within the network. This methodology consists of: (i) the application of centrality measures that involves the estimation of shortest paths, and (ii) the identification of node sets by means of community detection. The communities are subunits associated with the more highly interconnected parts used for determining the global organization in the network (Lancichinetti, Kivelä, Saramäki, Fortunato, 2010). Many methods have been developed for the identification of communities (Clauset et al., 2004, Girvan and Newman, 2002, Newman, 2004, Porter et al., 2009, Radicchi et al., 2004). We apply an efficient method reported in the literature (Condon and Karp, 2001, Lancichinetti and Fortunato, 2009) for grouping sets of nodes based on a modularity function. In addition, for the construction of these communities a formulation for computing the weights among cross points is proposed. This approach will help in analyzing different study regions and to characterize the fracture networks by means of the topological properties obtained, and hence it can identify conductive regions. Also these results can be used in combination with other geophysical or petrophysical properties from the fracture network.

The paper is organized as follows. In Section 2, previous work and basic concepts are described; in particular the centrality measures and a method for determining communities or regions are discussed. In Section 3, our general scheme is explained. In this part the association between the centrality measures and the identification of communities are described. In Section 4, we show our results, applying the methodology to fracture hand-sample images. Finally, in Section 5, we give our conclusions.

Section snippets

Previous works and theoretical framework

In the characterization of naturally fractured reservoirs (NFR) one of the main challenges in the hydrocarbon industry is the generation of a representative model for it (Aguilera, 1995, Baker, 2000, Narr et al., 2006, Nelson, 2001, Nikravesh, 2004). This characterization requires putting together different data sources about the whole reservoir (Bogatkov and Babadagli, 2007, Gauthier et al., 2002, Guerreiro et al., 2000). One of the important problems is the determination of the nature, and

Identification of conductive regions

The process of characterizing regions leads to analyze the capability to conduct fluid in the fracture network; here it is described in three steps represented in the second dashed box in Fig. 1. The first box includes the image processing of fractures, whose detailed description is presented in Santiago et al. (2012). In this paper, we describe the details of the second box.

Results

Other fracture network belonging to the same Cantarell reservoir is shown in Fig. 8. Note here the presence of many small components, even isolated fracture segments. The so-called component determination, gives us an indicator of the disconnectedness in the fracture network. The application of centrality measures helps to identify the location of the largest component. This fracture image has 234 cross points, 17 components, and 35 communities (weighting by distances). Results of the

Conclusions

In this work, a general methodology for the analysis of conductivity of fluid flow in fracture networks is presented using a complex network approach. The input data are networks generated from real images of fractured rocks where we assume that all fractures are conductive. More detailed geological analysis is necessary to determine the true nature of the fractures (either conductive or not). Nevertheless our methodology does not depend on this detail. Provided we have a fracture network the

Acknowledgements

This work was supported by SENER-CONACyT grant 143935 under project Y.00114 of the Mexican Petroleum Institute (IMP). We thank the fruitful discussions and insights of Dr. Luis G. Velasquillo, Dr. Ildar Batyrshin, Dr. Diego Del Castillo and Dr. Ernesto Estrada.

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