Fracture network mapping and estimation of its permeability constitute two major steps in static model preparation of naturally fractured reservoirs. Although several different analytical methods were proposed in the past for calculating fracture network permeability (FNP), different approaches are still needed for practical use. We propose a new and practical approach to estimate FNP using statistical and fractal characteristics of fracture networks. We also provide a detailed sensitivity analysis to determine the relative importance of fracture network parameters on the FNP in comparison to single fracture conductivity using experimental design approach.
The FNP is controlled by many different fracture network parameters such as fracture length, density, orientation, aperture, and single fracture connectivity. Five different data sets were generated for random and systematic orientations. In each data set, twenty different combinations of fracture density and length for different orientations were tested. For each combination, ten different realizations were generated. The length was considered as constant and variable. This yielded a total of one thousand trials. The FNPs were computed through a commercial discrete fracture network modeling simulator for all cases. Then, we correlated different statistical and fractal characteristics of the networks to the measured FNPs using multivariable regression analysis. Twelve fractal (sandbox, box counting and scanline fractal dimensions) and statistical (average length, density, orientation and connectivity index) parameters were tested against the measured FNP for synthetically generated fracture networks for a wide range of fracture properties. All cases were above the percolation threshold to obtain a percolating network and the matrix effect was neglected.
The correlation obtained through this analysis using four data sets was tested on the fifth one with known permeability for verification. High quality match was obtained.
Finally, we adopted experimental design approach to identify the most critical parameters on the FNP for different fracture network types. The results were presented as Pareto charts. It is believed that the new methodology and results presented in this paper will be useful for practitioners in static model development of naturally fractured reservoirs and will shed light on further studies on modeling and understanding the transmissibility characteristics of fracture networks.
The correct estimation of the flow properties of fractured rocks is crucial in modeling of hydrocarbon reservoirs, nuclear waste repositories, and geothermal reservoirs. The influence of fracture properties in particular is significant on the results as the fracture system preferentially controls the hydrodynamics of fractured reservoir (Mourzenko et al. 2001). Fracture network permeability (FNP) is one of the critical input data to the simulator and it is controlled by topological and geometrical properties of the networks. A great deal of effort has been devoted to characterize those properties (Berkowitz, 1994). But, studies relating those properties to the FNP are limited.
Semi-quantitative analyses showed that fracture network characteristics have direct implications on fracture network permeability. For example, fractures perpendicular to fluid flow direction have negative effect on fracture network permeability (Babadagli, 2001). As fracture aperture and density increase, the FNP increases (Zhang et al. 1996). The connectivity of a fracture network increases with increasing fracture density and length (Rossen et al. 2000).
The hydraulic properties of fractured reservoirs are primarily dependent on the degree of fracture interconnection. A fracture network must have a percolating cluster to be permeable. Hence, the connectivity is of the primary importance in this analysis. Other parameters including fracture length, density, aperture and orientation also play a critical role on the FNP.