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We demonstrate how topology-based measures of connectivity can be used to improve analytical estimates of effective permeability in 2-D fracture networks, which is one of the key parameters necessary for fluid flow simulations at the reservoir scale. Existing methods in this field usually compute fracture connectivity using the average fracture length. This approach is valid for ideally shaped, randomly distributed fractures, but is not immediately applicable to natural fracture networks. In particular, natural networks tend to be more connected than randomly positioned fractures of comparable lengths, since natural fractures often terminate in each other. The proposed topological connectivity measure is based on the number of intersections and fracture terminations per sampling area, which for statistically stationary networks can be obtained directly from limited outcrop exposures. To evaluate the method, numerical permeability upscaling was performed on a large number of synthetic and natural fracture networks, with varying topology and geometry. The proposed method was seen to provide much more reliable permeability estimates than the length-based approach, across a wide range of fracture patterns. We summarize our results in a single, explicit formula for the effective permeability.

Plain Language Summary Fluid flow through fractured rocks is of great importance in many applicationsfrom petroleum production to groundwater utilization and waste management. Since the rocks are beneath the surface, it may often be difficult to know how fast water or oil would move through the fractures. One piece of the puzzle is connectivity: do the fractures form a connected path through the rocks? And how many of the fractures contribute to the overall flow path? Some clues can be obtained by studying borehole rock samples, and analogous rock formations that are exposed on the surface. But the information gained from these sources has previously been analyzed using oversimplified methods. Part of the problem is that existing methods are dependent on the average fracture length. Not only is this property difficult to measure, but the link between fracture length and connectivity is only valid in special cases. In this work, we show how connectivity can be found using a different set of parameters: the relative amount of fracture intersections, abutments, and terminations, which are easily obtained from field studies. We test our methodology on a wide variety of fracture patterns, and demonstrate that the new method is superior to the length-based approach.