Flow in fractured media: A modified renormalization method

We present a methodology to account for fluid flow from microscales to macroscales in fractured media. Renormalization group (RG) theory coupled to a percolation approach provides a convenient tool to allow dealing with the complex connectivity of fracture systems and with the intricate relationship between the various scales involved and the observation scale. This method also provides us with a way to describe scale dependence of permeability (K). Two-and three-dimensional calculations can be performed for broad distributions of both conductances and fracture lengths. Here we introduce what we call a "modified renormalization" method. This method is then tentatively applied to the upper crust where many scales of fractures are present. The results are discussed relative to the 3- to 4-orders-of-magnitude increase in permeability which has been reported by some authors from sample scale to regional scale, and we examine how our model could be used to predict possible scaling laws.