The relationship of the degree of interconnection to permeability in fracture networks

The problem of determining the permeability of a rock mass containing a system of finite fractures is highly dependent on both the degree of interconnection between fractures and the heterogeneity of individual fracture characteristics. This paper examines how degree of interconnection affects both magnitude and nature of the fracture permeability. The interconnection between given fracture sets is a complex function of (1) fracture density, i.e., the number of fractures per unit volume, and (2) the fracture extent or size. Unfortunately, neither the density nor the extent of fractures is easily determined from borehole data. However, fracture frequency can be directly measured in a borehole because it is simply the number of fractures intersected per unit length of the borehole. The frequency is a measure of the product of fracture density and size because the probability of a fracture intersecting a borehole is proportional to this product. The effect of the degree of interconnection was investigated by numerically simulating flow in fracture networks where fracture size and density varied inversely, while the product of these two parameters was held fixed. Directional permeabilities of a number of such networks were determined, and the hydraulic behavior of each fracture system was compared to that of an ideal porous medium. The permeability of the rock matrix between the fractures was assumed to be low enough to be negligible. The results show that as fracture length increases, the degree of interconnection increases. Thus, for a given fracture frequency as measured in a borehole, the permeability of the system increases as fracture length is increased, and density is proportionally decreased. Also, fracture systems with shorter, but more dense fractures, behave less like porous media than do systems with longer but less dense fractures. Knowledge of fracture frequency and orientation alone is inadequate when determining permeability or deciding the important question of whether a given system behaves like a porous medium. For many cases where these parameters can be measured in the borehole it is critical to know fracture length in order to predict the degree of fracture network interconnection. However, for certain cases where fractures are larger than some critical size, it may not be necessary to know fracture lengths exactly.