Fracture connectivity from fracture intersections in borehole image logs

Abstract

The connectivity of fractures in subsurface rock formations is a key factor in understanding and predicting fracture flow in hydrocarbon reservoirs. We present a method to determine average number of fracture intersections per fracture, λ, and fracture length from borehole image logs. Fracture length is estimated from relative frequency of fractures with partial or complete circumferential traces on borehole image logs. When all fractures are interconnected fractures are above percolation threshold. Every fracture must intersect at least two other fractures for percolation, which means that percolation threshold corresponds to λ=2. We introduce the term sub-percolation threshold at λ=1 to define the transition from isolated fractures to fracture clusters. Fractures are isolated when λ<1 form clusters within sub-percolation range (1< λ<2) and generate a network above percolation threshold ( λ>2). Within sub-percolation range, the expected number of fractures, N, in a cluster is related to λ as follows: N=2 λ/(2− λ). This equation shows that fracture clusters remain small until λ reaches the percolation threshold value, at which point they interconnect in an explosive manner to form a network. Hence, only the areas where λ is greater than 2 need to be considered for fracture networks. Relative frequency of intersecting fractures, which is observed in borehole image logs, depends very much on fracture size. More than 50% of observed fractures must be intersecting for an average fracture length of 1 m at percolation threshold. The required frequency for percolation drops to 25% for an average fracture length of 2 m, and to 10% for 10 m average length.