A fast method for fracture intersection detection in discrete fracture networks

The detection of fracture intersections is an important topic in discrete fracture network modelling for assessments such as connectivity analysis and subsequent fluid flow evaluations. However, the standard method for such detection is very time-consuming especially for large fracture networks as the detection time often increases exponentially with the number of fractures in the network. In this paper, we introduce the bounding box and sweeping line (BBSL) method as a new fast algorithm to solve the problem. BBSL comprises two consecutive steps: filtering and refining. In the filtering step, an axis-aligned minimum bounding box (AABB) and an improved sweeping line method (SLR - sweeping line for rectangles in 2D or SLC - sweeping line for cuboids in 3D) are introduced to filter out pairs of fractures that have no possibility of intersection. The proposed refining in BBSL consists of coarse refining and fine refining. Coarse refining combines the inner and outer products of vectors to filter out non-intersecting pairs of fractures. Fine refining is then used to further assess fracture intersections and to determine the intersection coordinates. To demonstrate the application of the proposed method a series of comparison experiments were conducted using 2D and 3D discrete fracture networks with different fracture densities. For filtering, the results show that the proposed method is significantly more efficient than the commonly used methods such as brute force (BF) and sweeping and pruning (SAP). For refining, the proposed method significantly outperforms the commonly used refining method.