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The scale and level of detail at which flow models need to be carried out for nuclear waste repository studies, petroleum reservoir development, landfill design and mining often is beyond the capacity of modern computers. A new approach using algorithms developed in graph theory can greatly simplify the computations. An example of this approach applied to a hypothetical high-level waste repository in Sweden illustrates its advantages.
The hydrology, deformation and strength of fractured rock masses are important parameters for efficiently and cost-effectively protecting or recovering natural resources, engineering underground caverns and tunnels, and designing slopes. For example, connectivity of fracture networks strongly influences how much, how fast and how far fluids and any associated chemical species moves (La Pointe and others, 1993). It is not always clear how best to model flow in fracture systems, however. The dual continuum approach is commonly used in the petroleum industry. This method consists of dividing the rock mass into two continua: the matrix and the fractures. Both fracture and matrix components are locally characterized by symmetrical tensors and continuous flow fields. The problem with this type of approach is that it greatly oversimplifies the geometry and connectivity of the real fracture systems found in rock (Fig. 1). Its advantages are found in its ability to more realistically portray the chemical reactions and physical processes found in geological systems in a numerically efficient manner. Over the last decade, researchers have formulated new ways of modeling flow through fractured rock masses. These methods are generally called discrete fracture network models. Recent examples include Cacas and others (1990) and Dershowitz and others (1995). In these models, each fracture is represented by a polygon with associated geometrical properties such as orientation, shape, size and location, and fluid flow or mechanical properties such as transmissivity, storativity, shear strength or cohesion (Fig. 1). Fluid flow analysis of discrete fracture models consists of discretizing each fracture into finite elements, and then approximately solving the appropriate flow or mass transport equations. These discrete fracture models have considerable geological realism, and have been proven to accurately model flow in fracture systems when dual continuum approaches fail (Dershowitz and others, 1993), but they encounter numerical challenges when the number of fractures becomes large or the fracture network becomes highly connected. As the number of fractures increases and the connectivity increases, the matrices that must be solved grow very rapidly in size. Many fracture flow problems are at scales that are presently difficult to solve with existing discrete fracture codes, and have flow characteristics that are very different from the assumptions underpinning dual continuum models. These problems typically involve analysis of rock blocks on the order of several kilometers in each of three dimensions, typical of problems encountered in petroleum reservoir engineering, nuclear or hazardous waste disposal, or water resource development. In these situations, dual continuum codes give poor results and discrete fracture models may be too large for most computers.
