On iterative techniques for computing flow in large two-dimensional discrete fracture networks

Computation of flow in discrete fracture networks often involves solving for hydraulic head values at all intersection points of a large number of stochastically generated fractures inside a bounded domain. For large systems, this approach leads to the generation of problems involving highly sparse matrices which must be solved iteratively. Distributions of fracture lengths spanning over several orders of magnitude, and the randomness of fracture orientations and locations, lead to coefficient matrices that are devoid of any regular structure in the sparsity pattern. In addition to the rapid increase in computational effort with increase in the size of the fracture network, the spread in the distribution of fracture parameters, such as length and transmissivity, dramatically influences the convergence behavior of the system of linear equations. An overview of the discrete fracture network (DFN) methodology for computation of flow is presented along with a comparative study of various Krylov subspace iterative methods for the resulting class of sparse matrices. The rate of convergence of the iterative techniques is found to exhibit a systematic pattern with respect to changes in statistical parameters of the stochastically generated fracture networks. Salient features of the observed trends in the convergence pattern are discussed and guidelines for design of DFN algorithms are provided.