Summary The displacement discontinuity method (DDM) is frequently used in geothermal and petroleum applications for modeling the behavior of fractures in linear‐elastic rocks. The DDM requires O(N2) memory and O(N3) floating point operations (where N is the number of unknowns) to construct the coefficient matrix and solve the linear system of equations by direct methods. Therefore, the conventional implementation of the DDM is not computationally efficient for very large systems of cracks, often limiting its application to small‐scale problems. This work presents an approach for solving large‐scale fracture problems using the fast multipole method (FMM). The approach uses both the DDM and a kernel‐independent version of the FMM along with a preconditioned generalized minimal residual algorithm to accelerate the solution of linear systems of equations using desktop computers. Using the fundamental solutions for constant displacement discontinuity in a two‐dimensional elastic medium, several numerical examples involving fracture networks representing fractured reservoirs are treated. Numerical results show good agreement with analytical solutions and demonstrate the efficiency of the FMM implementation of the DDM for large‐scale simulations. Copyright © 2015 John Wiley & Sons, Ltd.

The displacement discontinuity method (DDM) is frequently used for modeling the behavior of fractures in reservoir modeling. However, the DDM is not computational efficient for large systems of cracks, limiting its application to small-scale situations. Recent fast summation techniques such as the Fast Multipole (FM) Method accelerate the solution of large fracture problems, demanding linear complexity O(N) in memory and execution time with very modest computational resources. In this work we use the FM-DDM method to simulate fracture response while considering fluid flow through the fracture network. This is a novel and efficient approach for solution of large scale coupled fluid flow-geomechanical problem in naturally fractured reservoirs. Several case studies involving fracture networks with several hundred thousands of boundary elements are presented. The results show a good level of accuracy and computational efficiency compared to the conventional DDM. In addition, the approach is shown to be very useful for the design of exploitation strategies in large-scale fracture network situations. The relative positions between injectors and producers and the fracture permeability variation with injection/extraction play an important role on the distribution of stresses in the fracture network, which in-turn, influence the conditions for the fluid-flow such as fluid pressure and fracture permeability.

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