Two models are described to simulate the waterflooding of a naturally fractured reservoir. The first is the relatively standard double porosity model in which the matrix is a distributed source to the fracture system. We explicitly describe the influence of the fracture system on the matrix by imposing the proper boundary conditions on the matrix equations. The second model is a limit form of this model for small matrix blocks. It assumes a capillary equilibrium between the matrix and fracture systems. Finite difference procedures are given for these models. These procedures completely separate the matrix block calculations from the fracture calculations. Numerical results are presented to illustrate and contrast the two models.

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