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**Analysis of the simulation of single phase flow through a naturally fractured reservoir.**
*(English)*
Zbl 0668.76130

A general form of the double porosity model for single phase flow through a naturally fractured reservoir is derived by explicitly considering fluid flow in individual matrix blocks. The Warren and Root model is shown to be a crude approximation to this model. The general model consists of a parabolic equation coupled to a series of parabolic equations. It is shown that the coupling term can be viewed as a positive-semidefinite perturbation of the time derivative, and hence it is verified that the model is well posed. A finite element method is presented to approximate the solution, and optimal order \(L^ 2\)-error estimates are derived.

### MSC:

76S05 | Flows in porous media; filtration; seepage |

35K99 | Parabolic equations and parabolic systems |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |