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

Arbogast, Todd

SIAM J. Numer. Anal. 26, No. 1, 12-29 (1989).

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

Keywords:

finite element method; double porosity model; single phase flow; naturally fractured reservoir; individual matrix blocks; series of parabolic equations; positive-semidefinite perturbation

Citations:

Zbl 0668.76131