| It's well known that the question of unstable seepage flow in heterogeneous reservoir is an important and difficult task in the research of porous media percolation mechanics. A series of research achievements about the theory and experiment show that many phenomenons of percolation mechanics in gas and oil reservoir have the property such as permeability distribution, porosity distribution, fractal network distribution in fractal gas and oil reservoir and so on. Since Warren-Root model in homogeneous reservoir is based on Euclid geometric and isn't suit for heterogeneous reservoir with pressure-sensitive deformation property. But fractal geometric theory is a facility and effective way to describe these properties with many different dimensions and poor connectivity, even terrific disorder in spatial distribute. In recent years, the seepage flow mathematical models in fractal reservoir have been extensively developed and applied and have become important methods to research nonlinear seepage flow regularity in complex reservoir. But all the developed fractal models have not researched the aspects of fractal reservoir with double media pressure sensitive deformation property. With the exploitation of gas and oil fields, it's no doubt that it is important to pursue simple and effective numeric methods to solve the mathematical models in order to meet the need of unsteady seepage flow theory study and application as well as necessary to further study of deformable reservoir.On the basis of the theory and knowledge of many learning branches such as fractal geometric, the percolation mechanics, the reservoir engineering, mathematic and physic method, numeric analysis method, compute graphic procession method, software engineering analysis method and so on, this thesis based on the developed research work, concludes the following a few facets to the unsteady seepage flow mathematical models in the pressure-sensitive deformable double media fractal reservoir. Fractal geometric theory and method are good approximations to describe the complicity and we can more easily analyze all kinds of the pressure-sensitive deformable double media fractal complex reservoirrelatively than others. Based on Warren-Root model, introducing fractal parameter (df and θ) and deformable coefficient (af,βf) this thesisconstructed all kinds of seepage flow mathematical models to the pressure-sensitive deformable double media fractal reservoir with the defined production or pressure in inside boundary and defined pressure or closet outside boundary when the effects caused by permeability and porosity company with the pressure change ware concerned. For the model with defined pressure on boundary both inside and outside, the thesis first proofed the discrete numeric solution existence of the general difference equation to the seepage mathematical model by discrete functional analysis; then it presented a concise and effective numeric solution, predicted-corrected method, and proofed the convergence of it.For the model with defined pressure on boundary both inside and outside, the thesis first proofed the discrete numeric solution existence of the general difference equation to the seepage mathematical model by discrete functional analysis; then it presented a concise and effective numeric solution, predicted-corrected method, and proofed the convergence of it.For the seepage mathematical model with second kind of boundary condition, the thesis developed the finite element method because of the great difficult in proof the discrete numeric solution existence and convergence of difference equation. The thesis first proofed the existence of the finite element numeric solution; then presented a kind of high accurary and convergence finite element method defined in Galerkin finite element space and proofed its convergence; finally, provided a kind of special linear finite element method also with high convergence. Through pressure curve, pressure derivative, permeability effect rate to pressure, the thesis detailedly analyz... |
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