6592

6592

Investigation of diffusion problems in naturallyfractured reservoirs of oil

master of science

applied mathematics

Autumn 2007

Autumn 2007

Advisor: prof. a.shidfar

Abstract: Today, because oil reserves in the world have decreased, specialists have investigated complex and complicated reservoirs. One of these complex types is naturally fractured reservoirs. In this thesis the spontanrous imbibition phenomenon in naturally fractured reservoirs will be investigated. First, mathematical model of the phenomenon has been presented. In this model a nonlinear diffusion equation has been obtained. Our purpose in this thesis is solving the problems related to this diffusion equation. For this purpose, finite differences method has been used. By using of finite differences approximations, diffusion equation has discritizated numerically. This work resulted a difference equation. By using of this difference equation in mesh points at the specified region, a system of equations has been obtained. Then solving of this system has been investigated. In last chapter a special diffusion equation has presented that is an inverse problem. By using of the finite differences and methods for solving of the inverse problems a numerical method for solving of this problem has presented. Stability and consistency of this method has been investigated. Next numerical results have been presented.