Pressure Performance Analysis Of Arbitrary Shaped Reservoirs With Boundary Element Method

The boundary element method, as a new numerical technique for solving partial differential equations, is superior to the domain methods (finite difference and finite-element method) in several ways. However, at present, the boundary element method is mainly be used to solve the problem of homogeneous reservoirs. Although, using the boundary element method, the flow problems in heterogeneous reservoirs have been studied by several foreign resercher, the flow problems in arbitrary shaped reservoir and reservoirs with impermeable barriers need to research further. So, on the base of the thing that forefathers studied, this paper in which the problems of the arbitrary shaped reservoirs with impermeable barriers are researched using the perturbation boundary element method, have done the following work mainly:First, the mathematical models which are applicable to steady-state flow and transient flow in arbitrary shaped heterogeneous reservoirs is built up. By using the regular perturbation method, the mathematical models are decomposed into a series of Poisson equations and modified Helmholtz equations. The fundamental solutions (free space Green's function) for the Poisson equations and modified Helmholtz equations are set up. The solution for two kinds governing equations is computed by the boundary element method. Fade approximants are employed to improve the perturbatin series convergence property.Second, a perturbation boundary element method for steady-state flow problems in heterogeneous meida is developed and various aspects of the model are verified against analytical solution for simpilified problems. The perturbation series obtained by the BEM gives the complete solution for the original governing equation. The characteristics of pressure traverse have been analysed. For highly heterogeneous problems, Pad6 approximants are effective to accelerate the rate of convergence and to convert a divergent series into a convergent solution. All kinds of the streamline distribution figures have been drawn and the characteristic of these have been analysed, which have established the foundation for analysing the characteristic of distribution of remaining oil.Third, a perturbation boundary element method for transient flow problems in arbitrary shaped heteogeneous reservoir is developed and Duhame! principle is employed to obtain the bottom hole pressure which take into account effects of skins and wellbore storage. The perturbation BEM formulated in Laplace space is verified against analytical solution for simplified heterogeneous problems. The type curves are generated and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barrier. We observed that the complicacy of heterogeneity and shape of reservoirs and the size, shape and orientation of impermeable region in reservoir can be knowed, by using well testing and combining with geological materials, because heterogeneity, arbitrary shape and impermeable region have a great influence on the transient pressure response.