基于源函数法的油层部分射开顶底封闭各向异性的三重介质油藏不稳定渗流

Solution to the unsteady flow problem in anisotropic triple-porosity reservoir with impermeable top and bottom boundaries and a partially penetrating vertical well based on the source function approach

为解决油层部分射开、顶底封闭、各向异性的三重介质油藏不稳定渗流问题,采用点源、线源的思想,得到无限大三维油藏中的连续点源解;使用镜像反映法及Poisson求和公式,得到顶底封闭时的连续点源解,沿射开层段积分,得到油藏不稳定渗流的均匀流线源解;根据有效平均压力点理论,得到无限导流线源解;利用Stehfest数值反演和程序设计绘制典型曲线,并根据渗流机理,分析影响曲线形态特征的因素,如储容比、窜流系数、射开程度、垂向各向异性系数等.结果表明:该方法有助于认识此类复杂油藏的渗流机理,也可用于试井分析、油藏产能研究等,为合理开发此类油藏提供理论依据.

In order to solve the unsteady flow problem in anisotropic triple-porosity reservoir with the impermeable top and bottom boundaries and a partially penetrating vertical well, firstly, we used 'Point Source' and 'Line Source' approach to obtain the point source solution in a infinite 3D reservoir, then utilized the 'mirror image' principle and Poisson summation equation to obtain the point source solution in a 3D reservoir with the impermeable top and bottom boundaries, then integrate the continuous point source solution along the penetrating formation to obtain the solution of the concerning problem under uniform-flux idealization. Then we utilized the conclusion about 'Efficient average pressure point' which was derived by Gringarten and Ramey to obtain the solution of an infinite-conductivity line source in concerning conditions. Finally he utilized the Stehfest numerical inversion and program design to draw typical curves, and analyzed the factors which affect the shape of the typical curves such as storativity, transfer coefficient, the penetrating ratio, and vertical anisotropy degree. The results help people to understand the flow mechanism of this type of reservoir and also can be employed for well test and productivity research and so on. It provides theoretical basis for people to reasonably develop reservoir.