变形介质油气藏压力动态分析的边界元方法

对于任意形状变形介质油气藏的井底压力分析只能采用数值解的方法，目前常用的数值计算方法是有限差分法、有限元法和边界元法。前两种方法在解数学模型时局限性较多、适应性差，而边界元法只需对区域的边界进行网格划分，计算量和存储量小，计算精度高，能够降维，因而对复杂形状的边界问题处理十分有效。在此，利用边界有限元法对不渗透区域任意形状变形介质油气藏不稳定渗流的数学模型进行求解，获得油气藏内任意点的压力，绘制了考虑渗透率变异系数、复杂边界以及油气藏内存在不渗透区域等因素影响的井底不稳定压力典型曲线，并分析了曲线特征，发现油气藏内的不渗透区域对压力典型曲线的晚期形态存在明显影响，使其压力导数曲线上翘时刻提前，该项研究为压敏性气藏试井分析提供了理论基础。

THE BOUNDARY ELEMENT METHOD FOR PRESSURE TRANSIENT ANALYSIS OF DEFORMED MEDIA RESERVOIR

The numerical solution is the only method for analyzing bottom hole pressure in deformed media reservoir with arbitrary shape. The commonly used numerical methods are finite difference method, finite element method and boundary element method. The first two methods have disadvantages of more limitations and poorer adaptability for solving mathematical models, while the boundary element method can just take the mesh generation of regional boundaries, having the advantages of less computation efforts and storage space, as well as dimension reduction, so as to process the border issue of complex shape very effectively. In this paper, by using the boundary finite element method to solve the mathematical model of unstable seepage flow in impermeable area of deformed media reservoir with arbitrary shape, the reservoir pressure of any point can be obtained. Thus, with the consideration of permeability variation coefficient, complex boundary and reservoir storage, the typical curve of unstable pressure in bottom hole is drawn. Then by analyzing curve features, it is found that the impermeable area in reservoirs has significant influence on the later stage shape of pressure typical curves, speeding the upwarping moment of pressure derivative curve. The study provides a theoretical basis for the pressure sensitivity gas reservoir well test analysis.