双渗四重介质试井分析模型的研究

Well Test Analysis Model for Dual-permeability Quadruple-media Reservoirs

针对碳酸盐油藏复杂储层特征和渗流规律,建立大裂缝、微裂缝、溶蚀孔洞和基岩双渗四重介质数学模型。采用Laplace变换对渗流微分方程进行求解,得到大裂缝和微裂缝的渗流微分方程组。将含有特征参数的通解代入到微分方程组,根据解的存在唯一性条件,求出特征参数。结合内外边界条件确定出微分方程的特解,从而获取Laplace空间井底压力的解析解,为双渗四重介质碳酸盐储层的试井分析提供理论依据。

The mathematical model of the dual-permeability quadruple-media with large-scale fractures, micro-fractures, vugs and matrix was established for the carbonate oil reservoirs of the complex reservoir characteristics and seepage laws. The Laplace transformation was used to solve the differential equations of seepage, and the differential equations of large-scale fractures and micro-fractures were obtained. The general solution containing the characteristic parameters was replaced by differential equations, and the characteristic parameters were obtained according to the uniqueness and the existence condition of the solution. The special solution of the differential equation was determined by combining the internal and external boundary conditions, and the analytical solution of the bottom hole pressure in the Laplace space was obtained, which provided the theoretical basis for well test analysis of carbonate reservoir with the dual-permeability quadruple-media.