双孔介质二维箱形水平井渗流模型的解

Solution to Two Dimensional Box Shaped Horizontal Well Seepage Model in Dual Porosity Media

摘要: 本文针对双孔介质二维箱形水平井渗流模型，分两种情况建立数学模型：不考虑井筒储集和表皮因子；考虑井筒储集和表皮因子。在此基础上，综合运用Laplace变换、Fourier变换、Duhamel原理，并结合相似构造法，系统求解顶底四种边界条件(顶底定压、顶底封闭、顶部定压底部封闭、顶部封闭底部定压)下的模型，获得无因次井底压力分布在Laplace空间解的相似结构。该成果清晰揭示了顶底四种边界条件下解的表达式之间的内在关联。本文拓展了相似结构理论的应用范围，为深入研究双孔介质水平井油藏渗流规律，提供了新理论基础与创新方法。

Abstract: Targeting the two dimensional box shaped horizontal well seepage model in dual porosity media, this paper develops mathematical models for two cases: excluding wellbore storage and skin factor; incorporating wellbore storage and skin factor. On this premise, through the comprehensive utilization of Laplace transform, Fourier transform, Duhamel’s principle, and in combination with the similar construction method, the models under four top bottom boundary conditions (top-bottom constant pressure, top bottom closed, top constant pressure with bottom closed, top closed with bottom constant pressure) are systematically solved. The similar structure of the dimensionless bottom hole pressure distribution in the Laplace space solution is derived. This outcome clearly uncovers the internal correlation among the solution expressions under the four top bottom boundary conditions. This paper extends the application scope of the similar structure theory and offers a novel theoretical foundation and innovative approach for in depth investigation into the seepage law of dual-porosity medium horizontal well reservoirs.