三维双孔介质圆柱气藏水平井渗流模型的解

Solution to the Seepage Model of Horizontal Wells in Three-Dimensional Dual-Porosity Cylindrical Gas Reservoirs

摘要: 本文针对三维双孔介质圆柱气藏水平井渗流模型，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，并获得了无因次井底压力在Laplace空间解的相似结构。结果清晰显示了三种外边界与四种顶底边界条件结合下解的表达式之间的联系。本文拓展了相似结构理论的应用范围，为深入研究三维双孔介质圆柱气藏水平井渗流规律，提供了新的方法。

Abstract: In this paper, aiming at the seepage model of horizontal wells in three-dimensional dual-porosity cylindrical gas reservoirs, mathematical models are established for two cases, namely excluding wellbore storage and skin factor and including wellbore storage and skin factor. On this basis, the Laplace transform, Fourier transform and Duhamel’s principle are comprehensively applied, combined with the similar structure method, to systematically solve the models under four types of top and bottom boundary conditions (constant pressure at both top and bottom, closed boundary at both top and bottom, constant pressure at the top with closed bottom, and closed top with constant pressure at the bottom). Furthermore, the similar structure of the dimensionless bottom-hole pressure solutions in the Laplace space is derived. The results clearly reveal the correlations among the solution expressions under the combination of three types of outer boundary conditions and four types of top and bottom boundary conditions. This paper expands the application scope of the similar structure theory and provides a new method for the in-depth study on the seepage laws of horizontal wells in three-dimensional dual-porosity cylindrical gas reservoirs.