边水气藏水平井压力动态点源解的计算方法

A CALCULATION METHOD OF POINT SOURCE SOLUTIONS FOR PRESSURE PERFORMANCE OF HORIZONTAL WELLS IN EDGE-WATER GAS RESERVOIRS

某气藏边水活跃,气水关系复杂,利用水平井开采有水气藏取得了较好的开发效果,因此边水气藏水平井试井解释方法技术有着广阔的应用前景。为此,利用点源函数的思想建立了边水气藏渗流数学模型并求得了其基本解;通过积分变换的办法获得了边水气藏水平井压力动态响应函数;利用贝塞尔函数积分性质和泊松叠加公式对其压力响应函数进行了数学变换和简化;利用杜哈美原理、stehfest反演算法、Muskat的方法求解了该模型,得到了考虑井储和表皮影响的顶、底封闭边水气藏水平井的无因次压力和压力导数对无因次时间双对数曲线,分析了边水气藏水平井渗流特征及其影响因素;绘制了一系列的边水气藏水平井无因次压力和压力导数对无因次时间双对数曲线的典型图版。

Through introducing a successful application of horizontal wells in some gas reservoirs with active edge-water and complex gas-water contact, this paper recommends the well test analysis for horizontal wells to be widely used in such complicated reservoirs. This study built up a mathematical model representing fluid flow in porous media for edge-water reservoirs and obtained its basic solutions based on the theory of point source function, then through calculus transformation acquired the responding function of pressure performance, which was transformed and simplified in a mathematic way according to Bessel function and Poisson's summation formula, and got the solution of this model based on Duhamel theory, Stehfest Inversion Method and Muskat method. Thus, with consideration of wellbore storage and skin effect, this study plotted log-log type curves of dimensionless pressure and pressure derivative vs. dimensionless time for horizontal wells in edge-water gas reservoirs with impermeable top and bottom boundaries, which could help describe the fluids flowing features and their influencing factors for horizontal wells in edge-water gas reservoirs. This study also demonstrated a series of classic plots like that.