论文部分内容阅读
文章首先建立了不考虑井筒储存和表皮效应影响的均质各向异性无限油（气）藏水平井三维不定常渗流的数学模型，同时利用杜哈美原理建立了考虑井筒储存和表皮效应影响时该类水平井不定常渗流的数学模型。在获得数学模型解的基础上，利用数值积分和拉氏变换的数值反演方法分别作出了水平井的无因次压力及压力导数典型曲线。同时，较详细地推导出水平井早期和晚期流动的无因次压力表达式。分析表明，当不考虑井筒储存和表皮效应影响时，早期为垂直于井轴平面内的径向流，晚期为水平面内的拟径向流。当考虑井筒储存影响时，早期表现为纯井筒储存效应影响，在无因次压力及压力导数与时间的双对数图上，为斜率是１的直线，晚期与不考虑井筒储存的压力动态一致。从而为水平井试井分析打下了理论基础。
Firstly, the mathematical model of 3-D unsteady seepage of a horizontal well with a homogeneous anisotropic infinite oil (gas) reservoir is established without considering the effect of wellbore storage and skin effect. At the same time, the influence of wellbore storage and skin effect is established by using the Duhamel principle. The mathematical model of unsteady seepage of such horizontal well. On the basis of obtaining the solution of mathematical model, the typical curves of dimensionless pressure and pressure derivative of horizontal well are made respectively by numerical inversion method of numerical integration and Laplace transform. At the same time, the dimensionless pressure expression of early and late horizontal well flow is derived in more detail. The analysis shows that the radial flow in the plane perpendicular to the well axis and the quasi-radial flow in the horizontal plane are advanced in the early stage when the effect of wellbore storage and skin effect is not considered. When considering the effect of wellbore storage, the early manifestation was the effect of pure wellbore storage. On the logarithmic plot of non-dimensional pressure and pressure derivative versus time, the slope was a straight line, and the late phase was consistent with the pressure without wellbore storage . Which has laid a theoretical foundation for horizontal well test analysis.