圆形封闭油藏变导流垂直裂缝井非稳态渗流数学模型

针对垂直裂缝不同位置导流能力不同的特点，应用点源函数的基本方法，在Laplace空间建立了垂直裂缝井的储层和裂缝的耦合模型，同时考虑了垂直裂缝变导流能力接直线、指数和对数变化的3种形式，并对其进行了数值求解。3种形式的变导流能力模型包含的系数不同，反映出沿裂缝的导流能力变化不一样，在图版上就表现为压力和压力导数也不一样，另外，圆形封闭边界对垂直裂缝导流能力早期的压力和压力导数没有影响，边界只对晚期的压力和压力导数有影响，研究垂直裂缝的变导流能力，能为水力压裂井的产量分析和预测以及为垂直裂缝井试井解释提供理论依据。

Mathematical model with unsteady-state filtering flow of vertically fractured well with varying conductivity for closed circle oil reservoir

Aimed at the flow conductivity of vertical fractures varies at different place, coupling model has been built up between reservoir and fractures of the vertically fractured well in Laplace space applying point source function method. Three forms of the linear, exponential, logistical varying conductivity are considered and numerically solved. The differences of the factors of three forms can respond the differences of the flow conductivity of the vertical fractures and the differences of the pressure and pressure derivative at the plate. The border of the closed circle oil reservoir can not affect the early pressure and pressure derivative of the flow conductivity of the vertical fractures and only affect the late pressure and pressure derivative. The study of varying flow conductivity with vertical fractures can provide theory foundation for output analysis and forecast and vertically fractured well test interpretation.