2 区复合油藏水平井试井模型与实例解释

目前关于复合油藏水平井不稳定试井理论与应用研究很少见，针对这一问题，建立了水平井2 区复合油藏不稳定试井模型，研究了一种利用拉普拉斯变换、分离变量及特征函数与特征值法等现代数学分析方法对模型进行求解的新方法，获得了拉普拉斯空间中不稳定试井井底压力表达式。利用数值反演，编程绘制了标准的试井分析样版曲线，并分析了2 区复合油藏井底压力动态响应特征。不同的外边界条件具有不同的外边界特征响应，对顶定压或底定压边界，压力导数曲线在早期迅速下掉，不能反映出2 区复合油藏的复合特性。对顶、底均为封闭边界，样版曲线明显反映出油藏的2 区复合特性。实例分析结果表明，该模型可以用于2 区复合状油藏水平井的不稳定试井解释，为油田开发生产服务。

Well Test Model of Horizontal Well in 2-Zoned Composite Reservoir andExample Interpretation

At present，the research on theory and application of transient well test of horizontal well in composite reservoirscan hardly be found in publications. Aiming to slove this problem，the transient well test model of horizontal well in 2-zonedcomposite reservoir is established. A new method to solve the model is studied by using modern mathematic methods，includingLaplace integral transformation，separation of variables，eigenvalue and eigenfunction etc.，and the solutions to the model inLaplace space are obtained. Type curves of well test are drawn up by using numerical inversion，and the characteristics of wellbore pressure dynamic response are analyzed. There are different typical responses for different external boundaries for topconstant pressure boundary or bottom constant pressure boundary，the pressure derivative curves go down early and swiftly，so it cannot reflect the traits of 2-zoned composite reservoir. For both top and bottom closed boundaries the type curves canreflect the traits of 2-zoned composite reservoir. The example analysis shows that this model can be applied to transient welltest analysis of horizontal well in 2-zoned composite reservoir.