多井干扰下有限导流裂缝井解析试井分析方法

Analytical well test method for finite conductivity fractured wells with multiple wells interference

低渗油藏中压裂井试井压力导数曲线在中后期出现“上翘”或“下掉”特征,目前试井分析常将该特征考虑为边界的影响,导致解释结果失真;另外常用的半解析方法计算时间长,不利于油田现场应用。因此提出导流能力影响函数来表征有限导流裂缝和无限导流裂缝井底压力响应的差异,利用叠加原理建立多井干扰下有限导流裂缝井解析试井模型,大幅提高计算速度,并构建数值模型验证解析模型的正确性。参数敏感性分析表明,邻井干扰下垂直裂缝井的试井典型曲线会出现“多台阶”特征,反映了干扰井的数量及干扰发生的顺序。利用Laplace解析反演、卷积变换、误差函数的性质、指数积分函数的性质获得模型的晚期近似解,从理论上证明多井干扰下压力导数曲线径向流段水平线的纵轴截距是测试井和产生影响的邻井无因次产量代数和的1/2。实际应用表明该方法能够评估邻井产生干扰的时间、干扰量和地层参数。

Well test pressure derivative curve of fractured wells in low-permeability reservoirs usually exhibits“upward”or“downward”characteristics in middle and late stages. Current well test analysis considers this characteristic as the influence of boundary,which causes interpretation distortion. In addition,common semi-analytical methods need much calculation time,which is not beneficial for field application. Therefore,conductivity influencing function is proposed to characterize differences of bottomhole pressure response for finite and infinite conductivity fractures. By means of superposing principle,analytical well test model for finite conductivity fractured well with multiple wells interference is established with calculation speeded up,and numerical model is established to verify correctness of the analytical model. Parameter sensitivity analysis shows that typical well test curve of vertical fractured well with adjacent well interference may have“multi-step”characteristic,reflecting amount of interfered wells and order in which interference occurs. The late approximate solution of the proposed model is obtained through Laplace analytical inversion,convolution transformation,error function and exponential integral function natures,and theoretically proves that longitudinal intercept of horizontal line of radial flow section is 1/2 of dimensionless production algebraic sum of the test well and interfering adjacent well. Actual application shows that this method can evaluate interference time,interference amount and formation parameters resulted from adjacent wells.