In this paper, a new rate decline analysis model of horizontal wells with variable conductivity and uneven distribution of multiple fractures is proposed. By Laplace transformation, point source integration, and superposition principle, solutions of multiple infinite conductivity fractures in closed reservoirs are obtained. By coupling Fredholm integral equation of variable conductivity, linear equations of variable conductivity fractures in Laplace space are obtained. Gauss-Newton iteration, Duhamel convolution, and Stehfest numerical inversion method are used to obtain the bottom hole production solution. The accuracy of the results is verified by comparing with Eclipse software simulation. Then, the influence of some important reservoir and fracture parameters on the production is analyzed. The calculative results show that the smaller the fracture spacing is, the earlier the fracture begins to decline, the more the production will decrease; the change of different fracture length with the total fracture length unchanged has almost no effect on the production; the angle between fracture and - axis has an important effect on the production; the smaller the angle between fracture and - axis is, the stronger the interference between fractures is, the higher the production; the initial fracture conductivity affects the early production behavior, and the higher the initial fracture conductivity, the higher the production; the larger the fracture declines index, the lower the production, but the decreasing range gradually decreases with the increase of the decline index; the larger the reservoir drainage radius, the later the energy depletion stage, the higher the production. At last, a good fitting effect is obtained by fitting an example of oil field. The model proposed in this paper enriches the model base of rate decline analysis of fractured horizontal wells and lays a theoretical foundation for efficient development and practice of tight reservoirs.

中文翻译：

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多变电导率和不均匀分布裂缝水平井速率递减分析

本文提出了一种新的具有可变导流能力和多条裂缝分布不均的水平井速率下降分析模型。通过拉普拉斯变换、点源积分和叠加原理，得到封闭储层中多条无限导流裂缝的解。通过耦合变导流能力的Fredholm积分方程，得到拉普拉斯空间变导流裂缝的线性方程组。采用高斯-牛顿迭代、Duhamel 卷积和 Stehfest 数值反演方法获得井底生产解。通过与Eclipse软件仿真对比验证了结果的准确性。然后，分析了一些重要的储层和裂缝参数对生产的影响。计算结果表明，裂缝间距越小，裂缝开始下降越早，产量下降越多；不同裂缝长度的变化在总裂缝长度不变的情况下对产量几乎没有影响；裂缝与轴的夹角对生产有重要影响；裂缝与-轴夹角越小，裂缝间干涉越强，产量越高；初始裂缝导流能力影响早期生产行为，初始裂缝导流能力越高，产量越高；裂缝下降指数越大，产量越低，但下降幅度随着下降指数的增加而逐渐减小；水库排水半径越大，能量消耗阶段越晚，产量越高。最后通过对油田实例进行拟合，得到了较好的拟合效果。本文提出的模型丰富了压裂水平井降速分析的模型基础，为致密储层的高效开发和实践奠定了理论基础。