页岩气水平井段内多簇裂缝同步扩展模型建立与应用

水平井分段多簇压裂技术是开发页岩气藏的核心技术手段，分析段内多裂缝同步扩展规律和进行段内簇间距优化设计对提升水平井压裂效果具有重要意义。基于多层压裂流量动态分配思想，考虑缝间应力干扰、射孔和摩阻压降损耗、滤失等影响建立多簇裂缝同步扩展数学模型，利用改进Picard法进行方程组求解并开展敏感性分析。研究结果表明，簇间距对多簇裂缝扩展的影响最为明显，当簇间距达到缝高高度时，缝间力学干扰则几乎可以忽略；簇间距越近，则整个缝簇系统受到应力干扰影响越为明显，而加大压裂液黏度则可以明显改变缝宽，一定程度上抵消应力干扰影响；地层滤失系数增加则会显著降低改造体积范围，射孔密度对缝簇扩展影响较小。提出的段内多裂缝扩展数值模型简化了数学建模步骤，综合考虑了影响裂缝扩展的岩石力学和工程因素，且计算速度快，精度可靠，可为水平井段内簇间距压裂优化设计工作提供技术支持。

Establishment and application of the model for the synchronous propagation of multi-cluster fractures in the horizontal section of shale-gas horizontal well

Multi-cluster staged fracturing technology of horizontal well is the core technology to develop shale gas reservoirs. In order to improve horizontal-well fracturing effect, therefore, it is of great significance to analyze the synchronous propagation laws of multiple fractures in the horizontal section and optimally design the cluster spacing in the horizontal section. In this paper, the mathematical model for the synchronous propagation of multi-cluster fractures was established based on the concept of dynamic flow rate distribution of multi-layer fracturing. In this model, the effects of stress interference between fractures, perforation, frictional pressure drop loss and filtration are taken into account. It was solved by means of the modified Picard method and then sensitivity analysis was conducted. It is shown that the effect of cluster spacing on multi-cluster fracture propagation is the most obvious, and when the cluster spacing is up to the fracture height, the stress interference between fractures is almost negligible. The shorter the cluster spacing, the more obvious the stress interference on the whole fracture cluster system. The fracture width can be improved significantly by increasing the viscosity of fracturing fluid, and in a way the effect of stress interference can be offset. The stimulated reservoir volume will be decreased significantly as the formation filtration coefficient increases, and the effect of perforation density on fracture cluster propagation is less. Finally, based on the proposed numerical model for the multi-fracture propagation in horizontal section, the mathematical model establishment procedure was simplified. It not only considers comprehensively the rock mechanics and engineering factors that have effect on fracture propagation, but also does the calculation fast, accurately and reliably. It provides the technical support for the design optimization of cluster spacing in horizontal sections.