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为满足工程设计的需要 ,以缝中流体单元的受力分析为基础 ,综合流体力学理论、弹性力学理论和物质平衡原理 ,重新建立了水平裂缝中压力分布、水平裂缝宽度和水平裂缝延伸半径等数学模型以及用差分法离散后的数值模型 ,并用牛顿迭代方法进行数值求解。这些模型综合考虑了压裂液滤失对缝中压力分布及流量分布的影响、能准确模拟水平裂缝延伸过程。研究结果表明 ,系统中考虑压裂液滤失对缝中流量和压力分布的影响而建立的水平裂缝延伸模型 ,由于考虑了水平裂缝中压裂液流量的实际分布 ,能准确描述水平裂缝延伸过程 ,模拟出的缝中流量沿裂缝半径逐渐减小至零 ,计算出的缝裂缝半径和缝宽均比原有模型结果小 ,符合水平裂缝压裂的现场实际。提出的迭代数值解法稳定可靠 ,其方法和思路为水平裂缝参数分析和施工设计奠定了基础。
In order to meet the needs of engineering design, the pressure distribution, horizontal crack width and horizontal crack extension radius of horizontal cracks are re-established on the basis of stress analysis of fluid elements in the seams, based on the theories of fluid mechanics, elasticity mechanics and material balance Mathematic model and the numerical model which is discretized by the difference method, and solved by Newton iterative method. These models comprehensively considered the influence of fracturing fluid loss on the pressure distribution and flow distribution in the fracture, and accurately simulated the horizontal fracture propagation. The results show that the horizontal crack propagation model considering the effect of fluid loss on fracture flow and pressure distribution in the system can accurately describe the horizontal crack propagation process due to the actual distribution of fracturing fluid flow rate in horizontal fractures , The flow rate in the simulated fracture decreases gradually along the fracture radius to zero. The calculated fracture radius and fracture width are smaller than those of the original model, which is in line with the actual situation of horizontal fracture. The proposed iterative numerical method is stable and reliable. The method and the idea of the iterative numerical method are the foundation for horizontal crack parameter analysis and construction design.