Computation model of proppant embedment depth based on dimensional analysis

Hydraulic fracturing is designed to form a high-conductivity fracture. The proppant will embed into the formation rock, especially in soft rock, owing to the interaction between proppant and fracture surface after fracture closure. Proppant embedment would reduce the fracture width and then lower the fracture conductivity. According to dimensional analysis, the rock is assumed to be an elastic material. Using the theory of elasticity to describe the stage of elastic deformation and analysis of the corresponding simplified embedding process, the study establish the static computation model of the two-dimensional infinite half plane and three-dimensional infinite half space model of the proppant embedment. According to laboratory results, the calculation model was modified, got an effective correction factor and analyzed the causes of errors, then discussed the factors which have impact on proppant embedment. The result calculated by the model in this paper can be reference of prop- pant optimization in on-site fracturing for a certainty degree.

基于拟力法的钢支撑非线性滞回行为模拟

钢支撑在轴力作用下会同时发生材料非线性和几何非线性,复杂的力与变形关系是数值模拟过程中的重点与难点。该文基于拟力法的基本理论,提出了支撑非线性滞回行为的计算模型,通过塑性转动铰来模拟由屈曲行为引起的塑性弯曲变形;通过滑动铰来模拟由拉伸屈服和增长效应产生的轴向塑性伸长行为,模型中计及了弹性弯曲变形本身的几何非线性行为。该模型物理意义简单、力学行为明确,在模拟支撑非线性滞回行为的过程中保持初始刚度不变,塑性铰的变形可直观地衡量支撑的屈曲程度。数值模拟与试验结果对比验证了该方法的精确性与适用性。将该模型应用于某钢框架-支撑结构地震反应分析中,计算结果表明:该方法可以模拟支撑在复杂荷载作用下的非线性行为,具备拟力法所特有的精确、高效及稳定等优点。