Based on the material balance principle, the fluid mechanics theory, the theory of elastic mechanics, and the fracture mechanics theory, the authors have established a model of a quasi three-dimensional crack extension of the artificial interlayer fracture, combined with the boundary conditions and the initial conditions. Based on the analysis and the solution of the established quasi three dimensional crack extension model, the simultaneous equation of continuity, the pressure drop equation, the equation of the crack width, and the equation of the fracture height are obtained. The analysis results show that the fracture height decreases with the increase in the sand content. When the proppant sinks to the bottom of the fracture, the artificial plugging section is formed. The fracture height decreases with the increase in the buoyancy agent content in the reservoir. With increase in the displacement, the fracture length tends to increase. With increase in the Poisson’s ratio, the fracture length decreases.

基于材料平衡原理、流体力学理论、弹性力学理论和断裂力学理论，结合边界条件和断裂力学理论，建立了人工层间断裂准三维裂纹扩展模型。初始条件。在对建立的准三维裂纹扩展模型进行分析和求解的基础上，得到了连续性联立方程、压降方程、裂纹宽度方程和断裂高度方程。分析结果表明，裂缝高度随着含砂量的增加而减小。当支撑剂下沉至裂缝底部时，形成人工封堵段。裂缝高度随着储层中浮力剂含量的增加而减小。随着位移的增加，断裂长度趋于增加。随着泊松比的增加，裂缝长度减小。