计算砂岩出砂临界压力梯度的新方法

摘要：将毛管束模型引入到出砂问题的研究中来，同时考虑了表皮效应，建立了出砂毛管束物理模型，该模型能够将复杂的多孔介质固液耦合问题转化为宏观的管流流动问题，通过分析砂岩颗粒在毛管束中的受力和运动，建立了砂岩出砂数学模型，分析了出砂过程动态机理，推导了出砂临界压力梯度公式，该公式从理论上对出砂问题进行了定量表征。敏感性分析表明：随着表皮和表皮厚度的增大，临界压力梯度增大；随着砂粒半径的增大，临界压力梯度也随之增大。为了验证公式的有效性，设计了砂岩出砂物理模拟实验，结果表明平均误差为16%，和实验符合较好。

A new way to calculate the critical pressure gradient of sand production

Abstract: A capillary-tube model is proposed in this work which could transform the porous medium solid liquid coupling problems to duct flow problems, and the dynamic mechanism of sand production is studied according to the fluid mechanics as well as skin effect considered. The critical pressure gradient formula is as a quantifying characterization for the sand production. Based on sensitivity analysis, the critical pressure gradient rises with the skin effect and its thickness increasing. With the sand particle radius increasing, the critical pressure gradient also rises. In order to validate the effectiveness of the formula, a physical simulation experiment is designed. The formulae has a good agreement with experimental, and the average error is only 16%.