颗粒尺度下砂岩出砂几何约束条件及毛管束模型

 对疏松砂岩油藏开发过程中的出砂问题进行研究，从细观尺度分析了砂岩颗粒的受力状态，明确了出砂的力学条件，提出砂岩出砂的3 个几何约束条件。分析认为，力学条件及几何条件同时约束砂粒的运移。将地层孔隙用毛管束表示，通过分析流体和砂岩颗粒在毛管束中的受力情况，建立了砂岩出砂毛管束模型，推导出砂岩出砂临界流速公式。研究表明，砂粒直径、孔隙度和岩石颗粒摩擦角增大，临界流速增大；流体黏度增大，临界流速变小。建立的临界流速公式与实验结果对比，平均误差为15.9%，符合较好。砂岩出砂几何约束条件丰富了砂岩出砂机理，建立的临界流速公式简明，可方便应用于矿场实践。

Geometrical Constraints and Capillary Bundle Model for Sand Production in Sandstone Reservoir at Particle Scale

The sand production for loose sandstone reservoirs is studied. The stress conditions from the microscopic scale are analyzed with a clear understanding of the mechanical condition. Three geometrical constraints for the sand production are considered. For the reservoir to produce sands, the geometrical conditions and mechanical conditions must simultaneously be satisfied. The formation pore is expressed by the capillary bundle. The capillary bundle model for the sand production is established by analyzing the stress conditions between the fluid and the sand particles. A formula for the critical velocity is obtained. The critical velocity increases with the increase of the sand diameter, the porosity and the sand particle frictional angle. The critical velocity decreases with the increase of the viscosity. The formula gives results in a good agreement with experiments,and the average error is only 15.9%. This geometrical constraints are proposed which may help the mechanism of the sand production. The formula of the critical velocity presented in this paper can be used conveniently in the oil field.