考虑位置随机性的固体颗粒起动临界流速研究

水平井钻井、砾石充填及冲砂等作业都涉及到固液两相流动的固体颗粒起动问题。液流作用下颗粒的起动与其在床面上的沉没位置有关,沉没位置的随机性导致颗粒起动的随机性。引入颗粒无因次沉没度随机变量,将其概率密度视为均匀分布,考虑颗粒重力、水流推力、上举力、水柱静压力和粒间粘结力以及各力臂与沉没度的关系,通过力矩平衡分析,建立了考虑颗粒起动随机性的临界流速公式。结合无因次沉没度的概率分布函数,在临界流速与颗粒起动标准之间建立了定量关系,为一定颗粒起动标准下的临界流速计算提供了实用公式。用得出的公式进行了实例计算,并将计算结果与已有试验结果进行了对比,在0.001～10mm粒径范围内两者吻合较好。

Critical velocity model for grain incipient motion in consideration of the randomness of grain location

Incipient motion of solid grain in solid-liquid two\|phase flow is often concerned in many petroleum technologies, such as horizontal drilling, gravel-packing and sand washing. The random deposit location of grains on the bed surface causes the randomness of the incipient motion of solid grains. A random variable of dimensionless submergence was introduced to denote the location randomness. The probability of the variable distribution was counted as uniform. In consideration of buoyant weight, fluid thrust force, uplift force, cohesive force of grains, and the relationship between force arm and submergence, a calculation model for critical velocity of solid grain was established by means of moment equilibrium analysis. Integrating the critical velocity equation and submergence probability distribution equation, a quantitative relationship between the critical velocity and the incipient motion velocity of grains was built, which offers a practical formula for calculation of the critical velocity under certain incipient motion criterion. The results of this work agree well with the experimental data for the grain with diameter range from 0.001 mm to 10 mm.