顶部水泥脉冲振动的数学模型

THE MATHEMATICAL MODELS OF TOP CEMENT PULSATION

介绍了顶部水泥脉冲振动技术的基本原理和方法。文中根据牛顿定律、质量守恒定律及水泥浆的宾汉塑性流变性 ,在顶部水泥脉冲振动作用下 ,建立了水泥浆中 ,一维压力传播的波动方程的数学模型。同时根据弹性理论和液体可压缩性 ,推导出了井眼岩石、水泥浆及套管共同作用下的当量体积弹性模量 ,并讨论了顶部水泥脉冲振动波动方程数学模型的物理意义及其具体应用时所要考虑的问题 ,为固井时 ,顶部水泥脉冲振动的优化设计、压缩机的优化及优选提供了理论依据。

The basic principle and approach of Top Cement Pulsation(TCP) technology was introduced in the paper. According to the Newton's second law of motion, the law of conservation of mass,and Bingham plastic flow equation of slurry,as well as under top cement pulsation,the mathematical models of one dimensional pressure pulse propagation downwards in the cement column was established.At the same time,on the basis of elastic theory and liquid compressibility,the effective bulk elastic modulus under the joint action of wellbore rock,slurry and casing was derived.The physical meaning of TCP wave mathematical models and its concrete problems in applications were also discussed. It provides the mathematical models for the optimal design of top cement pulsation and parameters of compressor.