井下泡沫水泥浆密度计算模型修正

Revision of Mathematical Model of Foamed Cement Slurry Density under Down-Hole Conditions

为准确描述泡沫水泥浆密度与井深的关系,研究了泡沫水泥浆密度在不同温度和不同压力条件下的变化规律。以真实气体状态方程为基础,综合考虑温度、压力对泡沫水泥浆密度的影响,建立了泡沫水泥浆密度随压力和温度变化的计算模型。通过室内模拟试验对建立的计算模型进行了验证和修正,得到了可以定量计算井下任意井深处泡沫水泥浆真实密度的计算模型,对该修正模型进行隐函数积分,便可得到井下任意井深处的泡沫水泥浆真实密度和静液柱压力。修正后的模型综合考虑了温度和压力以及水泥浆泡沫体积分数对密度的影响,可为平衡压力固井设计奠定良好的基础。

In order to describe the relationship between the depth and the density of foamed cement slurry, the behavior of foamed cement slurry density at different temperature and pressure was investiga- ted. Based on the equation of state of real gas, considering the effect of temperature and pressure on foamed cement slurry density,a mathematical model of foamed cement slurry density at different temperature and pressure was set up. By laboratory the mathematical model was verified and corrected, and a mathematical model which could quantitatively calculate the foamed cement slurry density at any depth was worked out. By the implicit function integral on the revised model, foam cement slurry density at any depth of the well and hydrostatic pressure could be calculated. The revised model, considering the effects of temperature and pressure as well as the bubble volume in cement slurry on density,lays solid foundation for cementing de- sign with balanced pressure.