卡森模式流变参数的合理表达及公式推导分析

The Reasonable Expression of Rheological Parameters of Casson Model and the Analysis of Formula Derivation

钻井液卡森模式中流变参数ηc^(1/2)、τc^(1/2)的计算公式在各类资料中不尽相同,给卡森模式的推广应用带来困扰。现从卡森模式的两个基本经验公式出发对流变参数ηc^(1/2)、τc^(1/2)进行推导,对比分析并找出公式差异的原因:除个别因采用基本经验公式的细微差异造成不同外,其余均为使用单位的不统一和^(1/2)次方共同作用的结果。其中,流变参数τc^(1/2)因基本经验公式差异而得出两种不同表达,进一步将两种τc^(1/2)用于24种钻井液不同速梯下的切力推算,并与实测钻井液切力数据进行精度对比分析,评估更为合理的经验公式。根据验算结果并参照常用钻井液单位习惯,推荐卡森模式流变参数的合理表达为:ηc^(1/2)=1.195(θ600^(1/2)-θ100^(1/2)),mPa·S;τc^(1/2)=0.493[(6θ100)^(1/2)-θ600^(1/2)],Pa。结尾对卡森模式应用于钻井液流变学的优势特点及下部需要深入研究的方向进行了展望。

Calculation formulas of rheological parameters ηc^(1/2) and τc^(1/2) in the Casson model of drilling fluid are different in all kinds of data which makes Casson model difficult to popularize.From the rheological parameters ηc^(1/2) and τc^(1/2) derived from the two basic empirical formulas of the Casson model it is concluded that different expressions of rheological parameters ηc^(1/2) and τc^(1/2) are the result of the disunity of units and the interaction of ^(1/2) power except on a case-by-case basis.According to the checking results and reference to commonly used drilling fluid units,the recommended reasonable expressions of rheological parameter are ηc^(1/2)=1.195(θ600^(1/2)-θ100^(1/2)),mPa·S;τc^(1/2)=0.493[(6θ100)^(1/2)-θ600^(1/2)],Pa.The advantages of Carson model in drilling fluid rheology are reviewed and the future direction of further research is prospected.