Four-Parameter Rheological Model and Its Application in Cementing Slurry
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摘要: 为了提高固井作业中水泥浆顶替效率的计算精度,提出用四参数流变模式描述固井水泥浆的流变性能。采用回归分析的数学方法得到了宾汉、幂律、卡森、赫-巴及四参数模式的流变参数,然后用残差平方和的均值Sr来表征各模式与实测值的拟合效果。充分考虑各种力系的平衡关系建立了四参数模式下水泥浆在倾斜偏心环空中顶替钻井液的数学模型。并选择应用于现场的6种适用于复杂井固井的新型水泥浆体系的流变性测量数据进行了验证。四参数流变模式在各水泥浆体系不同剪切速率下的计算值与实测值的残差平方和的均值都小于1.1,一般在0.2左右,最小达到了0.04,其残差平方和均值之和2.81,远小于宾汉、幂律、卡森和赫-巴模式。验证结果表明,四参数流变模式在各水泥浆体系不同剪切速率下的计算值与实测值的残差平方和的均值都最小,拟合最为精确,能在全剪切速率范围内精确描述水泥浆的流变性,适用于各种水泥浆体系,其顶替模型适用于各类井型。Abstract: In order to improve the calculation accuracy of slurry displacement efficiency in cementing operation,four-parameter rheological model was proposed for exact description of slurry rheological performance.The parameters of Bingham,Power-law,Carson,H-B and four-parameter rheological models were obtained by mathematical regression analysis.The fitting result between the calculated values of each model and the measured values is described by the mean of the residual sum of squares (Sr).Considering the balance of all the forces,a mathematical model of slurry displacing drilling fluid in inclined eccentric annulus with four-parameter model was developed.The rheological models were verified by measured rheological data of six types of cementing slurries.The means of the residual sum of squares between measured values and calculated values,six slurries with four-parameter rheological model,are all less than 1.1,generally at about 0.2,and minimum value is 0.04.Moreover,the residual sum of squares is 2.81,much less than that of Bingham,Power-law,Carson,H-B models.The results showed that the mean of the residual sum of squares with four-parameter rheological model for six kinds of slurries is the smallest,it can precisely describe cementing slurry rheological characteristics at the full range of shear rate,and the displacement models are suitable for all kinds of slurries in all well types.
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