为精确模拟井眼蠕变历程,预测和预防井壁坍塌、套管挤毁和卡钻等工程事故,在前人研究的基础上,将弹簧壶元件引入经典元件模型中,得到了分数阶模型的蠕变柔量,并验证了分数阶模型的拟合效果。研究认为分数阶模型能够实现少参数、高精度的模拟,并且相应参数的物理意义也更加明确。通过黏弹对应性原理,模拟了钻进和压井过程中的井眼蠕变情况,通过调整求导阶数可以使该模型在理想弹性体模型和标准固体模型之间转化,因此,基于标准固体本构方程和理想弹性体本构方程建立的井眼缩径模型仅是该模型的特例。分析模拟结果认为调整分数阶元件的阶数,可以在加快瞬态蠕变的同时降低稳态蠕变的速度,对蠕变曲线进行非对称调整,经典模型则无法通过调整单一参数达到这一目的,分数阶黏弹性本构方程拟合高度非线性实验数据的能力更强。图6参25
To simulate the evolution of wellbore creep accurately, predict and prevent severe accidents such as borehole wall sloughing, casing collapse and sticking of the drill, based on previous studies, the springpot element was introduced into the classical element model and the creep compliances of the fractional constitutive models were deduced. The good fitting effect of fractional constitutive model was verified. The study shows the fractional constitutive model can simulate creep with high accuracy and less input parameters, and the physical significance of the input parameters are clearer. According to the correspondence principle of viscoelastic theory, a wellbore creep model including drilling and killing processes was built up. By adjusting the value of fractional orders, the model can transform between the models of ideal elastic material and standard solid, which implies the classical wellbore shrinkage model based on standard solid model and ideal elastic model are just special cases of this model. If the fractional order is adjusted, the creep curve will change asymmetrically, which can be can be regulated by the speeding up of the transient creep and lowering the rate of steady creep, which can not be accomplished by adjusting one parameter in the classical models. The fractional constitutive model can fit complicated non-linear creep experiment data better than other models.
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