A wellbore creep model based on the fractional viscoelastic constitutive equation

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.