New approach for predicting time-dependent deformation of shale rock: a modified fractional-order creep constitutive model

Time-dependent deformation is critical for ensuring safety and efficiency in horizontal well stability and the long-term permeability of shale gas. Purely empirical methods that lack a physical background cannot reflect the mechanism of shale creep, and classical elemental models lack control over both viscous and elastic parameters, leading to poor nonlinear behavior. Moreover, an appropriate amount of time is necessary to perform time-dependent deformation testing as such testing usually takes a long time. Additionally, reports on radial creep data for shale are rare. In this study, several short-term and long-term deformation experiments were conducted on shale samples to evaluate their deformation behavior. Furthermore, a modified creep constitutive model was proposed to fit the measured data; the result was a perfect fitting. The experimental results showed that axial deformations have significant anisotropy and differential stress dependence, whereas radial deformations do not. Volumetric deformations can form three types of strain-time profiles. Creep compliance (3 h) was negatively correlated with Young's modulus and Poisson's ratio. Model validation showed that the shale creep deformation would be incorrectly estimated without the new model, which outperformed the classical model in the deceleration stage. Model parameters alpha and beta, which reflect the degree of viscoelasticity in the shale, were negatively correlated with Young's modulus and the differential stress. In addition, using the new model to predict the behavior of creep deformation through short-term (48 h) creep experiments is feasible.