Modeling the viscoelasticity of shale by nanoindentation creep tests

To investigate the viscoelastic behavior of shale, clay-rich and quartz rich shale samples were examined by nanoindentation creep tests. Moreover, the effects of different holding times (0, 15, 60, 120, and 220 s) on the mechanical and viscoelastic properties of the shales were compared. The experimental results show that the shale sample with the shortest holding time has the highest rock hardness and Young's modulus values, and the sample with the longest holding time has the lowest values, reflecting the effect of the creep on mechanical behavior. Contact creep compliance and cut-off time decreased with increasing loading rate. In contrast, an increase in reduced modulus, hardness, displacement variation and contact creep compliance variation during the holding time was noticed. In addition, the measurements were converted into viscoelastic parameters by the three-element Voigt, Burgers, and two-dashpot Kelvin models. All of these three rheological models were able to produce good fits to actual nanoindentation measurements. The two-dashpot Kelvin model provides the results with the highest accuracy, but the standard deviation is the highest, indicating more fitting parameters can induce model instability. The elastic time fitting parameters decrease with increased holding, while the viscous fitting parameters increase with increasing time, indicating that the viscosity increases with increasing time. By using this model, the data from laboratory tests can be extrapolated to predict shale's long-term creep behavior. Comparing to other two models, the regression parameter of two-dashpot Kelvin model is relatively lower. The fitting time constants and the regression parameters calculated by the same models for clay rich sample is relatively lower than that of quartz rich sample, which is all mainly related to the soft clay and kerogen contents. Thus, the utilization of existing creep experimental data for predicting viscous parameters of clay-rich shale with two-dashpot Kelvin model should be careful.