A Viscoplasticity Model for Shale Creep Behavior and Its Application on Fracture Closure and Conductivity

Hydraulic fracturing is the main means for developing low-permeability shale reservoirs. Whether to produce artificial fractures with sufficient conductivity is an important criterion for hydraulic fracturing evaluation. The presence of clay and organic matter in the shale gives the shale creep, which makes the shale reservoir deform with time and reduces the conductivity of the fracture. In the past, the influence of shale creep was ignored in the study of artificial fracture conductivity, or the viscoelastic model was used to predict the conductivity, which represents an inaccuracy compared to the actual situation. Based on the classical Perzyna viscoplastic model, the elasto-viscoplastic constitutive model was obtained by introducing isotropic hardening, and the model parameters were obtained by fitting the triaxial compression creep experimental data under different differential stresses. Then, the constitutive model was programmed in a software platform using the return mapping algorithm, and the model was verified through the numerical simulation of the triaxial creep experiment. Then, the creep calculation results of the viscoplastic constitutive model and the power law model were compared. Finally, the viscoplastic constitutive model was applied to the simulation of the long-term conductivity of the fracture to study the influence of creep on the fracture width, and sensitivity analysis of the influencing factors of the fracture width was carried out. The results show that the numerical calculation results of the viscoplastic model were in agreement with the experimental data. The decrease in fracture width caused by pore pressure dissipation and reservoir creep after 72 h accounts for 32.07% of the total fracture width decrease.