Upscaling the creep behavior of clay-rich and quartz-rich shales from nanoindentation measurements: Application to the Wufeng-Longmaxi shale, China

Creep of shale controls the stability of fault gouge in sedimentary rocks, aseismic deformation in the upper crust, and several engineering operations, such as proppant embedment, reservoir subsidence, and wellbore stability during unconventional shale gas exploitation. However, measuring the creep properties of shale is challenging due to the multi-scale structure of this rock. Here, our goal is to assess how creep parameters measured at the core sample scale depend on those measured at the nanoscale in shales. We selected three clay-rich and quartz-rich shale samples and conducted a series of experiments on shale samples at two scales: nanoindentation creep measurements on thin sections, and uniaxial creep tests on core samples. The creep parameters, including creep displacement (Δh), indentation creep (CIT), creep strain rate sensitivity (m), contact creep modulus (C), and viscoelastic parameters (E1, E2, η1, and η2) of the Burgers' model, were calculated by fitting the nanoindentation creep data of each single-phase component of shale matrix. From these data, we upscale the creep parameters (E1, E2, and C) of shale matrix to those of the bulk shale. Upscaled E2 and C values based on the Mori-Tanaka scheme are found to be relatively close to those measured in previous microindentation study on Longmaxi shale and are consistent with our measurements in uniaxial creep tests on core samples of clay-rich shale and quartz-rich shale. The upscaling value of the elastic parameters, E1, is almost twice larger than the results from uniaxial creep test. We interpret this difference as due to low elastic stiffness along grain contacts of the shale that nanoindentation measurements underestimate. Our results show a consistency of some creep parameters upscaled from nanoindentation data and those measured at a macroscopic scale on core samples.