A Thermo-Visco-Plastic Study of the Wolfcamp Shale: Experiments and Modeling
Authors: Rassouli F. S. , Haghighat E. , Juanes R. , Zoback M. D. 
Published: August 2024

ABSTRACT:
Here, we present a preliminary laboratory study of visco-plastic deformation at representative reservoir temperatures. We performed three loading and unloading stages on each sample, measuring time-dependent deformation after each stage. For two samples, we started at room temperature (24 °C), then increased temperature to 50 °C and then from 50°C to 80°C. We reported that the elevated temperatures soften the samples and increase the creep deformation rate. However, the creep behavior of the sample under a cyclic loading pattern and at a constantly elevated reservoir temperature is similar to what we observed at room temperature in our previous studies, following creep-hardening processes. To better isolate the visco-plastic deformation at elevated temperatures, we performed one experiment at 80 °C and then applied the loading and unloading cycles to the sample. This sample showed creep hardening after applying three cycles of creep loading at 80°C. We extended a visco-plastic creep model that accurately reproduced room temperature experiments to account for the model's temperature dependence on visco-plastic parameters. Here, our modeling is focused on describing the mechanism, however, we realize the need for anisotropic considerations, which we postpone to a later study.

1. INTRODUCTION
Propagation of hydraulic fractures requires the pressure inside the fractures to exceed the magnitude of the least principal stress. In this context, vertical propagation of hydraulic fractures in unconventional shale formations is controlled by variations of the magnitude of the least principal stress with depth. In previous papers, we showed that the magnitude of stress variation is a function of the relative degree of viscoplastic stress relaxation (Sone and Zoback, (2014), Rassouli and Zoback (2016), Ma and Zoback (2017), and Xu et al. (2017)). This time-dependent viscoplastic behavior is affected by the mechanical and mineralogical properties of the rocks, as well as the reservoir stress and thermal conditions.
The degree of anisotropy and the direction of the applied differential stress with respect to the bedding plane of the rock formations are correlated with their time-dependent deformation. In general, a higher viscoplastic deformation is expected in isostress conditions, where the direction of the applied differential stress is orthogonal to the orientation of bedding planes. (Sone and Zoback (2013), and Rassouli and Zoback (2016)). Shale rocks with higher porosity and preexisting micro-cracks show higher creep compliance (Sone and Zoback (2014), and Rassouli and Zoback (2018)). Variations in the lithology of the formation change the viscoplastic response of the reservoirs (Alalli and Zoback (2018)). Higher clay, kerogen, and soft mineral contents in addition to the presence of porous carbonate minerals enhance the viscoplastic deformation of the rocks (Sone and Zoback (2014), Rassouli and Zoback (2016), Ma and Zoback (2017), and Rassouli and Zoback (2018)). Water content increases the time-dependent deformation of shales by reducing the frictional coefficient between the grains (Rassouli and Zoback (2018)). As the ductile flow of minerals is known as a thermally activated process, the higher temperature at reservoir depths increases the time-dependent deformation of shales (Rassouli (2017), and Rybacki et al. (2017)). The stress regime and the level of the reservoir anisotropy have a direct effect on the viscoplastic deformation of shales. Higher confining pressure increases the shear strength and reduces the ductile deformation of rocks (Sone and Zoback (2014), and Geng et al. (2017)). The viscoplastic deformation in normal/strike-slip faulting systems results in stress relaxation, meaning that the three principal stresses become more isotropic such that the least principal stress increases (Sone and Zoback (2014)). This would make some formations more difficult to fracture hydraulically or it could create stress regime barriers to the vertical propagation of hydraulic fractures from other intervals (Xu et al. (2017)).