Rate and State Simulation of Two Experiments with Pore Fluid Injection Under Creep Conditions

Recent industrial processes that involve injection of fluids, such as geothermal stimulation, disposal of waste water from hydraulic fracturing and carbon sequestration, have induced seismicity that has caused concern and resulted in discontinuation of the activity. Although field observations are the ultimate test of the effects of pore fluid on failure, their interpretation is complicated by heterogeneity of hydrologic and mechanical structure, and pumping and loading history. In particular circumstances, well-designed field tests can overcome some of these limitations. Laboratory experiments, despite their limited size and time scales, provide a more controlled environment that can yield an understanding of fundamental processes. Simple models that simulate the experiments can assess whether the mechanisms included in the models are sufficient to describe well the response or more complex formulations are needed. In addition, simulations can extend results for parameter values and loading programs beyond those achievable in experiments and aid in extrapolation to field applications.

This work uses a spring-block model and rate and state friction to simulate experiments conducted in a double direct shear apparatus on simulated carbonate fault gouge (Scuderi et al., EPSL, 2017) and on a shale bearing rock (Scuderi and Collettini, JGR, 2018). Both sets of experiments used the same loading protocol and injected pore fluid under creep conditions. When velocity strengthening rate and state friction is used to simulate the experiments on the simulated carbonate fault gouge the results agree well with the observed onset of tertiary creep in the experiment. Thus, the simulation reinforces the observation that pore fluid injection can induce rapid slip even when the friction relation is velocity strengthening. The rate and state framework provides an interpretation alternative to the standard one of the Mohr's circle moving to the left as pressure increases. In the rate and state framework, the friction coefficient must increase with pore pressure increase. The shale has a very low nominal friction coefficient (0.28) and is much more velocity strengthening than the carbonate. The simulation agrees with the observations that increases in pore pressure induce an increase in slip velocity but the magnitudes reach only about 100 µm/s by the end of the experiment. The simulation predicts reasonably well the times at which representative values of the slip velocity and displacement occur but the overall agreement of simulation and observation is not as good as for the carbonate. Mechanisms other than rate and state friction, for example, direct dependence of the friction coefficient on slip and porosity changes, may be significant.