Shapiro, Serge A. and Dinske, Carsten (2009) Scaling of seismicity induced by nonlinear fluid-rock interaction. Journal of Geophysical Research, 114 (B9). DOI: https://doi.org/10.1029/2008JB006145
Full text not available from this repository.Abstract
Fluid injections into geothermal systems sometimes can produce significant seismic events with magnitudes of up to 4. However, in the case of hydraulic fracturing of hydrocarbon reservoirs, such events occur extremely seldom. In the last case, in contrast to the former one, the structure of rocks is being actively destroyed (e.g., opening of tensile fractures) and the fluid-rock interaction is strongly nonlinear (e.g., a strong increase of permeability). What is the role of this nonlinearity? We consider nonlinear pore pressure diffusion to explain features of seismicity. We formulate seismicity triggering front. Its propagation is sensitive to a grade of nonlinearity, to spatial dimension of diffusion, and to the injection rate. We show that a probability of an event with a magnitude larger than a given one increases proportionally to the injected mass. An increase of this probability with time is insensitive to the nonlinearity. We compare different borehole experiments. In some cases the injection produces clearly nonlinear impact on rocks. In others this impact is approximately linear. We find a well agreement with our theory. We observe an insensitivity of temporal increments of magnitude probability to the grade of nonlinearity. These increments are controlled by injection-rate increments. In contrast, nonlinear fluid-rock interactions are characterized by a strong dominance of small earthquakes. Defects activated by a nonlinear diffusion possibly obey Gutenberg-Richter statistics with anomalous high b values. In the case of a linear diffusion, magnitude distributions of events are probably inherited from pre-existing fracture systems.