Fluid injections into unconventional reservoirs, performed for fluid-mobility
enhancement, are accompanied by microseismic activity also after the
injection. Previous studies revealed that the triggering of seismic events can
be effectively described by nonlinear diffusion of pore fluid pressure
perturbations where the hydraulic diffusivity becomes pressure dependent. The
spatiotemporal distribution of postinjection-induced microseismicity has two
important features: the triggering front, corresponding to early and distant
events, and the back front, representing the time-dependent spatial envelope
of the growing seismic quiescence zone. Here for the first time, we describe
analytically the temporal behavior of these two fronts after the injection
stop in the case of nonlinear pore fluid pressure diffusion. We propose a
scaling law for the fronts and show that they are sensitive to the degree of
nonlinearity and to the Euclidean dimension of the dominant growth of
seismicity clouds. To validate the theoretical finding, we numerically model
nonlinear pore fluid pressure diffusion and generate synthetic catalogs of
seismicity. Additionally, we apply the new scaling relation to several case
studies of injection-induced seismicity. The derived scaling laws describe
well synthetic and real data
