We have already seen that the method of passive seismic monitoring has significant potential for characterizing physical processes related to fluid stimulations of rocks. One of its important modern applications is spatial mapping of hydraulic fracturing. On the other hand, understanding spatio-temporal dynamics of microseismic clouds contributes to reservoir characterization. It helps to monitor and to describe hydraulic fractures.

We will start this chapter with a simple intuitive approach to the quantitative interpretation of hydraulic-fracturing-induced seismicity. The approach is based on a volume-balance model of the growth of long thin simple-geometry (nearly 1D) tensile hydraulic fractures. Then we will introduce a case study from a gas shale showing fracturing of a 3D rock volume. This motivates a more-general formulation of non-linear fluid–rock interaction by hydraulic stimulations of reservoirs. We show that linear pore-pressure relaxation and hydraulic fracturing are two asymptotic end members of a set of non-linear diffusional phenomena responsible for seismicity triggering. We formulate a general non-linear diffusion equation describing the pore-pressure evolution and taking into account a possibly strong enhancement of the medium permeability. Both linear pore-pressure relaxation and hydraulic fracturing can be obtained as special limiting cases of this equation.

From this formulation we derive an expression for the triggering front of fluid-induced seismicity, which is valid in the general case of non-linear pore-pressure diffusion. Our results are valid for an arbitrary spatial dimension of diffusion and a power-law time dependence of the injection rate. They show that, the larger the non-linearity of the fluid–rock interaction, the more strongly propagation of the triggering front depends on the mass of the injected fluid. Further, we investigate the nature of diffusivity estimates obtained from the triggering front of non-linear diffusion-induced seismicity. Finally, we introduce a model of anisotropic non-linear diffusion and show its application to the gas-shale data set mentioned earlier.

Seismicity induced by hydraulic fracturing

Here, we show that evaluation of spatio-temporal dynamics of a cloud of induced microseismic events can contribute to characterization of the hydraulic-fracturing process.