Microseismic estimates of hydraulic diffusivity in case of non-linear fluid-rock interaction

As a rule, rock stimulation by fluid injection induces microearthquakes. Assuming that pore-fluid pressure diffusion is responsible for this phenomenon, one can use seismicity to estimate the hydraulic properties of rocks. Previously, for the estimation of hydraulic transport properties from the triggering front, it has been assumed that they are independent of time and pressure. However, fluid injections can strongly change permeability of rocks (e.g. hydraulic fracturing). In this paper, we investigate what kind of diffusivity estimates are provided by the triggering front in cases where hydraulic transport properties are functions of pore-fluid pressure (i.e. they are changing during the injection). In this case, the pressure relaxation results in a non-linear pore-fluid pressure diffusion associated with heterogeneously and time-dependent distributed permeability. We consider numerically two models of pressure-dependent hydraulic diffusivity, a power law and an exponential law. We generate synthetic microseismicity by solving corresponding 1-, 2- and 3-D non-linear diffusion equations. Our results show that the triggering front provides reasonable estimates of the effective diffusivity approximately corresponding to the hydraulic diffusivity resulting from the stimulation (including hydraulic fracturing) of rocks and thus constitute a significant conceptual update of the seismicity-based reservoir characterization approach.