S U M M A R YAs a rule, rock stimulation by fluid injection induces microearthquakes. Assuming that porefluid 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.

S U M M A R YMost fractured porous rocks show a strong dependence of their fluid transport properties on the effective pressure and thus on the pore-fluid pressure. We investigate the case where the hydraulic transport properties are exponentially dependent on pore-fluid pressure. As a consequence, the process of pore-fluid pressure diffusion is governed by a non-linear diffusion equation. Solutions of this equation that describe fluid injection experiments are analysed and the associated microseismic signatures are explored. In particular, it is shown that this process of non-linear pore-fluid pressure diffusion allows us to define two signatures. One which is the triggering front corresponding to the triggering of microseismic events without changing the fluid transport properties significantly. The other signature is the so-called fracturing domain. It triggers the majority of microseismic events and alters the fluid transport properties significantly. Evidence for the microseismic signature of a fracturing domain at the Fenton Hill hydrofrac experiment is given.

For the successful development and operation of hydrocarbon or geothermal reservoirs, knowledge of the hydraulic transport is of crucial importance. Because fundamental physical processes of borehole fluid injections are still insufficiently understood, gathering information about transport properties of rocks under field conditions is quite difficult. However, a substantial contribution in determining the permeability evolution can be obtained by understanding the distribution of induced seismicity in space and time. We have analyzed spatio-temporal characteristics of seismicity recorded during a hydraulic fracturing treatment in the Barnett Shale. In this study, we show that the fluid-rock interaction is nonlinear. To explain corresponding spatio-temporal features of induced seismicity, we considered pore pressure diffusion based on a power-law pressure dependence of permeability. A scaling approach was used to transform clouds of hypocenters of events obtained in a hydraulically anisotropic nonlinear medium into a cloud which would be obtained in an equivalent isotropic but still nonlinear medium. For this, we used a concept of a factorized anisotropic pressure dependence of permeability and found that it is in agreement with the microseismic data under consideration. We used a numerical modeling approach to generate synthetic seismicity by solving nonlinear diffusion equations. The pore-pressure field obtained from flow rates was calibrated with the pore-pressure field computed for injection pressures. This yielded an estimate of the uniaxial storage coefficient and permitted us to compute the permeability evolution inside the fracture stimulated reservoir. Following our modeling, we generated synthetic seismicity whose spatio-temporal features are similar to the ones observed in the case study. This indicates that a nonlinear diffusion with a pressure-dependent permeability seems to provide a reasonable model of the hydraulic-fracture stimulation under consideration. A power-law pressure dependence of stimulated permeability may be a more general characteristic for shales.

A B S T R A C TBorehole fluid injections are accompanied by microseismic activity not only during but also after termination of the fluid injection. Previously, this phenomenon has been analysed, assuming that the main triggering mechanism is governed by a linear pressure diffusion in a hydraulically isotropic medium. In this context the socalled back front of seismicity has been introduced, which allows to characterize the hydraulic transport from the spatiotemporal distribution of post-injection induced events. However, rocks are generally anisotropic, and in addition, fluid injections can strongly enhance permeability. In this case, permeability becomes a function of pressure. For such situations, we carry out a comprehensive study about the behaviour and parametrization of the back front. Based on a model of a factorized anisotropic pressure dependence of permeability, we present an approach to reconstruct the principal components of the diffusivity tensor. We apply this approach to real microseismic data and show that the back front characterizes the least hydraulic transport. To investigate the back front of non-linear pore-fluid pressure diffusion, we numerically consider a power-law and an exponential-dependent diffusivity. To account for a post-injection enhanced hydraulic state of the rock, we introduce a model of a frozen (i.e., nearly unchanged after the stimulation) medium diffusivity and generate synthetic seismicity. We find that, for a weak non-linearity and 3D exponential diffusion, the linear diffusion back front is still applicable. This finding is in agreement with microseismic data from Ogachi and Fenton Hill. However, for a strong non-linear fluid-rock interaction such as hydraulic fracturing, the back front can significantly deviate from a time dependence of a linear diffusion back front. This is demonstrated for a data set from the Horn River Basin. Hence, the behaviour of the back front is a strong indicator of a non-linear fluid-rock interaction. I N T R O D U C T I O NFor the successful development and operation of hydrocarbon and geothermal reservoirs, knowledge of the hydraulic transport is of crucial importance. Although today's quantification of the reservoir permeability is mainly based on log measurements, these measurements only provide very time-restricted information in the ultimate vicinity of the wellbore. In such a way these measurements therefore cannot capture hydraulic processes linked to, for instance, hydraulic stimulation *