We present an approach to characterise the hydraulic transport during borehole fluid injections. We introduce a new type of scaling to transform clouds of seismicity from a hydraulically anisotropic medium into an effective isotropic medium. For this we assume that the pressure-dependence of permeability is independent of a specific direction although the permeability is anisotropic. We apply our approach to seismicity recorded during a hydraulic fracturing treatment in the Barnett Shale. We analyse spatio-temporal characteristics of transformed seismicity. Our results show a significant nonlinear fluid-rock interaction. To explain our findings we suppose a nonlinear diffusional relaxation of the pore-fluid pressure perturbation. In particular, we consider a hydraulic transport which is governed by a power-law pressure-dependence of permeability. For this type of nonlinear fluid-rock interaction we present a numerical modelling approach to generate synthetic seismicity distributions. Their spatio-temporal features are similar to the ones which we observe in Barnett Shale. Additionally, our approach allows us to compute the permeability evolution inside of the fracture stimulated rock. Our results indicate that the fluid transport during the hydraulic fracturing treatment in the Barnett Shale may be described by a nonlinear pressure diffusion based on a power-law dependent permeability.


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