Non-linear Diffusion of Pore-fluid Pressure during Hydraulic Fracturing - A Three-dimensional Modelling Approach

Fluid injections into reservoir rocks under high pressure are performed to enhance hydraulic transport properties of the rock. Often, these reservoir stimulations are accompanied by microseismicity which can be used for the characterization of hydraulic rock properties. Previous studies, based on radial-symmetric 3D models, showed that the occurence of microseismic events can be attributed to non-linear diffusion of pore-fluid pressure. For rocks with neglectable diffusivities they proposed a power-law model for the pressure-dependent diffusivity. The main purpose of this work is to test the feasibility of modelling the non-linear diffusion process in full-3D, based on hydraulic-fracturing induced microseismicity from the Barnett Shale. In order to do so, we set up 3D models and solve numerically for the non-linear equation of diffusion. This yields pore-fluid pressure distributions in time and space as well as estimations for the initial rock diffusivity. We show that the derived diffusivity values are in agreement with previously obtained ones. Furthermore, we generate synthetic seismic event clouds and compare the spatio-temporal distribution to the real Barnett Shale seismicity. Our results reveal that modelling of pore-fluid pressure perturbation during hydraulic fracturing stimulations is possible in full-3D and thus, provides a significant contribution to further studies.