Hydraulic fracturing technique has been widely applied in the enhanced geothermal systems, to increase injection rates for geologic sequestration of CO2, and most importantly for the stimulations of oil and gas reservoirs, especially the unconventional shale reservoirs. One of the key points for the success of hydraulic fracturing operations is to accurately estimate the redistribution of pore pressure and stresses around the induced fracture and predict the reactivations of pre-existing faults. The fracture extension as well as pore pressure and stress regime around it are affected by: poro- and thermoelastic phenomena as well as by fracture opening under the combined action of applied pressure and in-situ stress. A couple of numerical studies have been done for the on this for the purpose of analyzing the potential for fault reactivation resulting from pressurization of the hydraulic fracture. In this work, a comprehensive analytical model is constructed to estimate the stress and pore pressure distribution around an injection induced fracture from a single well in an infinite reservoir. The model allows the leak-off distribution in the formation to be three-dimensional with the pressure transient moving ellipsoidcally outward into the reservoir with respect to the fracture surface. The pore pressure and the stress changes in three dimensions at any point around the fracture caused by thermo- and poroelasticity and fracture compression are investigated. Then, the problem of constant water injection into a hydraulic fracture in Barnett shale is presented. In particular, with Mohr-Coulomb failure criterion, we calculate the fault reactivation potential around the fracture. This study is of interest in interpretation of micro-seismicity in hydraulic fracturing and in assessing permeability variation around a stimulation zone, as well as in estimation of the fracture spacing during hydraulic fracturing operations.

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