A three-dimensional poroelastic model is developed to investigate the poroelastic effect of fluid injection into a geothermal reservoir. In the model, the fluid flow in the fracture is assumed to be lubrication flow and is modeled by the finite element method. The three-dimensional pore fluid diffusion in the matrix and the induced stresses are modeled by the boundary integral equation method. The numerical results have been verified through comparing to the analytical solutions given in Nygren and Ghassemi  for an infinite radial fracture problem. Thereafter, the numerical model is used to study the pore pressure and stress fields in the rock matrix resulting from injection/extraction in a circular fracture.
The production of geothermal energy from low permeability reservoirs is achieved by water circulation in natural and/or man-made fractures, and is often referred to as enhanced or engineered geothermal systems (see Fig. 1). Cold water injection perturbs the in-situ stress state within the reservoir leading to fracture initiation and/or activation of discontinuities such as faults and joints which is often manifested as multiple microseismic events. Detection and interpretation of microseismic events using downhole receiver arrays (e.g. [2, 3]) can be monitored and analyzed to provide useful information on the stimulated zone, fracture growth, and geometry of the geological structures and the in-situ stress state [3-5]. Micro-seismic events are believed to be associated with rock failure in shear, and shear slip on new or pre-existing fracture planes . Effective interpretation of micro-seismicity can benefit from the knowledge of the hydro-thermo-mechanical mechanisms associated with injection in the reservoir, and the resulting stress variations that play a key role in rock failure around the main hydraulic fracture. These include the stresses due to the opening of a hydraulic fracture, and thermoelastic and poroelastic stresses due to rock cooling and fluid leak-off into the rock mass. In general, an injection-induced fracture problem consists of (1) fluid flow and heat transport within the fracture, (2) fluid flow in the matrix, (3) conductive and advective heat transport in the matrix, and (4) fracture propagation. Some solutions for problems involving the first three parts have been presented [1, 7, 8]. Most of these as well as other studies of the subject were based on some simplifications such as uniform pressure in line fractures, special reservoir geometry and onedimensional fluid diffusivity in the matrix, etc. Other 3D models use the finite element method (e.g., ). A threedimensional boundary element model has been developed by Ghassemi et al.  to study the impact of thermal stresses on the reservoir matrix and the fracture without considering poroelastic effects.
Fig. 1. Fluid circulation in geothermal reservoir.(available in full paper)
In this paper, a three-dimensional poroelastic model is developed to study the poroelastic response of the reservoir to fluid injection into an irregularly-shaped fracture or a fractured zone. The fluid flow in the fracture is assumed to be lubrication flow and is modeled using the finite element method. The threedimensional pore fluid diffusion in the rock matrix and the induced stresses is treated by the boundary integral equation method; and the displacement discontinuity boundary element method is used to model the fracture itself.