A water-steam two-phase fractured geothermal reservoir model is presented in this paper. Coupled flow and thermal processes are solved in the reservoir and fractures using the pressure-enthalpy formulation and water-steam phase behavior correlations. Both an implicit pressure, explicit enthalpy and a fully implicit solution algorithm have been developed. After model validation, this simulator is used to model the heat extraction rate from enhanced geothermal systems (EGS). The temperature and energy flux from the production well are plotted and analyzed. The effects of several key parameters on enhanced geothermal systems are investigated. It is found that injection rate, fracture spacing, well spacing, and effective fracture surface area have the biggest impact on the heat extraction rate. It is also found that heat conduction is the main contributor to the heat flux while convective fluid flow does not contribute much when the reservoir permeability i.e., the rate of gravity driven convection is low. The heat flux from the earth does not affect short-term EGS production but can be an important factor for long-term EGS development. The geothermal reservoir simulator presented in this paper can be used to optimize and design EGS in geothermal fields (fracture spacing, well spacing, injection rate, etc.).