A model for the flow of water and steam in a fractured geothermal reservoir is presented. The flow is coupled with thermal processes and phase behavior in the reservoir and fractures using the pressure-enthalpy formulation and water-steam phase behavior. Both an implicit pressure, explicit enthalpy and a fully implicit solution algorithm have been developed. The model is validated with analytical solutions. The model is then used to demonstrate the factors that control the heat extraction rate from enhanced geothermal systems (EGS). It is found that injection rate, fracture spacing, well spacing, and effective fracture surface area have the biggest impact on the heat extraction rate. 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 general, 3-D, multi-phase, geothermal reservoir model presented in this paper can be used to optimize and design EGS in geothermal fields (fracture spacing, well spacing, injection rate, etc.).