Extraction of heat from an enhanced geothermal system (EGS) is a renewable and environmentally benign technology. Process involves circulation of colder water in hot rock through a flow path consisting of injection well, several vertical fractures, and production well. In this process, distribution of water among the vertical fractures is one of the key factors for optimization of heat recovery. Geometry such as dimensions or total flow area and fluid velocity in wells and fractures play major role in the hydrodynamics in the loop. A mathematical model is developed from the analogy of electrical circuit applying Kirchhoff's law to determine the pressure drop between two points. Accordingly, the flow rates through fractures are calculated. Maintenance of sufficient pressure in a fracture is necessary to avoid closure due to horizontal stress. In this model, variation of fracture width with pressure is considered. The impacts of injection rate, well diameter and number of fractures on the distribution of flow in fractures are also investigated in this study. Since the frictional loss along the well decreases with the increase in well diameter, less variations of flow rates in fractures are observed. Similarly, low fluid velocity due to low total flow rate causes less frictional loss, thus more even distributions of flow in the fracture is observed. The number of fractures completed in an EGS is an important parameter for optimization. The flow distribution among the fractures depends on the total number of fractures present in the system. Although, more fractures improve the heat recovery, the cost of completion increases with the number of fracture. The analytical model for flow distribution developed in this study is helpful to evaluate the effectiveness of an EGS and to optimize the completion and operational parameters.