PROCEEDINGS, Thirty-Sixth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, January 31 - February 2, 2011 SGP-TR-191 SUSTAINABLE HEAT FARMING OF GEOTHERMAL SYSTEMS: A CASE STUDY OF HEAT EXTRACTION AND THERMAL RECOVERY IN A MODEL EGS FRACTURED RESERVOIR Daniel Sutter 1, 2 , Don B. Fox 1 , Brian J. Anderson 3 , Donald L. Koch 4 , Philipp Rudolf von Rohr 2 , and Jefferson W. Tester 1,* 1 Atkinson Center for a Sustainable Future and the Cornell Energy Institute, Cornell University, Ithaca, NY 14853, USA 2 Institute of Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland 3 College of Engineering and Mineral Resources, West Virginia University, Morgantown, WV 26506, USA 4 School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA * Corresponding author: jwt54@cornell.edu ABSTRACT To address the question of renewability of Enhanced Geothermal Systems (EGS) a conduction-dominated, model EGS reservoir was evaluated as a representative “worst case” to estimate heat extraction during production and thermal recovery following shut down. In the model system water is injected at specified rates and temperatures into a single rectangular fracture surrounded by an infinite amount of impermeable hot rock. During the extraction phase, water moves along the fracture extracting heat from the adjacent rock matrix leading to local cooling and thermal drawdown of the reservoir. When the water injection is stopped, conductive heat transfer from the surrounding hotter rock regions leads to thermal recovery of the cooler zones in the reservoir. The rate of recovery is controlled locally by the temperature gradient that is induced during the thermal drawdown. A two- dimensional mathematical model was developed to describe heat transfer for both extraction and recovery. Regarding the recovery, an advanced analytical approach was developed that is capable of describing the temperature during recovery at every position along the fracture. Our approach leads to the same result for the temperature at the inlet position, as presented in earlier research using a different approach. In addition, numerical simulations were carried out using the TOUGH2 code to study the importance of the assumptions employed in the analytical description and to extend the applicability of the model by enabling simulation of operating cycles with alternating extraction and recovery times. The effect of neglecting heat conduction in the rock in the direction parallel to the flow in the fracture was analyzed by comparison of the analytical model to the TOUGH2 simulations. For a fixed fracture area, low flow rates can result in thermal drawdown localized around the fluid inlet with heat conduction in the parallel direction becoming significant. BACKGROUND AND MOTIVATION One important feature of any operating geothermal reservoir system has to do with its anticipated production sustainability over the long term. Although geothermal reservoirs can be depleted during production if recharge rates are insufficient to overcome local cooling of rock and losses of fluid pressure, with proper management hydrothermal reservoirs have been shown to be productive for long periods of time. In Engineered Geothermal Systems the situation is different with no record of long term field testing and as a result the renewability of EGS in general is often questioned. Axelsson et al. (2001) define the renewability of a geothermal source as the ability to maintain the installed capacity indefinitely. Thermally, the reservoir would be in steady-state condition, i.e. the rate of heat extraction by the working fluid and the recharge rate from the bulk rock are equal. However, the renewable capacity is frequently too small for commercial development due to economy of scale in infrastructure development and operation costs (Sanyal 2005). Therefore, considerations about the sustainability of geothermal systems must also include the recovery effect after a stop of heat extraction (Megel and Rybach 2000). Sanyal (2005) defines the sustainable capacity of a geothermal reservoir as the capacity, that can be economically maintained over the amortized life time of a power plant. According to his review of operating hydrothermal plants around the world, the sustainable capacity is 5 to 45 times the renewable capacity with the factor being most likely around 10. Although, exploiting the sustainable capacity eventually results in significant cooling of the reservoir and recovery times in the order of hundreds of years, there are good reasons to define such geothermal resource operation as sustainable. • Complete recovery of the thermal energy is eventually guaranteed and even with recovery time